WEBVTT 00:00:01.170 --> 00:00:03.510 The following content is provided under a Creative 00:00:03.510 --> 00:00:04.930 Commons license. 00:00:04.930 --> 00:00:07.120 Your support will help MIT OpenCourseWare 00:00:07.120 --> 00:00:11.230 continue to offer high-quality educational resources for free. 00:00:11.230 --> 00:00:13.770 To make a donation or to view additional materials 00:00:13.770 --> 00:00:17.730 from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:17.730 --> 00:00:18.610 at ocw.mit.edu. 00:00:23.542 --> 00:00:25.750 GABRIEL SANCHEZ-MARTINEZ: Any questions on Homework 1 00:00:25.750 --> 00:00:26.680 before we get started? 00:00:29.308 --> 00:00:30.190 AUDIENCE: Yeah. 00:00:30.190 --> 00:00:33.100 GABRIEL SANCHEZ-MARTINEZ: OK, fire away. 00:00:33.100 --> 00:00:36.940 AUDIENCE: I guess, first, do you think 00:00:36.940 --> 00:00:39.400 we have like this minimum cycle time, 00:00:39.400 --> 00:00:42.360 like a theoretical minimum cycle time and then what was actually 00:00:42.360 --> 00:00:45.630 [INAUDIBLE] cycle time? 00:00:45.630 --> 00:00:49.890 GABRIEL SANCHEZ-MARTINEZ: So cycle time, just to review-- 00:00:49.890 --> 00:00:54.540 it's the time that it takes a bus to-- 00:00:54.540 --> 00:00:57.620 from the time [AUDIO OUT] for a trip. 00:00:57.620 --> 00:01:01.530 It goes all the way one way, has to wait at the other end 00:01:01.530 --> 00:01:05.010 to recover the schedule, comes back, waits to recover, 00:01:05.010 --> 00:01:07.290 and is ready to begin the next round. 00:01:07.290 --> 00:01:09.890 So that's a cycle. 00:01:09.890 --> 00:01:14.040 AUDIENCE: Since you have [INAUDIBLE] going on, 00:01:14.040 --> 00:01:17.579 if you had 4.1 buses, then you use a cycle time. 00:01:17.579 --> 00:01:18.995 Then obviously, you can't do that? 00:01:18.995 --> 00:01:19.930 [INTERPOSING VOICES] 00:01:19.930 --> 00:01:21.315 GABRIEL SANCHEZ-MARTINEZ: So you would need five buses-- 00:01:21.315 --> 00:01:21.610 AUDIENCE: Yeah. 00:01:21.610 --> 00:01:23.860 GABRIEL SANCHEZ-MARTINEZ: --if that's what you've got. 00:01:23.860 --> 00:01:26.892 Or you would have to do a trade-off with reliability 00:01:26.892 --> 00:01:27.850 if that were to happen. 00:01:31.650 --> 00:01:33.312 AUDIENCE: I think most of my questions 00:01:33.312 --> 00:01:35.440 were on this very last couple of questions. 00:01:35.440 --> 00:01:38.368 GABRIEL SANCHEZ-MARTINEZ: Yeah. 00:01:38.368 --> 00:01:41.680 AUDIENCE: We were aggregating a bunch of data for-- 00:01:41.680 --> 00:01:45.094 [INAUDIBLE] you did it across both directions 00:01:45.094 --> 00:01:46.510 and then asked, how does it change 00:01:46.510 --> 00:01:49.650 when you would like to evaluate each direction separately 00:01:49.650 --> 00:01:51.062 in layover time? 00:01:51.062 --> 00:01:53.520 GABRIEL SANCHEZ-MARTINEZ: This is the penultimate question, 00:01:53.520 --> 00:01:53.880 correct? 00:01:53.880 --> 00:01:54.120 AUDIENCE: Yeah. 00:01:54.120 --> 00:01:54.510 GABRIEL SANCHEZ-MARTINEZ: So that's 00:01:54.510 --> 00:01:55.920 the hardest question on the assignment. 00:01:55.920 --> 00:01:56.670 AUDIENCE: OK. 00:01:56.670 --> 00:01:58.836 GABRIEL SANCHEZ-MARTINEZ: It is a challenge question 00:01:58.836 --> 00:02:02.430 because there are different cases that you have to analyze. 00:02:02.430 --> 00:02:05.330 That's maybe the hint, right? 00:02:05.330 --> 00:02:07.330 There are some cases. 00:02:07.330 --> 00:02:09.537 And for each case, there is a probability 00:02:09.537 --> 00:02:10.620 that that case will occur. 00:02:10.620 --> 00:02:11.830 AUDIENCE: Yeah. 00:02:11.830 --> 00:02:22.334 GABRIEL SANCHEZ-MARTINEZ: And-- let's see if this starts-- 00:02:22.334 --> 00:02:23.750 there's a probability that it will 00:02:23.750 --> 00:02:30.090 occur and then a consequence, or something happens in that case. 00:02:30.090 --> 00:02:32.990 So you have to look at each case and then aggregate the cases 00:02:32.990 --> 00:02:34.880 together, if that make sense. 00:02:34.880 --> 00:02:36.146 AUDIENCE: Yes. 00:02:36.146 --> 00:02:38.770 GABRIEL SANCHEZ-MARTINEZ: We're taking questions for Assignment 00:02:38.770 --> 00:02:40.090 1, which is due on Thursday. 00:02:43.740 --> 00:02:44.880 Any other questions? 00:02:44.880 --> 00:02:47.565 AUDIENCE: That's it. 00:02:47.565 --> 00:02:48.440 AUDIENCE: [INAUDIBLE] 00:02:48.440 --> 00:02:51.200 GABRIEL SANCHEZ-MARTINEZ: It is due at 4:00 00:02:51.200 --> 00:02:54.620 so at class time essentially, yeah. 00:02:54.620 --> 00:02:56.410 I actually [AUDIO OUT] if you 4:00. 00:02:56.410 --> 00:02:58.960 I said 4:05, so you have five minutes. 00:03:01.876 --> 00:03:05.035 AUDIENCE: Can you [INAUDIBLE] what assumptions there 00:03:05.035 --> 00:03:06.250 are [INAUDIBLE]? 00:03:10.485 --> 00:03:12.276 GABRIEL SANCHEZ-MARTINEZ: In what question? 00:03:12.276 --> 00:03:14.463 AUDIENCE: When you said it seems to be 00:03:14.463 --> 00:03:17.622 the reasoning or assumption about the schedule [INAUDIBLE]?? 00:03:17.622 --> 00:03:20.052 Which metric do you use? 00:03:20.052 --> 00:03:22.757 Based on the data, which [INAUDIBLE]?? 00:03:22.757 --> 00:03:25.340 GABRIEL SANCHEZ-MARTINEZ: Yeah, so that's Question 3, correct? 00:03:25.340 --> 00:03:25.965 AUDIENCE: Yeah. 00:03:25.965 --> 00:03:28.887 GABRIEL SANCHEZ-MARTINEZ: So I can't really explain. 00:03:28.887 --> 00:03:30.720 I can't give you the answer to the question. 00:03:30.720 --> 00:03:34.250 So what I'm looking for there is your intuition 00:03:34.250 --> 00:03:38.870 and your understanding of why you would pick which statistics 00:03:38.870 --> 00:03:45.240 from Question 2, where it tells you calculate all these things. 00:03:45.240 --> 00:03:48.500 Now I'm saying pick from those statistics 00:03:48.500 --> 00:03:52.370 what you would use for t and for r. 00:03:52.370 --> 00:03:54.770 And you may want to combine different statistics 00:03:54.770 --> 00:03:57.450 for the computation of r. 00:03:57.450 --> 00:03:57.950 Yeah? 00:03:57.950 --> 00:04:02.132 AUDIENCE: [INAUDIBLE] multiple valid responses but-- 00:04:02.132 --> 00:04:04.590 GABRIEL SANCHEZ-MARTINEZ: Yes, some more valid than others, 00:04:04.590 --> 00:04:06.510 but some that are definitely invalid 00:04:06.510 --> 00:04:12.900 and some that are almost 100% valid but not 100% valid. 00:04:12.900 --> 00:04:15.670 So there are several correct answers, 00:04:15.670 --> 00:04:18.130 and some that are very good answers 00:04:18.130 --> 00:04:21.220 because you can justify the choice of the statistic 00:04:21.220 --> 00:04:23.310 conceptually. 00:04:23.310 --> 00:04:24.380 Yeah. 00:04:24.380 --> 00:04:26.920 Any other questions on Homework 1? 00:04:26.920 --> 00:04:30.860 I can take some more questions after class, if that's OK. 00:04:30.860 --> 00:04:36.260 So we had a snow day if you had a good time, and/or at least, 00:04:36.260 --> 00:04:37.910 you could use it to catch up. 00:04:37.910 --> 00:04:40.430 So the schedule is a little different now. 00:04:40.430 --> 00:04:43.260 I've posted an update about that on Stellar (class site). 00:04:43.260 --> 00:04:44.930 There's a new syllabus. 00:04:44.930 --> 00:04:47.970 And we're going to do some [AUDIO OUT] different 00:04:47.970 --> 00:04:49.890 [AUDIO OUT]. 00:04:49.890 --> 00:04:53.370 You may remember that we have three introductory classes 00:04:53.370 --> 00:04:56.370 on topics of [INAUDIBLE]. 00:04:56.370 --> 00:04:59.140 And then, we had model characteristics and roles. 00:04:59.140 --> 00:05:02.100 And then, [AUDIO OUT]. 00:05:02.100 --> 00:05:03.788 We're going to shuffle a little bit. 00:05:03.788 --> 00:05:08.770 [AUDIO OUT] Microphone working? 00:05:08.770 --> 00:05:13.360 So because the second assignment is on data collection, 00:05:13.360 --> 00:05:14.770 we're going to cover that today. 00:05:14.770 --> 00:05:16.769 And we're going to give you that homework today, 00:05:16.769 --> 00:05:19.810 so that you can get started on the data collection side. 00:05:19.810 --> 00:05:23.080 Then, we're going to cover some of the short-range [INAUDIBLE] 00:05:23.080 --> 00:05:24.670 of planning concepts. 00:05:24.670 --> 00:05:25.910 Nema is going to do that-- 00:05:25.910 --> 00:05:26.480 Nema Nassir. 00:05:26.480 --> 00:05:29.540 You might recall him from the previous lecture. 00:05:29.540 --> 00:05:33.370 And then, we'll finish with [INAUDIBLE] and costs 00:05:33.370 --> 00:05:36.250 in March the 2nd, OK? 00:05:36.250 --> 00:05:39.860 So remember, there's no class on Monday the 21st. 00:05:44.410 --> 00:05:46.400 AUDIENCE: You mean Tuesday? 00:05:46.400 --> 00:05:49.131 GABRIEL SANCHEZ-MARTINEZ: Sorry, yes, Tuesday. 00:05:49.131 --> 00:05:50.630 I think, there's no class on Monday. 00:05:50.630 --> 00:05:52.190 And then, Tuesday there are classes. 00:05:52.190 --> 00:05:53.420 But it's Monday's schedule. 00:05:53.420 --> 00:05:55.250 So we don't have class. 00:05:55.250 --> 00:05:58.320 Thank you for bringing that up. 00:05:58.320 --> 00:05:59.630 OK. 00:05:59.630 --> 00:06:03.610 I'll leave Homework 2 for when we finish with the lecture. 00:06:03.610 --> 00:06:06.370 But I'll distribute it later. 00:06:06.370 --> 00:06:09.240 So let's just get started on that. 00:06:09.240 --> 00:06:11.430 So data collection techniques and program design-- 00:06:11.430 --> 00:06:13.999 that's the topic for today. 00:06:13.999 --> 00:06:14.790 Here's the outline. 00:06:14.790 --> 00:06:17.660 So we're going to cover a summary of current practice 00:06:17.660 --> 00:06:18.747 quite quickly. 00:06:18.747 --> 00:06:21.330 Then, we're going to talk about data collection program design 00:06:21.330 --> 00:06:25.050 process, the needs, the data needs, the techniques for data 00:06:25.050 --> 00:06:26.301 collection, the sampling. 00:06:26.301 --> 00:06:28.050 We're going to get into the details of how 00:06:28.050 --> 00:06:29.890 we get sample slices. 00:06:29.890 --> 00:06:32.730 And we're going to finish with special considerations 00:06:32.730 --> 00:06:35.200 for surveys and surveying techniques. 00:06:37.740 --> 00:06:38.610 so where are we? 00:06:38.610 --> 00:06:42.090 Where is the transit industry in terms of data collection, 00:06:42.090 --> 00:06:44.370 and sampling, and these things? 00:06:44.370 --> 00:06:45.810 Largely, there's been a transition 00:06:45.810 --> 00:06:48.047 from manual to automatic data collection. 00:06:48.047 --> 00:06:50.130 As you might imagine, with the internet of things, 00:06:50.130 --> 00:06:52.800 and sensors, and the internet, and wireless, 00:06:52.800 --> 00:06:54.720 it used to be that if you wanted to have 00:06:54.720 --> 00:06:56.100 statistics on your running times, 00:06:56.100 --> 00:06:57.690 you had to send people out. 00:06:57.690 --> 00:06:59.880 We call those people checkers. 00:06:59.880 --> 00:07:03.330 And those checkers would have notebooks and record 00:07:03.330 --> 00:07:05.400 running times, and number of people boarding, 00:07:05.400 --> 00:07:06.660 and these things. 00:07:06.660 --> 00:07:09.950 Nowadays, with the modern systems, especially 00:07:09.950 --> 00:07:13.920 the modern systems, we have several sensors and types 00:07:13.920 --> 00:07:16.410 of sensors that collect some of that data for us. 00:07:16.410 --> 00:07:20.085 So we're going to cover both approaches. 00:07:20.085 --> 00:07:23.054 [INAUDIBLE] data collection to supplement 00:07:23.054 --> 00:07:24.220 [INAUDIBLE] data collection. 00:07:24.220 --> 00:07:27.730 And if you happen to be consulting for a developing 00:07:27.730 --> 00:07:32.560 country that is working with a system that has not yet brought 00:07:32.560 --> 00:07:35.500 in automatic data collection technologies, 00:07:35.500 --> 00:07:39.100 it's also useful to know all about the manual design 00:07:39.100 --> 00:07:42.120 and manual data collection process. 00:07:42.120 --> 00:07:44.710 [AUDIO OUT] took this class and ended up 00:07:44.710 --> 00:07:47.980 working in large consulting firms have gone off 00:07:47.980 --> 00:07:52.369 to help countries put in new transit systems. 00:07:52.369 --> 00:07:54.160 And one of the first things they have to do 00:07:54.160 --> 00:07:59.222 is back to these slides and see what the plan is going to be, 00:07:59.222 --> 00:08:01.180 and how many people you need, and how much it's 00:08:01.180 --> 00:08:01.930 going to cost. 00:08:01.930 --> 00:08:04.510 So very useful topic. 00:08:04.510 --> 00:08:07.519 So as I said, there's automatic data collection. 00:08:07.519 --> 00:08:08.810 There's manual data collection. 00:08:08.810 --> 00:08:11.860 There's sometimes a mix of data collection techniques. 00:08:11.860 --> 00:08:14.470 Often, what happens is that we just send people 00:08:14.470 --> 00:08:15.970 out and collect data. 00:08:15.970 --> 00:08:19.420 Or we just extract a sample of automatically collected data. 00:08:19.420 --> 00:08:21.970 And we don't really think about sampling, and the confidence 00:08:21.970 --> 00:08:24.750 interval, and how sure are we of that result 00:08:24.750 --> 00:08:27.490 that we're going to influence policy or make decisions 00:08:27.490 --> 00:08:29.260 that will affect service. 00:08:29.260 --> 00:08:31.390 How sure are we of those? 00:08:31.390 --> 00:08:33.640 So statistical validity. 00:08:33.640 --> 00:08:37.179 Often, there's an efficient use of data. 00:08:37.179 --> 00:08:41.919 And ADCS, which is Automatic Data Collection Systems-- 00:08:41.919 --> 00:08:44.260 we'll use that abbreviation throughout the course- 00:08:44.260 --> 00:08:47.020 presents a major opportunity for strengthening data 00:08:47.020 --> 00:08:48.260 to support decision making. 00:08:48.260 --> 00:08:49.790 We'll talk about how that happens. 00:08:49.790 --> 00:08:52.520 Let's first compare manual and automatic data collection. 00:08:52.520 --> 00:08:54.386 So what happens with manual data collection? 00:08:54.386 --> 00:08:55.510 You hire people, as I said. 00:08:55.510 --> 00:08:56.950 You hired checkers. 00:08:56.950 --> 00:08:59.860 So initially, there's no setup cost. 00:08:59.860 --> 00:09:01.950 There's a low capital cost to that. 00:09:01.950 --> 00:09:04.210 But there's a high marginal cost because if you 00:09:04.210 --> 00:09:06.680 want to collect more data, you have to hire more people. 00:09:06.680 --> 00:09:08.134 Does that make sense? 00:09:08.134 --> 00:09:10.300 If you want to bring in an automatic data collection 00:09:10.300 --> 00:09:12.341 system, you might have to retrofit all your buses 00:09:12.341 --> 00:09:13.930 with AVL sensors. 00:09:13.930 --> 00:09:16.410 And that's going to cost you initially. 00:09:16.410 --> 00:09:19.710 So that's a high capital cost relatively. 00:09:19.710 --> 00:09:22.420 But low marginal cost-- once you have those systems in place, 00:09:22.420 --> 00:09:24.160 they keep collecting data for you. 00:09:24.160 --> 00:09:25.300 And it's almost free. 00:09:25.300 --> 00:09:27.760 You do need some maintenance on these equipments. 00:09:27.760 --> 00:09:31.510 But comparing to manual data collection, 00:09:31.510 --> 00:09:33.310 you have low marginal cost. 00:09:33.310 --> 00:09:35.770 Because of that marginal cost difference, 00:09:35.770 --> 00:09:38.320 it tends to happen that when you have manual data collection, 00:09:38.320 --> 00:09:41.920 you only pay checkers for small sample sizes-- 00:09:41.920 --> 00:09:43.300 just what you need. 00:09:43.300 --> 00:09:46.930 Whereas, once you put in automatic data collection 00:09:46.930 --> 00:09:49.720 systems, they keep collecting data. 00:09:49.720 --> 00:09:52.110 So you get much bigger data. 00:09:52.110 --> 00:09:53.950 Bless you. 00:09:53.950 --> 00:09:57.430 OK, in both cases, we can collect data and analyze it 00:09:57.430 --> 00:09:59.860 for aggregate analysis and disaggregate analysis. 00:09:59.860 --> 00:10:01.720 So you might want passenger-specific data 00:10:01.720 --> 00:10:02.620 on things. 00:10:02.620 --> 00:10:06.400 Or you might want things like just averages 00:10:06.400 --> 00:10:09.340 and aggregate things, total number of passengers 00:10:09.340 --> 00:10:10.960 using the system. 00:10:10.960 --> 00:10:12.940 And when you're doing manual data collection, 00:10:12.940 --> 00:10:14.890 you can look at quantitative things, things 00:10:14.890 --> 00:10:16.440 you can measure and count. 00:10:16.440 --> 00:10:19.820 Or you can also observe things qualitatively. 00:10:19.820 --> 00:10:22.090 One example that I saw in a recent paper 00:10:22.090 --> 00:10:26.680 was considering the [? therivation ?] 00:10:26.680 --> 00:10:28.719 by student in some country. 00:10:28.719 --> 00:10:30.760 And they didn't ask people if they were students. 00:10:30.760 --> 00:10:32.582 They were looking at people's-- 00:10:32.582 --> 00:10:33.790 more or less, are they young? 00:10:33.790 --> 00:10:35.410 Are they carrying a backpack? 00:10:35.410 --> 00:10:38.390 And that would be the labeling for your student. 00:10:38.390 --> 00:10:42.010 So that's something that a sensor might not do so well. 00:10:42.010 --> 00:10:44.270 Although now with machine learning, who knows? 00:10:44.270 --> 00:10:45.890 But we haven't seen that so. 00:10:45.890 --> 00:10:48.580 So you can do qualitative observations 00:10:48.580 --> 00:10:50.410 when you're doing manual data collection. 00:10:50.410 --> 00:10:52.810 Manual data collection tends to be unreliable, 00:10:52.810 --> 00:10:56.020 especially when people aren't very well trained 00:10:56.020 --> 00:10:59.320 and when you have a group of different people collecting 00:10:59.320 --> 00:10:59.830 data. 00:10:59.830 --> 00:11:01.621 So each person might have different biases. 00:11:01.621 --> 00:11:05.020 It's hard to reproduce the exact bias across persons. 00:11:05.020 --> 00:11:07.870 With automatic data collection, you do the errors. 00:11:07.870 --> 00:11:10.450 And often, they are not corrected. 00:11:10.450 --> 00:11:14.260 But if you do correct them, and you estimate those biases 00:11:14.260 --> 00:11:18.550 just for them, you can end up with a better result. 00:11:18.550 --> 00:11:21.280 Because of the small sample sizes in manual data 00:11:21.280 --> 00:11:25.180 collection, you tend to have to have limited spatial 00:11:25.180 --> 00:11:27.290 and temporal coverage of data. 00:11:27.290 --> 00:11:29.650 So for example, if you're interested in ridership 00:11:29.650 --> 00:11:34.900 in the system, it's unlikely that you will cover ridership 00:11:34.900 --> 00:11:38.650 in holidays for [INAUDIBLE] system 00:11:38.650 --> 00:11:40.330 because there are only a few holidays. 00:11:40.330 --> 00:11:44.350 And usually, you're not mostly interested in holidays. 00:11:44.350 --> 00:11:48.160 So chances are, you won't have data collection for holidays. 00:11:48.160 --> 00:11:50.320 Whereas once you install automatic data collection 00:11:50.320 --> 00:11:51.880 systems, they keep collecting data. 00:11:51.880 --> 00:11:56.500 So you get data at midnight on President's Day. 00:11:56.500 --> 00:11:59.350 So they're always on. 00:11:59.350 --> 00:12:01.210 They're always collecting data. 00:12:01.210 --> 00:12:06.170 Manual data needs to be checked, cleaned, analyzed, coded, 00:12:06.170 --> 00:12:08.670 and sometimes put into systems before they can be analyzed. 00:12:08.670 --> 00:12:09.670 That could take a while. 00:12:09.670 --> 00:12:11.320 You need to hire people to do that. 00:12:11.320 --> 00:12:15.490 Whereas automatic data collection systems often 00:12:15.490 --> 00:12:17.969 send their data to databases in real-time or very 00:12:17.969 --> 00:12:18.760 close to real-time. 00:12:18.760 --> 00:12:24.580 [INAUDIBLE] you can start analyzing things the next day. 00:12:24.580 --> 00:12:28.750 So you arrive in the morning to your desk at a transit agency, 00:12:28.750 --> 00:12:30.790 and you have performance metrics for yesterday. 00:12:30.790 --> 00:12:33.520 So you wouldn't be able to do that unless you have people 00:12:33.520 --> 00:12:36.250 working very hard if you're using manual data 00:12:36.250 --> 00:12:37.870 collection system. 00:12:37.870 --> 00:12:41.050 When we talk about automatic data collection systems, 00:12:41.050 --> 00:12:42.220 there are many. 00:12:42.220 --> 00:12:47.630 But there are three types that we refer to very, very often. 00:12:47.630 --> 00:12:51.250 And so the first one in AFC, Automatic Fare Collection 00:12:51.250 --> 00:12:52.180 Systems. 00:12:52.180 --> 00:12:54.710 This is your fare box or your fare gates in your smart card, 00:12:54.710 --> 00:12:55.370 your Charlie Card. 00:12:55.370 --> 00:12:56.078 You're in Boston. 00:12:56.078 --> 00:12:57.210 You tap to enter the bus. 00:12:57.210 --> 00:13:00.040 And you tap to enter the subway system. 00:13:00.040 --> 00:13:03.220 Increasingly, it's based on contactless smart cards. 00:13:03.220 --> 00:13:04.660 And those contactless smart cards 00:13:04.660 --> 00:13:06.760 have some sort of RFID technology 00:13:06.760 --> 00:13:08.440 with a unique identifier. 00:13:08.440 --> 00:13:10.780 When you tap that card to the sensor, 00:13:10.780 --> 00:13:13.240 the sensor will read that identifier. 00:13:13.240 --> 00:13:16.240 And it'll do things like fare calculation for you. 00:13:16.240 --> 00:13:18.760 But that record gets sent to a database. 00:13:18.760 --> 00:13:23.680 And it's there for people like us to analyze and make 00:13:23.680 --> 00:13:25.340 good use of it for planning. 00:13:25.340 --> 00:13:29.770 So it tends to provide entry information almost always. 00:13:29.770 --> 00:13:34.810 In some systems, like the Washington, DC metro or the TFL 00:13:34.810 --> 00:13:37.600 subway, you tap in to enter and exit. 00:13:37.600 --> 00:13:41.320 So you have both origin and destinations. 00:13:41.320 --> 00:13:43.690 And if you always have the systems on, 00:13:43.690 --> 00:13:47.050 then you have full spatial and temporal coverage 00:13:47.050 --> 00:13:51.100 of all of the use of the system at an individual passenger 00:13:51.100 --> 00:13:51.600 level. 00:13:51.600 --> 00:13:55.040 So very disaggregate-- sorry about that. 00:13:55.040 --> 00:13:57.320 Traditionally, these systems are not real-time. 00:13:57.320 --> 00:14:01.340 So it might take a while for those transactions 00:14:01.340 --> 00:14:03.170 to make it to the data warehouse, where 00:14:03.170 --> 00:14:05.810 they're available for planners to analyze it. 00:14:05.810 --> 00:14:10.070 The calculation of how much fare in some systems 00:14:10.070 --> 00:14:11.000 is in real-time. 00:14:11.000 --> 00:14:13.400 In other systems like the Charlie Card, 00:14:13.400 --> 00:14:17.210 the stored value that you have is stored on your card. 00:14:17.210 --> 00:14:21.020 So it may take a while if you tap at a bus for that bus 00:14:21.020 --> 00:14:23.570 to go to a garage and get probed-- 00:14:23.570 --> 00:14:25.940 and for the data that has been stored in that bus 00:14:25.940 --> 00:14:31.500 to be extracted from that bus to the central server. 00:14:31.500 --> 00:14:33.171 There is a move-- 00:14:33.171 --> 00:14:34.920 and we'll talk more about this when we get 00:14:34.920 --> 00:14:37.020 to fare policy and technology-- 00:14:37.020 --> 00:14:39.810 towards using mobile phone payments 00:14:39.810 --> 00:14:42.820 and using contactless bank card payment systems. 00:14:42.820 --> 00:14:45.840 And those systems often do the full transaction 00:14:45.840 --> 00:14:47.040 over the air in real-time. 00:14:47.040 --> 00:14:49.770 So we're starting to look at the possibility 00:14:49.770 --> 00:14:52.170 of having all this data in real-time or almost 00:14:52.170 --> 00:14:53.130 in real-time. 00:14:53.130 --> 00:14:54.110 But it's not there yet. 00:14:54.110 --> 00:14:56.360 AUDIENCE: [INAUDIBLE] can I ask a question about that? 00:14:56.360 --> 00:14:56.980 GABRIEL SANCHEZ-MARTINEZ: Yeah, of course. 00:14:56.980 --> 00:14:59.305 AUDIENCE: In terms of smart card, 00:14:59.305 --> 00:15:01.449 where this balance is stored on the card-- 00:15:01.449 --> 00:15:02.740 GABRIEL SANCHEZ-MARTINEZ: Yeah. 00:15:02.740 --> 00:15:06.134 AUDIENCE: --if one can figure out how to hack that card-- 00:15:06.134 --> 00:15:07.425 GABRIEL SANCHEZ-MARTINEZ: Yeah. 00:15:07.425 --> 00:15:08.966 AUDIENCE: --then what can [INAUDIBLE] 00:15:08.966 --> 00:15:12.877 fares through an elaborate technology that I couldn't do 00:15:12.877 --> 00:15:14.320 and most people couldn't do. 00:15:14.320 --> 00:15:15.290 But maybe some could. 00:15:15.290 --> 00:15:17.081 GABRIEL SANCHEZ-MARTINEZ: Yeah, definitely. 00:15:17.081 --> 00:15:19.880 So the Charlie Card system is an example about-- 00:15:19.880 --> 00:15:23.480 actually, MIT students were the first to hack it. 00:15:23.480 --> 00:15:24.980 AUDIENCE: I'm not surprised. 00:15:24.980 --> 00:15:28.310 GABRIEL SANCHEZ-MARTINEZ: So it's older technology. 00:15:28.310 --> 00:15:30.530 It used a low-bit encryption key. 00:15:30.530 --> 00:15:32.660 That's a symmetric encryption key. 00:15:32.660 --> 00:15:35.731 And they just brute forced it. 00:15:35.731 --> 00:15:36.980 They figured what the key was. 00:15:36.980 --> 00:15:39.260 They happened to use the same key for every card. 00:15:39.260 --> 00:15:43.250 So once you broke that key, you could take any card. 00:15:43.250 --> 00:15:45.844 And with the right hardware, you could add however much value 00:15:45.844 --> 00:15:46.760 you want to that card. 00:15:46.760 --> 00:15:47.260 And-- 00:15:47.260 --> 00:15:48.140 AUDIENCE: [INAUDIBLE] 00:15:48.140 --> 00:15:50.390 GABRIEL SANCHEZ-MARTINEZ: Yeah, yeah, exactly. 00:15:50.390 --> 00:15:52.700 We don't think it's been a major problem. 00:15:52.700 --> 00:15:54.590 AUDIENCE: But it happens. 00:15:54.590 --> 00:15:56.798 GABRIEL SANCHEZ-MARTINEZ: I haven't seen MIT students 00:15:56.798 --> 00:15:58.550 selling special MIT cards. 00:15:58.550 --> 00:16:02.690 But that would be criminal, of course. 00:16:02.690 --> 00:16:06.450 Yeah, so newer systems have much stronger encryption. 00:16:06.450 --> 00:16:10.410 And they have different encryption keys for each card. 00:16:10.410 --> 00:16:13.970 And certainly, when we're moving towards contactless bank cards, 00:16:13.970 --> 00:16:17.570 we're talking about a much more secure encryption. 00:16:17.570 --> 00:16:20.270 It's your credit card that you're using to tap 00:16:20.270 --> 00:16:21.539 or your Android or Apple Pay. 00:16:21.539 --> 00:16:23.080 AUDIENCE: Account based [INAUDIBLE].. 00:16:23.080 --> 00:16:24.788 GABRIEL SANCHEZ-MARTINEZ: Account based-- 00:16:24.788 --> 00:16:27.860 and essentially, what you have is a token with an ID. 00:16:27.860 --> 00:16:32.020 And then, the balance is not even stored on your card. 00:16:32.020 --> 00:16:36.320 The account server is handling the balance and those things. 00:16:36.320 --> 00:16:39.740 So much more difficult to break. 00:16:39.740 --> 00:16:42.380 Yup. 00:16:42.380 --> 00:16:45.950 OK, AVL systems, or Automatic Vehicle Location systems-- 00:16:45.950 --> 00:16:49.250 so these are systems that track vehicle movement. 00:16:49.250 --> 00:16:51.490 So for bus, they tend to be based on GPS. 00:16:51.490 --> 00:16:54.520 You have GPS on a bus, on the top of the bus, a little hub. 00:16:54.520 --> 00:16:58.960 And it collects data every five seconds or every 10 seconds. 00:16:58.960 --> 00:17:04.119 And these positions might get sent either in real-time, 00:17:04.119 --> 00:17:07.089 or maybe they get stored on the onboard computer 00:17:07.089 --> 00:17:10.920 and then are extracted when the bus reaches the garage. 00:17:10.920 --> 00:17:17.160 So just GPS-- sophisticated AVL systems for bus 00:17:17.160 --> 00:17:21.930 also have gyroscopes to do inertial navigation and dead 00:17:21.930 --> 00:17:25.380 reckoning, especially when the GPS precision drops. 00:17:25.380 --> 00:17:28.830 And that happens especially with the urban canyon effect. 00:17:28.830 --> 00:17:31.540 If you have tall buildings, GPS signal bounces around. 00:17:31.540 --> 00:17:36.950 The dilution of precision messes up the position of the bus. 00:17:36.950 --> 00:17:38.790 Or maybe you're entering a tunnel, 00:17:38.790 --> 00:17:42.210 and you want to continue to get updates 00:17:42.210 --> 00:17:43.800 of positions inside the tunnel. 00:17:43.800 --> 00:17:45.390 So this is a temporary system that 00:17:45.390 --> 00:17:49.500 kicks in and interpolates positions and figures 00:17:49.500 --> 00:17:51.780 out how the bus is moving. 00:17:51.780 --> 00:17:54.119 For a train, it's usually based on track circuits. 00:17:54.119 --> 00:17:56.160 So we're going to talk more about track circuits. 00:17:56.160 --> 00:17:59.160 But essentially, a track knows if a train 00:17:59.160 --> 00:18:02.640 is occupying that segment or not occupying that segment. 00:18:02.640 --> 00:18:09.570 And there are often some sensors that read with RFID technology 00:18:09.570 --> 00:18:11.670 the ID number of a car. 00:18:11.670 --> 00:18:14.190 And sometimes, you have a sensor in the front of each car 00:18:14.190 --> 00:18:15.750 and [AUDIO OUT] each car. 00:18:15.750 --> 00:18:20.490 And so a computer will look up the sequence of readings 00:18:20.490 --> 00:18:23.610 and follow track circuits as they are being occupied 00:18:23.610 --> 00:18:25.560 and unoccupied-- 00:18:25.560 --> 00:18:29.530 and in that manner, track trains throughout the system. 00:18:29.530 --> 00:18:32.790 These systems were put in place mostly for safety 00:18:32.790 --> 00:18:35.670 to prevent train crashes. 00:18:35.670 --> 00:18:39.330 And because of that, you would need it to know buses 00:18:39.330 --> 00:18:41.310 or where a train was. 00:18:41.310 --> 00:18:42.900 They are available in real-time. 00:18:42.900 --> 00:18:44.460 They were designed from the beginning 00:18:44.460 --> 00:18:46.000 to track vehicles in real-time. 00:18:46.000 --> 00:18:48.086 So that's what we have. 00:18:48.086 --> 00:18:49.710 I guess what's newer is that now, we're 00:18:49.710 --> 00:18:52.650 collecting them and keeping them in a data warehouse 00:18:52.650 --> 00:18:54.730 so that we can analyze running times. 00:18:54.730 --> 00:18:56.895 AUDIENCE: [INAUDIBLE] these systems have benefit 00:18:56.895 --> 00:18:58.320 to the consumer? 00:18:58.320 --> 00:18:58.680 GABRIEL SANCHEZ-MARTINEZ: They do. 00:18:58.680 --> 00:19:00.638 And that's the newest thing that has happened-- 00:19:00.638 --> 00:19:02.460 that nobody thought about consumers when 00:19:02.460 --> 00:19:04.080 they were put in place. 00:19:04.080 --> 00:19:07.110 So yeah, we are talking about tracking, 00:19:07.110 --> 00:19:09.780 knowing how many minutes I have to wait for my bus, 00:19:09.780 --> 00:19:10.725 for example. 00:19:10.725 --> 00:19:13.380 And those things are pushed through a public API, 00:19:13.380 --> 00:19:16.200 so that if I'm a smartphone app developer, 00:19:16.200 --> 00:19:19.950 I can go ahead and pull data from this next bus app 00:19:19.950 --> 00:19:20.979 and make an app. 00:19:20.979 --> 00:19:23.520 And so people can download it, and they know how many minutes 00:19:23.520 --> 00:19:24.380 they have to wait. 00:19:24.380 --> 00:19:27.800 Yeah, so definitely. 00:19:27.800 --> 00:19:31.170 So we have seen a lot of AVL being pushed in that manner. 00:19:31.170 --> 00:19:35.850 We have not seen so much AFC data or APC data being pushed. 00:19:35.850 --> 00:19:37.980 Obviously, you wouldn't want all the details 00:19:37.980 --> 00:19:39.840 of AFC being pushed. 00:19:39.840 --> 00:19:42.540 But you might want to know how crowded is my next bus, 00:19:42.540 --> 00:19:45.100 or how crowded is my next train. 00:19:45.100 --> 00:19:46.860 And you might actually alter your decision 00:19:46.860 --> 00:19:48.780 whether to wait for a crowded train 00:19:48.780 --> 00:19:52.640 or walk a longer time based on that information. 00:19:52.640 --> 00:19:54.127 So that's coming. 00:19:54.127 --> 00:19:55.710 I think, in the next few years, that's 00:19:55.710 --> 00:19:57.900 going to start happening. 00:19:57.900 --> 00:20:00.690 So passenger counting-- many different technologies exist. 00:20:00.690 --> 00:20:05.700 For bus, we tend to have these optical sensors in the back. 00:20:05.700 --> 00:20:08.640 You might see them if you pay attention-- 00:20:08.640 --> 00:20:09.740 broken beam sensors. 00:20:09.740 --> 00:20:12.210 They look like two little eyes with two little mirrors 00:20:12.210 --> 00:20:13.320 on each door. 00:20:13.320 --> 00:20:16.260 And so when you cross the beams, if you 00:20:16.260 --> 00:20:18.870 press one beam first and then the other, 00:20:18.870 --> 00:20:20.280 that sensor will know-- 00:20:20.280 --> 00:20:22.230 is a person coming into the bus? 00:20:22.230 --> 00:20:24.270 Or is a person exiting the bus? 00:20:24.270 --> 00:20:26.100 And you have that at each door. 00:20:26.100 --> 00:20:31.470 And it counts those beams going in and going out. 00:20:31.470 --> 00:20:34.110 And often, this is slightly inaccurate. 00:20:34.110 --> 00:20:36.780 So you might get more boardings and lightings for a given trip. 00:20:36.780 --> 00:20:39.150 So at the end of a trip, whatever 00:20:39.150 --> 00:20:41.950 remains in terms of imbalance between boardings and lightings 00:20:41.950 --> 00:20:42.900 gets zeroed out. 00:20:42.900 --> 00:20:46.910 And the area is distributed throughout that trip 00:20:46.910 --> 00:20:48.372 that was just run. 00:20:48.372 --> 00:20:50.580 And often, you still have to do some error correction 00:20:50.580 --> 00:20:51.360 after that. 00:20:51.360 --> 00:20:54.420 But it's a way of counting people getting on and off. 00:20:54.420 --> 00:20:57.060 And that's useful to get how many people are riding 00:20:57.060 --> 00:21:00.330 the system and also the passenger miles-- 00:21:00.330 --> 00:21:02.720 the passengers multiplied by distance, which is often 00:21:02.720 --> 00:21:07.380 a required reporting element in things like the NTB, 00:21:07.380 --> 00:21:10.020 the National Transit Database. 00:21:10.020 --> 00:21:14.420 So for rail systems, we have gates 00:21:14.420 --> 00:21:16.231 that count how many times they open 00:21:16.231 --> 00:21:17.480 and how many times they close. 00:21:17.480 --> 00:21:21.530 So you might have that kind of counting in rail. 00:21:21.530 --> 00:21:23.150 You also have video-based counting-- 00:21:23.150 --> 00:21:27.710 so camera feeds that can be hooked up 00:21:27.710 --> 00:21:31.990 to a system that will essentially track nodes moving 00:21:31.990 --> 00:21:33.270 inside that frame. 00:21:33.270 --> 00:21:36.260 And you can count things that cross a certain line, 00:21:36.260 --> 00:21:37.370 for example. 00:21:37.370 --> 00:21:42.020 And you could do that to count flows. 00:21:42.020 --> 00:21:45.200 And then for train, we also have the weight systems. 00:21:45.200 --> 00:21:47.870 So this is only in trains. 00:21:47.870 --> 00:21:50.780 The braking systems in trains apply braking force 00:21:50.780 --> 00:21:53.780 in proportion to the load on each car. 00:21:53.780 --> 00:21:55.340 So if you have a very heavy car, you 00:21:55.340 --> 00:21:58.490 need to apply stronger braking force than in a car that 00:21:58.490 --> 00:22:00.050 is almost empty. 00:22:00.050 --> 00:22:04.400 If you don't do that, then you apply a lot more force 00:22:04.400 --> 00:22:06.430 per weight on the lighter car. 00:22:06.430 --> 00:22:10.070 That car is going to be the one pushing the other cars 00:22:10.070 --> 00:22:12.530 or pulling the other cars through the coupling. 00:22:12.530 --> 00:22:14.480 And that will eventually break the [INAUDIBLE] 00:22:14.480 --> 00:22:15.360 at a faster rate. 00:22:15.360 --> 00:22:18.560 So what you want is, each car to slow down 00:22:18.560 --> 00:22:21.690 at the same rate by itself as much as possible. 00:22:21.690 --> 00:22:24.620 And for that, you need to brake in proportion to the weight. 00:22:24.620 --> 00:22:26.630 And therefore, you have these weight systems. 00:22:26.630 --> 00:22:29.000 They used to just do that. 00:22:29.000 --> 00:22:30.680 And more recently, we hooked them 00:22:30.680 --> 00:22:33.770 up to a little storage device that 00:22:33.770 --> 00:22:36.830 keeps track of the weight and maybe Wi-Fi, 00:22:36.830 --> 00:22:39.410 so that each time it reaches a station or the terminal, 00:22:39.410 --> 00:22:40.930 it sends the data off. 00:22:40.930 --> 00:22:47.240 And we might have a rather somewhat [? unprecise ?] 00:22:47.240 --> 00:22:50.600 idea of how many people are in the car just based 00:22:50.600 --> 00:22:54.440 on an average weight of a person. 00:22:54.440 --> 00:22:56.940 And these are traditionally not available in real real-time. 00:22:56.940 --> 00:22:57.710 [INAUDIBLE] you have questions? 00:22:57.710 --> 00:22:58.090 Yeah? 00:22:58.090 --> 00:22:59.410 AUDIENCE: You could also just reconcile it 00:22:59.410 --> 00:23:00.760 with the other system, right? 00:23:00.760 --> 00:23:01.370 GABRIEL SANCHEZ-MARTINEZ: Of course, yeah. 00:23:01.370 --> 00:23:02.250 AUDIENCE: So if you have-- 00:23:02.250 --> 00:23:02.460 [INTERPOSING VOICES] 00:23:02.460 --> 00:23:02.945 GABRIEL SANCHEZ-MARTINEZ: Yeah. 00:23:02.945 --> 00:23:05.370 AUDIENCE: --people early can transport to get on to. 00:23:05.370 --> 00:23:05.520 GABRIEL SANCHEZ-MARTINEZ: Yeah. 00:23:05.520 --> 00:23:06.250 AUDIENCE: [INAUDIBLE] 00:23:06.250 --> 00:23:07.420 GABRIEL SANCHEZ-MARTINEZ: Yeah, definitely. 00:23:07.420 --> 00:23:07.920 Yeah. 00:23:07.920 --> 00:23:11.900 And that's cutting edge research that's happening right now. 00:23:11.900 --> 00:23:14.570 How do you do data fiction and merge different systems? 00:23:14.570 --> 00:23:15.650 They all have errors. 00:23:15.650 --> 00:23:17.100 And how do you detect when one is 00:23:17.100 --> 00:23:18.350 more erroneous than the other? 00:23:18.350 --> 00:23:20.420 And how do you mix these data sources 00:23:20.420 --> 00:23:23.847 to get the most precise, not just loads, but paths 00:23:23.847 --> 00:23:25.430 within a network and things like that. 00:23:25.430 --> 00:23:26.460 Yeah. 00:23:26.460 --> 00:23:31.039 So any questions on these three very important automatic data 00:23:31.039 --> 00:23:31.830 collection systems? 00:23:31.830 --> 00:23:32.640 AUDIENCE: [INAUDIBLE] 00:23:32.640 --> 00:23:33.889 GABRIEL SANCHEZ-MARTINEZ: Yup. 00:23:33.889 --> 00:23:41.426 AUDIENCE: So if there [INAUDIBLE] 00:23:41.426 --> 00:23:45.782 AVL, what kind of reason can be [INAUDIBLE]?? 00:23:45.782 --> 00:23:47.490 GABRIEL SANCHEZ-MARTINEZ: So the question 00:23:47.490 --> 00:23:52.780 is, why might some of these technologies produce errors? 00:23:52.780 --> 00:23:55.150 And in particular, you're asking about AVL. 00:23:55.150 --> 00:23:58.090 So each of these has a different behavior. 00:23:58.090 --> 00:24:01.030 And within each of these categories of technologies, 00:24:01.030 --> 00:24:04.870 each vendor's system might have specific things that happen. 00:24:04.870 --> 00:24:06.730 With AVL, the most common thing is 00:24:06.730 --> 00:24:10.900 end of root problems-- detecting when a trip actually 00:24:10.900 --> 00:24:12.460 begins and ends. 00:24:12.460 --> 00:24:17.020 So AVL systems, you have this GPS 00:24:17.020 --> 00:24:18.450 coming in every five seconds. 00:24:18.450 --> 00:24:20.950 Depending on your chip set, you might get it more frequently 00:24:20.950 --> 00:24:21.450 than that. 00:24:21.450 --> 00:24:25.230 But you also actually sometimes hook it to the doors. 00:24:25.230 --> 00:24:28.420 So if the door is opening, you say, well, I must be at a stop. 00:24:28.420 --> 00:24:30.880 And therefore, let me find which one is closest. 00:24:30.880 --> 00:24:32.540 So there are ways to correct it. 00:24:32.540 --> 00:24:34.750 But when you get to the end of the route, 00:24:34.750 --> 00:24:37.430 it's not clear always-- have you finished your trip? 00:24:37.430 --> 00:24:41.290 Or rather, are you starting your trip already? 00:24:41.290 --> 00:24:45.970 So maybe if the terminal is at the same place on the trip-- 00:24:45.970 --> 00:24:47.710 the previous trip ends at the same place 00:24:47.710 --> 00:24:49.960 that the next trip begins, there might 00:24:49.960 --> 00:24:53.950 be a time where the doors open and close various times. 00:24:53.950 --> 00:24:56.140 And the trip isn't ready to leave yet. 00:24:56.140 --> 00:24:58.810 And so you really have to wait to see the bus leaving 00:24:58.810 --> 00:25:00.370 that terminal and moving. 00:25:00.370 --> 00:25:01.900 Sometimes, there are false starts. 00:25:01.900 --> 00:25:06.040 So maybe another bus comes along, and it needs that space. 00:25:06.040 --> 00:25:10.270 So the driver moves the bus a few meters forward. 00:25:10.270 --> 00:25:13.880 And the system thinks my trip has started. 00:25:13.880 --> 00:25:16.130 And then, when you're looking at aggregate data, 00:25:16.130 --> 00:25:19.120 you're looking at, say, running times at the trip level. 00:25:19.120 --> 00:25:21.940 You see these outliers with very long times. 00:25:21.940 --> 00:25:23.500 And if you were to plot them by stop, 00:25:23.500 --> 00:25:25.510 you see that the link between the first stop 00:25:25.510 --> 00:25:29.360 and the second step is sometimes very high, 15 minutes. 00:25:29.360 --> 00:25:30.880 And so you can throw those out. 00:25:30.880 --> 00:25:33.850 Or you can do some interpolation or imputation of data. 00:25:33.850 --> 00:25:36.880 Some systems that care very much about that 00:25:36.880 --> 00:25:40.240 will purposely place the terminal 00:25:40.240 --> 00:25:45.310 stops sufficiently far apart to prevent that 00:25:45.310 --> 00:25:48.210 from happening because it is a problem. 00:25:48.210 --> 00:25:52.050 And this data is crucial to planning service and figuring 00:25:52.050 --> 00:25:54.610 out how much resource you're going to put into each route. 00:25:54.610 --> 00:25:56.856 So yup. 00:25:56.856 --> 00:26:03.758 AUDIENCE: For tap cards, [INAUDIBLE] and metros, 00:26:03.758 --> 00:26:07.702 some of them we have to tap out to exit. 00:26:07.702 --> 00:26:09.903 It is because of variable [INAUDIBLE].. 00:26:09.903 --> 00:26:11.153 GABRIEL SANCHEZ-MARTINEZ: Yes. 00:26:11.153 --> 00:26:14.604 AUDIENCE: But in some systems, it's still a flat fare. 00:26:14.604 --> 00:26:16.083 You still have to tap out. 00:26:16.083 --> 00:26:18.548 Is the reason behind that mostly data collection? 00:26:18.548 --> 00:26:20.766 Or is there anything [INAUDIBLE] you're 00:26:20.766 --> 00:26:22.695 going to still have to tap out [INAUDIBLE]?? 00:26:22.695 --> 00:26:24.170 GABRIEL SANCHEZ-MARTINEZ: So yeah, no examples of it 00:26:24.170 --> 00:26:24.999 come to mind. 00:26:24.999 --> 00:26:25.790 You might know one. 00:26:25.790 --> 00:26:27.360 AUDIENCE: MARTA? 00:26:27.360 --> 00:26:29.460 GABRIEL SANCHEZ-MARTINEZ: OK, I haven't visited. 00:26:29.460 --> 00:26:31.890 So yeah, data collection might be a reason to do that. 00:26:31.890 --> 00:26:35.640 But I'll have to get back to you on why MARTA did that. 00:26:35.640 --> 00:26:41.090 But yeah, most systems that have controls in and out 00:26:41.090 --> 00:26:43.680 are for fare policy reasons and not 00:26:43.680 --> 00:26:46.560 for data collection reasons. 00:26:46.560 --> 00:26:49.980 We're starting to see more interest in data collection 00:26:49.980 --> 00:26:53.797 and in investing on these technologies just 00:26:53.797 --> 00:26:54.630 for data collection. 00:26:54.630 --> 00:26:58.220 So maybe-- but I'll have to check and get back to you. 00:26:58.220 --> 00:27:01.177 AUDIENCE: You mentioned some systems separate their depots 00:27:01.177 --> 00:27:03.260 to not confuse the end [? from the start point. ?] 00:27:03.260 --> 00:27:03.515 [INTERPOSING VOICES] 00:27:03.515 --> 00:27:04.760 GABRIEL SANCHEZ-MARTINEZ: Their terminal stops, yeah. 00:27:04.760 --> 00:27:06.720 AUDIENCE: What are some examples of those? 00:27:06.720 --> 00:27:10.510 GABRIEL SANCHEZ-MARTINEZ: TFL will do that in London, yeah. 00:27:10.510 --> 00:27:11.960 Yeah, so they'll monitor this. 00:27:11.960 --> 00:27:17.110 And if they see that this is occurring often, 00:27:17.110 --> 00:27:20.319 they will separate the stops a bit. 00:27:20.319 --> 00:27:22.110 And the reason they do that is because they 00:27:22.110 --> 00:27:26.190 have people whose job it is to impute data 00:27:26.190 --> 00:27:27.420 when it's incorrect. 00:27:27.420 --> 00:27:30.330 So if they don't do that, and the system is consistently 00:27:30.330 --> 00:27:32.170 producing bad data, then that means 00:27:32.170 --> 00:27:35.850 they're going to have to spend human resources on correcting 00:27:35.850 --> 00:27:37.050 that data. 00:27:37.050 --> 00:27:38.520 So at some point, it's just easier 00:27:38.520 --> 00:27:40.350 to move the stop a little bit. 00:27:40.350 --> 00:27:42.427 It doesn't have to be a long distance. 00:27:42.427 --> 00:27:43.135 AUDIENCE: Got it. 00:27:43.135 --> 00:27:45.260 GABRIEL SANCHEZ-MARTINEZ: It does not make the same 00:27:45.260 --> 00:27:48.030 and make it far enough apart that the geo fences can 00:27:48.030 --> 00:27:51.180 be told apart from each other. 00:27:51.180 --> 00:27:51.680 Alright? 00:27:51.680 --> 00:27:54.382 AUDIENCE: Really small scale data of the EZRide who I work 00:27:54.382 --> 00:27:57.922 for, actually you could see real-time bus loads 00:27:57.922 --> 00:27:59.340 [INAUDIBLE]-- 00:27:59.340 --> 00:28:02.349 GABRIEL SANCHEZ-MARTINEZ: Oh, interesting. 00:28:02.349 --> 00:28:04.890 AUDIENCE: --which was actually helpful if you're dispatching, 00:28:04.890 --> 00:28:07.950 and you know a bus is getting through people on it. 00:28:07.950 --> 00:28:08.450 [INAUDIBLE] 00:28:08.450 --> 00:28:10.450 GABRIEL SANCHEZ-MARTINEZ: Yeah, for real-time control. 00:28:10.450 --> 00:28:11.070 [INTERPOSING VOICES] 00:28:11.070 --> 00:28:12.778 AUDIENCE: But the terminal at our station 00:28:12.778 --> 00:28:15.082 had a drop-off point and a pick-up point. 00:28:15.082 --> 00:28:18.004 The drop-off point was before layover [INAUDIBLE] 00:28:18.004 --> 00:28:21.570 was after for this exact reason to make sure 00:28:21.570 --> 00:28:23.361 that it will go through the drop-off point, 00:28:23.361 --> 00:28:25.009 reset, until people get off of it. 00:28:25.009 --> 00:28:26.300 GABRIEL SANCHEZ-MARTINEZ: Yeah. 00:28:26.300 --> 00:28:27.192 Yeah, so it happens. 00:28:27.192 --> 00:28:28.025 [INTERPOSING VOICES] 00:28:28.025 --> 00:28:28.900 AUDIENCE: Definitely. 00:28:28.900 --> 00:28:31.179 [INAUDIBLE] 00:28:31.179 --> 00:28:33.262 GABRIEL SANCHEZ-MARTINEZ: That sounds about right. 00:28:36.324 --> 00:28:37.740 OK, if there are no more questions 00:28:37.740 --> 00:28:41.859 on the three very important categories of automated data 00:28:41.859 --> 00:28:43.650 collection systems, let's talk a little bit 00:28:43.650 --> 00:28:46.360 about the data collection program design process. 00:28:46.360 --> 00:28:49.920 So this comes from before automatic data collection. 00:28:49.920 --> 00:28:53.179 And nowadays, we think a little bit less about this. 00:28:53.179 --> 00:28:54.220 But it's still important. 00:28:54.220 --> 00:28:59.010 So if you do need to collect some data, 00:28:59.010 --> 00:29:01.500 there's a structure that you can follow to do it properly 00:29:01.500 --> 00:29:03.660 and to make sure that you collect data efficiently, 00:29:03.660 --> 00:29:06.624 so that you don't spend too much resources on data collection 00:29:06.624 --> 00:29:08.790 and that you can answer your policy or your planning 00:29:08.790 --> 00:29:09.840 questions. 00:29:09.840 --> 00:29:15.060 So based on your needs and the properties of your agency, 00:29:15.060 --> 00:29:17.400 I say here, determine property characteristics. 00:29:17.400 --> 00:29:18.630 That's a North American term. 00:29:18.630 --> 00:29:20.050 A property is an agency. 00:29:20.050 --> 00:29:23.259 So if you see that, that's an agency. 00:29:23.259 --> 00:29:25.800 So based on the characteristics of the service you're running 00:29:25.800 --> 00:29:28.811 and your data needs, you can select some data collection 00:29:28.811 --> 00:29:29.310 technique. 00:29:29.310 --> 00:29:31.690 We'll get into what some of these are. 00:29:31.690 --> 00:29:35.070 Then, you can develop route-by-route sampling plans 00:29:35.070 --> 00:29:39.810 based on how variable the data is in each case. 00:29:39.810 --> 00:29:41.900 And you can determine how many checkers do I need. 00:29:41.900 --> 00:29:44.760 A checker is a person who goes out and collects data. 00:29:44.760 --> 00:29:46.770 And then from that, the cost-- 00:29:46.770 --> 00:29:47.790 so human resources. 00:29:47.790 --> 00:29:49.440 It's a planning exercise. 00:29:49.440 --> 00:29:52.740 And what we do usually is that we conduct a baseline phase. 00:29:52.740 --> 00:29:57.280 So that's the first time you go out and collect data. 00:29:57.280 --> 00:30:00.150 You don't know much about what you're 00:30:00.150 --> 00:30:01.970 wanting to collect data on. 00:30:01.970 --> 00:30:06.870 So it might be only matrices, or loads, 00:30:06.870 --> 00:30:09.600 the people getting on and off. 00:30:09.600 --> 00:30:13.350 So you have to go out and do a bigger effort. 00:30:13.350 --> 00:30:15.810 And that's called the baseline phase effort. 00:30:15.810 --> 00:30:19.020 Once you've done that and you've established some tendencies, 00:30:19.020 --> 00:30:22.080 you might want to monitor that to see if it changes. 00:30:22.080 --> 00:30:25.530 So then, you do a lighter weight data collection effort, where 00:30:25.530 --> 00:30:29.220 you go out and less frequently, using fewer resources, 00:30:29.220 --> 00:30:31.980 you collect sometimes the same thing. 00:30:31.980 --> 00:30:37.890 Or sometimes, you observe something else that is related 00:30:37.890 --> 00:30:41.100 or can be correlated with what you really want. 00:30:41.100 --> 00:30:44.340 And then based on a relationship between the two, 00:30:44.340 --> 00:30:46.560 you can estimate what you really want. 00:30:46.560 --> 00:30:50.090 So you can monitor what you collected. 00:30:50.090 --> 00:30:51.870 And then, if you detect that there's 00:30:51.870 --> 00:30:54.360 been a trend or a change, and you need to investigate it 00:30:54.360 --> 00:30:57.420 further, you might go ahead and repeat the baseline phase 00:30:57.420 --> 00:30:59.530 to increase your accuracy. 00:30:59.530 --> 00:31:04.080 So one of the catches of this is that to determine 00:31:04.080 --> 00:31:06.600 sampling plans, to determine required sample 00:31:06.600 --> 00:31:09.700 sizes to achieve some confidence interval, 00:31:09.700 --> 00:31:12.120 you need to know how variable your data is. 00:31:12.120 --> 00:31:15.030 And if you haven't collected it yet, you don't know. 00:31:15.030 --> 00:31:18.350 So you might have some default values that you resort to. 00:31:18.350 --> 00:31:20.800 And we'll get to that later in this lecture. 00:31:20.800 --> 00:31:22.770 But you might also do a pre-test, where 00:31:22.770 --> 00:31:24.270 you send some people out, and you 00:31:24.270 --> 00:31:27.150 collect some data to really start 00:31:27.150 --> 00:31:30.030 to get a sense of how variable is it, 00:31:30.030 --> 00:31:35.090 and how big will my sample requirements be, 00:31:35.090 --> 00:31:37.560 and how much will it cost for me to do this. 00:31:37.560 --> 00:31:40.810 So this is the process that you might follow. 00:31:40.810 --> 00:31:44.622 And there are different data needs by the question 00:31:44.622 --> 00:31:45.830 that you're trying to answer. 00:31:45.830 --> 00:31:48.430 So one way of looking at that is, are you 00:31:48.430 --> 00:31:51.130 collecting things that are for specific routes, 00:31:51.130 --> 00:31:54.070 or for specific route segments, or at the stop level? 00:31:54.070 --> 00:31:57.950 Or are you using more aggregate system level data collection? 00:31:57.950 --> 00:32:00.100 Are your questions more system level? 00:32:00.100 --> 00:32:02.920 So system-level things are more about reporting, 00:32:02.920 --> 00:32:06.730 and they might be tied to things like federal funding. 00:32:06.730 --> 00:32:09.610 Whereas route-level things and stop-level things 00:32:09.610 --> 00:32:12.020 are more important for planning. 00:32:12.020 --> 00:32:14.860 So when we talk about route and route segment level, 00:32:14.860 --> 00:32:17.350 we're looking at things like loads at the peak load points 00:32:17.350 --> 00:32:18.580 or at some other key points. 00:32:18.580 --> 00:32:20.900 How many people are in the bus? 00:32:20.900 --> 00:32:23.980 The running time is by the segment 00:32:23.980 --> 00:32:26.260 to do schedule that has time points 00:32:26.260 --> 00:32:30.010 or maybe end-to-end to your operations plan. 00:32:30.010 --> 00:32:32.470 Schedule adherence-- are these buses running on time? 00:32:32.470 --> 00:32:34.870 Or are my schedules not realistic? 00:32:34.870 --> 00:32:37.120 Total boardings or revenue, two things 00:32:37.120 --> 00:32:41.590 that are highly correlated-- so number of passenger trips. 00:32:41.590 --> 00:32:44.014 Boardings by fare category-- so you might say, 00:32:44.014 --> 00:32:45.430 well, I want boardings, but I want 00:32:45.430 --> 00:32:47.170 to know how many seniors are using this, 00:32:47.170 --> 00:32:50.500 and how many students are using this, and how many people are 00:32:50.500 --> 00:32:52.540 using monthly passes, and how many people are 00:32:52.540 --> 00:32:55.750 using pay-per-ride. 00:32:55.750 --> 00:32:58.600 So you have different fare categories. 00:32:58.600 --> 00:33:03.430 And you might want to segregate the data by that. 00:33:03.430 --> 00:33:05.920 You might want passenger boarding and lighting by stop. 00:33:05.920 --> 00:33:07.840 So that's what APC would give you 00:33:07.840 --> 00:33:10.900 if you have an automated system. 00:33:10.900 --> 00:33:13.540 But you might also use a write checker, who sits on the bus 00:33:13.540 --> 00:33:16.660 and counts people boarding in a lighting. 00:33:16.660 --> 00:33:19.690 Transfer rates between routes-- to see you maybe you're 00:33:19.690 --> 00:33:23.460 looking at changing service so that people 00:33:23.460 --> 00:33:25.920 don't have to transfer. 00:33:25.920 --> 00:33:28.440 Passenger characteristics and attitudes-- this usually 00:33:28.440 --> 00:33:31.020 requires some degree of survey, where 00:33:31.020 --> 00:33:35.622 you ask people things, passenger travel patterns. 00:33:35.622 --> 00:33:37.080 At the system level, we have things 00:33:37.080 --> 00:33:39.840 like unlinked passenger trips, passenger miles, linked 00:33:39.840 --> 00:33:40.817 passenger trips. 00:33:40.817 --> 00:33:42.150 This had the whole system level. 00:33:42.150 --> 00:33:45.990 So sometimes, you do route level or route segment level 00:33:45.990 --> 00:33:47.400 analysis, and then, you aggregate 00:33:47.400 --> 00:33:48.750 to get the system-level things. 00:33:48.750 --> 00:33:50.970 That's usually how you proceed. 00:33:50.970 --> 00:33:54.120 But the requirements in terms of how many of these 00:33:54.120 --> 00:33:56.204 you have to sample might be different. 00:33:56.204 --> 00:33:58.620 So if you want to achieve a certain accuracy at the system 00:33:58.620 --> 00:34:01.260 level, you don't need to achieve the accuracy 00:34:01.260 --> 00:34:04.830 for each of the routes that are in that system 00:34:04.830 --> 00:34:07.740 because you might have-- 00:34:07.740 --> 00:34:11.400 so if you want to say 90% confidence 00:34:11.400 --> 00:34:15.810 in some system-level data element, 00:34:15.810 --> 00:34:19.239 you might only need 80% or 70% of the element level. 00:34:19.239 --> 00:34:21.000 And once you bring those altogether, 00:34:21.000 --> 00:34:23.159 you achieve the 90% that you need. 00:34:23.159 --> 00:34:27.840 So data inference, I talked about how sometimes we 00:34:27.840 --> 00:34:33.280 can infer items if we don't observe them directly. 00:34:33.280 --> 00:34:36.540 So from AFC with AFC is a low-fare collection system, 00:34:36.540 --> 00:34:39.449 we have boardings because people are tapping into the bus 00:34:39.449 --> 00:34:41.560 or tapping into the subway system. 00:34:41.560 --> 00:34:44.909 And if we have APC, we count people getting on. 00:34:44.909 --> 00:34:49.360 So we can look at total number of boardings that way, 00:34:49.360 --> 00:34:50.670 if that makes sense. 00:34:50.670 --> 00:34:51.690 That's pretty direct. 00:34:51.690 --> 00:34:54.300 Sometimes, you want to correct for errors in the APC system, 00:34:54.300 --> 00:34:57.271 or you might have things like variation affecting 00:34:57.271 --> 00:34:59.520 that number-- like it goes from AFC to how many people 00:34:59.520 --> 00:35:00.720 were actually in that bus. 00:35:00.720 --> 00:35:02.100 How many people actually boarded? 00:35:02.100 --> 00:35:05.160 So you might do a little bit of manual surveys 00:35:05.160 --> 00:35:09.450 to check what that relationship is and apply some correction. 00:35:09.450 --> 00:35:11.340 For passenger miles, we need to know 00:35:11.340 --> 00:35:15.330 how many people are at the bus between each stop here. 00:35:15.330 --> 00:35:18.930 So AFC gives you boardings and only boardings. 00:35:18.930 --> 00:35:20.820 APC gives you ons and offs. 00:35:20.820 --> 00:35:23.700 If every bus had APC, then you could calculate passenger miles 00:35:23.700 --> 00:35:24.630 directly. 00:35:24.630 --> 00:35:28.710 But often, you have systems where only a portion 00:35:28.710 --> 00:35:29.970 of the fleet has APC. 00:35:29.970 --> 00:35:33.240 So maybe 15% of your fleet is equipped with APC. 00:35:33.240 --> 00:35:38.220 And from that, you get the sample OD matrix. 00:35:38.220 --> 00:35:40.080 And you can use that OD matrix to convert 00:35:40.080 --> 00:35:43.560 from boardings only to the distribution and the ons 00:35:43.560 --> 00:35:45.810 and offs at all bus routes. 00:35:45.810 --> 00:35:47.760 And from that, you can get passenger miles. 00:35:47.760 --> 00:35:50.280 Or you might just use your buses that 00:35:50.280 --> 00:35:54.720 have APC, if that suffices for your data collection unit. 00:35:54.720 --> 00:35:59.070 Same thing with peak point load-- similar idea. 00:35:59.070 --> 00:36:01.200 The AFC only measures boardings. 00:36:01.200 --> 00:36:03.940 So it doesn't give you the peak point load automatically. 00:36:03.940 --> 00:36:05.670 But from APC, you could get it. 00:36:05.670 --> 00:36:09.390 And it you can establish a relationship between boardings 00:36:09.390 --> 00:36:11.460 and the peak load point, then you 00:36:11.460 --> 00:36:14.730 can use that model to infer the peak load 00:36:14.730 --> 00:36:16.200 point from just boardings. 00:36:16.200 --> 00:36:19.620 So this is a key thing to be efficient about data 00:36:19.620 --> 00:36:20.580 collection. 00:36:20.580 --> 00:36:24.194 Any questions on this idea? 00:36:24.194 --> 00:36:25.176 Yup. 00:36:25.176 --> 00:36:27.140 AUDIENCE: So to get passenger miles, 00:36:27.140 --> 00:36:29.104 you're also going to have a GPS system 00:36:29.104 --> 00:36:31.068 as well to know the distance? 00:36:31.068 --> 00:36:33.277 Or are we just basically [INAUDIBLE] this 00:36:33.277 --> 00:36:34.699 is the routing [INAUDIBLE]? 00:36:34.699 --> 00:36:35.990 GABRIEL SANCHEZ-MARTINEZ: Both. 00:36:35.990 --> 00:36:36.790 AUDIENCE: [INAUDIBLE] 00:36:36.790 --> 00:36:37.730 GABRIEL SANCHEZ-MARTINEZ: Yeah, both. 00:36:37.730 --> 00:36:39.190 AUDIENCE: [INAUDIBLE] 00:36:39.190 --> 00:36:41.106 GABRIEL SANCHEZ-MARTINEZ: What tends to happen 00:36:41.106 --> 00:36:44.770 is that the APC, it'll come in. 00:36:44.770 --> 00:36:47.720 And it'll say, at this stop, this many people boarded. 00:36:47.720 --> 00:36:48.940 This many people are lighted. 00:36:48.940 --> 00:36:52.740 So you have other layers in your database 00:36:52.740 --> 00:36:55.780 that say where the buses and what the distance 00:36:55.780 --> 00:37:00.450 is between stops and the stop pair level. 00:37:00.450 --> 00:37:03.267 So you then essentially know how many people 00:37:03.267 --> 00:37:05.350 are riding on each link and how long that link is, 00:37:05.350 --> 00:37:06.391 and you multiply the two. 00:37:06.391 --> 00:37:09.000 So yeah, passenger miles. 00:37:09.000 --> 00:37:10.640 Yeah, more questions. 00:37:10.640 --> 00:37:13.420 AUDIENCE: Yeah, for these checks that are going on 00:37:13.420 --> 00:37:14.649 like the more manual checks-- 00:37:14.649 --> 00:37:15.940 GABRIEL SANCHEZ-MARTINEZ: Yeah. 00:37:15.940 --> 00:37:17.100 AUDIENCE: --I know often, there's 00:37:17.100 --> 00:37:18.900 derivation checkers who are coming into a check. 00:37:18.900 --> 00:37:20.775 GABRIEL SANCHEZ-MARTINEZ: That's right, yeah. 00:37:20.775 --> 00:37:23.480 AUDIENCE: Do they also use that data to cross-reference 00:37:23.480 --> 00:37:25.370 the passenger counts? 00:37:25.370 --> 00:37:26.790 As in, [? this ?] person gets on, 00:37:26.790 --> 00:37:28.939 and they check everyone's voice to [INAUDIBLE] DFL. 00:37:28.939 --> 00:37:30.230 GABRIEL SANCHEZ-MARTINEZ: Yeah. 00:37:30.230 --> 00:37:32.970 AUDIENCE: They then know exactly how they go on the bus. 00:37:32.970 --> 00:37:34.220 GABRIEL SANCHEZ-MARTINEZ: Yes. 00:37:34.220 --> 00:37:34.615 Yeah. 00:37:34.615 --> 00:37:35.800 AUDIENCE: Do they use that data? 00:37:35.800 --> 00:37:36.740 GABRIEL SANCHEZ-MARTINEZ: Yeah, they can. 00:37:36.740 --> 00:37:39.350 In the APC, sometimes there's reliability problems, 00:37:39.350 --> 00:37:41.200 especially when vehicles are very 00:37:41.200 --> 00:37:43.090 full because sometimes, people will 00:37:43.090 --> 00:37:44.530 block the sensor by the door. 00:37:47.230 --> 00:37:49.030 Actually, people like to stand by the door 00:37:49.030 --> 00:37:50.821 all the time, even when the bus isn't full. 00:37:50.821 --> 00:37:53.235 And that kind of affects APC. 00:37:53.235 --> 00:37:54.610 You might notice this on the one. 00:37:54.610 --> 00:37:55.600 If you take the one-- 00:37:55.600 --> 00:38:00.970 so yeah, you sometimes have a little bit of a manual effort 00:38:00.970 --> 00:38:01.840 to figure out. 00:38:01.840 --> 00:38:03.730 Just learn about your APC system, 00:38:03.730 --> 00:38:06.190 and what are the errors, and when do you see them. 00:38:06.190 --> 00:38:09.430 It often happens that you have more variation when 00:38:09.430 --> 00:38:10.540 you have very high loads. 00:38:10.540 --> 00:38:12.400 And that's when APC is least accurate. 00:38:12.400 --> 00:38:15.880 So it all comes together. 00:38:15.880 --> 00:38:17.294 Yeah. 00:38:17.294 --> 00:38:18.210 Questions on the back? 00:38:18.210 --> 00:38:19.330 I think I saw a question. 00:38:19.330 --> 00:38:19.829 No? 00:38:19.829 --> 00:38:22.864 AUDIENCE: Yeah, I noticed that in Chicago, 00:38:22.864 --> 00:38:26.720 when the bus would be crowded, then people get off the bus. 00:38:26.720 --> 00:38:28.180 They let people off-- 00:38:28.180 --> 00:38:28.660 GABRIEL SANCHEZ-MARTINEZ: That's right. 00:38:28.660 --> 00:38:28.990 AUDIENCE: --and then back on. 00:38:28.990 --> 00:38:29.510 GABRIEL SANCHEZ-MARTINEZ: Yeah. 00:38:29.510 --> 00:38:30.010 Yeah. 00:38:30.010 --> 00:38:31.210 These double things. 00:38:31.210 --> 00:38:33.296 But somebody might be by the door just blocking 00:38:33.296 --> 00:38:34.295 the two little sensors-- 00:38:34.295 --> 00:38:34.990 [INTERPOSING VOICES] 00:38:34.990 --> 00:38:36.990 GABRIEL SANCHEZ-MARTINEZ: --the two little eyes. 00:38:36.990 --> 00:38:40.710 And that's it, no records of people getting on or off. 00:38:44.369 --> 00:38:46.660 So if you're doing a little data collection, as I said, 00:38:46.660 --> 00:38:48.010 we use checkers. 00:38:48.010 --> 00:38:50.260 And actually, your second assignment, you 00:38:50.260 --> 00:38:52.630 will be checkers of some kind. 00:38:52.630 --> 00:38:55.550 The typical checkers which you won't be in this assignment 00:38:55.550 --> 00:38:57.940 are ride checkers and point checkers. 00:38:57.940 --> 00:39:02.050 So a ride checker sits in the vehicle and rides 00:39:02.050 --> 00:39:03.370 with the vehicle. 00:39:03.370 --> 00:39:07.540 And the typical thing that these ride checkers are looking at 00:39:07.540 --> 00:39:10.380 is, how long did it take to cover some distance? 00:39:10.380 --> 00:39:12.479 So what was the running time for that trip? 00:39:12.479 --> 00:39:14.020 And also, people getting on and off-- 00:39:14.020 --> 00:39:16.090 so they act as APC essentially. 00:39:16.090 --> 00:39:18.140 And they act as AVL. 00:39:18.140 --> 00:39:20.770 So AVL and APC together might replace 00:39:20.770 --> 00:39:23.170 most of the functionality of a ride checker. 00:39:23.170 --> 00:39:26.980 Although a ride checker often can conduct an onboard survey, 00:39:26.980 --> 00:39:30.250 asking passengers about where are they going, 00:39:30.250 --> 00:39:33.590 or their trip purpose, or things related to social demographics, 00:39:33.590 --> 00:39:38.530 which are qualitative and cannot be collected with the sensors. 00:39:38.530 --> 00:39:40.900 Point checkers stand outside of the vehicle. 00:39:40.900 --> 00:39:43.720 They stay at a specific place, and they 00:39:43.720 --> 00:39:46.360 can look at headways between buses-- 00:39:46.360 --> 00:39:49.570 so how long did it take between each bus to come by, 00:39:49.570 --> 00:39:52.120 and how loaded were these buses? 00:39:52.120 --> 00:39:55.540 So if you're interested in the peak load point, 00:39:55.540 --> 00:39:57.400 and you know where the peak load point is, 00:39:57.400 --> 00:40:01.612 and you just want to observe, measure 00:40:01.612 --> 00:40:03.070 what are the loads of the peak load 00:40:03.070 --> 00:40:05.530 point, then you can just station a point 00:40:05.530 --> 00:40:06.880 checker at the peak load point. 00:40:06.880 --> 00:40:09.310 And if that person is strained, we'll 00:40:09.310 --> 00:40:13.270 be able to more or less say how many people are in the vehicle 00:40:13.270 --> 00:40:16.680 from looking at the vehicle. 00:40:16.680 --> 00:40:19.212 With automated data collection systems-- 00:40:19.212 --> 00:40:21.420 yeah, with a fair system, we have passenger accounts. 00:40:21.420 --> 00:40:23.410 We have transaction data, which is very rich. 00:40:23.410 --> 00:40:25.440 It will tell you not only that somebody 00:40:25.440 --> 00:40:27.930 is entering or exiting, but also how much they're 00:40:27.930 --> 00:40:32.430 paying, sometimes information about the fare product 00:40:32.430 --> 00:40:36.510 type, which might help you infer if this person is 00:40:36.510 --> 00:40:39.630 a senior, or a student, or a frequent user, an infrequent 00:40:39.630 --> 00:40:40.290 user-- 00:40:40.290 --> 00:40:43.490 so many things that are very useful for planning. 00:40:43.490 --> 00:40:46.060 And we'll get to play with some of these later in the course. 00:40:46.060 --> 00:40:49.750 And then, there's Automatic Passenger Counters, APC. 00:40:49.750 --> 00:40:54.880 So as more and motor systems switch to automatic data 00:40:54.880 --> 00:40:57.940 collection, we still use some manual data collection, 00:40:57.940 --> 00:41:01.000 but not in the traditional sense. 00:41:01.000 --> 00:41:02.920 Now, we reserve those resources for things 00:41:02.920 --> 00:41:07.180 like surveys about social demographics and other things. 00:41:07.180 --> 00:41:10.640 And we also carry out web-based surveys, 00:41:10.640 --> 00:41:12.640 which would have some biases. 00:41:12.640 --> 00:41:16.260 But if people registered their cards, 00:41:16.260 --> 00:41:18.010 and you have email accounts, you can maybe 00:41:18.010 --> 00:41:21.730 send a mass email to everyone and carry out surveys. 00:41:21.730 --> 00:41:23.110 The MBTA does that. 00:41:23.110 --> 00:41:25.090 Maybe some of you are in the panel 00:41:25.090 --> 00:41:27.670 of people who are e-mailed every now and then. 00:41:27.670 --> 00:41:29.370 Is anybody in that panel? 00:41:29.370 --> 00:41:30.350 No hands. 00:41:30.350 --> 00:41:31.410 I'm in that panel. 00:41:31.410 --> 00:41:35.006 But I know somebody must be. 00:41:35.006 --> 00:41:37.630 So yeah, they send an email, and they ask about your last ride. 00:41:37.630 --> 00:41:39.370 And they say, where did you start from? 00:41:39.370 --> 00:41:41.350 What were you doing this trip for? 00:41:41.350 --> 00:41:43.900 How long did you have to walk? 00:41:43.900 --> 00:41:45.450 Are you happy with the system? 00:41:45.450 --> 00:41:47.130 Was your bus on time? 00:41:47.130 --> 00:41:48.130 Yeah, things like that-- 00:41:48.130 --> 00:41:51.000 how satisfied are you? 00:41:51.000 --> 00:41:53.200 It's a survey with qualitative questions 00:41:53.200 --> 00:41:55.450 that you couldn't collect automatically. 00:41:55.450 --> 00:41:57.850 It's [INAUDIBLE] seeing things about your experience 00:41:57.850 --> 00:42:03.370 outside of the bus, which there are no sensors for. 00:42:03.370 --> 00:42:05.170 All right, sampling strategies-- a bunch 00:42:05.170 --> 00:42:08.200 of different ones and the simplest one 00:42:08.200 --> 00:42:12.200 is called simple random sampling-- very, very simple. 00:42:12.200 --> 00:42:14.310 So when you have sample random sampling, 00:42:14.310 --> 00:42:16.060 what happens is that every trip, if you're 00:42:16.060 --> 00:42:18.850 looking at surveying trips, for things like how many people 00:42:18.850 --> 00:42:19.930 boarded this trip-- 00:42:19.930 --> 00:42:22.960 let's take that as an example. 00:42:22.960 --> 00:42:24.920 Then, if you're using simple random sampling, 00:42:24.920 --> 00:42:27.490 every trip has equal likelihood of being picked and being 00:42:27.490 --> 00:42:28.330 surveyed. 00:42:28.330 --> 00:42:33.610 So if you go through your process, 00:42:33.610 --> 00:42:35.560 and you determine that you need to observe 100 00:42:35.560 --> 00:42:38.550 trips to get an average reliably. 00:42:38.550 --> 00:42:42.380 And you're going to use that to plan something, 00:42:42.380 --> 00:42:44.450 then you need to look at 100 trips. 00:42:44.450 --> 00:42:46.270 So if you use simple random sampling, 00:42:46.270 --> 00:42:50.020 you take your schedule, and you randomly pick 100 trips. 00:42:50.020 --> 00:42:51.190 And that's your sample. 00:42:51.190 --> 00:42:53.860 Those are the ones that you send people out to collect data. 00:42:53.860 --> 00:42:56.450 Now, there's a little bit of a problem with that. 00:42:56.450 --> 00:42:57.880 It's not the most efficient method 00:42:57.880 --> 00:42:59.713 because if you're going to send someone out, 00:42:59.713 --> 00:43:03.340 and that person is going to be active, and require some time 00:43:03.340 --> 00:43:06.520 to get to the site and some time to return, then 00:43:06.520 --> 00:43:08.260 once they're out there, you want them 00:43:08.260 --> 00:43:10.240 to collect as much as they can. 00:43:10.240 --> 00:43:12.100 So that's not simple random sampling. 00:43:12.100 --> 00:43:14.600 That's cluster sampling. 00:43:14.600 --> 00:43:16.460 Before we get to that systematic sampling-- 00:43:16.460 --> 00:43:21.350 so typically, instead of picking randomly, we say, 00:43:21.350 --> 00:43:26.000 OK, we need to get 10% of the trips. 00:43:26.000 --> 00:43:30.290 So let's just make it such that we count. 00:43:30.290 --> 00:43:33.680 And maybe it's every five trips, we have to survey it. 00:43:33.680 --> 00:43:35.780 So now, it's evenly spaced. 00:43:35.780 --> 00:43:38.850 And this is useful for some things. 00:43:38.850 --> 00:43:41.180 One example is weekday, picking the weekday 00:43:41.180 --> 00:43:43.610 that you're going to survey on. 00:43:43.610 --> 00:43:47.340 So the technique that is often used is sample every six days. 00:43:47.340 --> 00:43:49.581 Why would that be? 00:43:49.581 --> 00:43:50.080 Yeah. 00:43:50.080 --> 00:43:53.000 So if you do it every seven, then you always have a Monday. 00:43:53.000 --> 00:43:54.655 And that's going to get some bias 00:43:54.655 --> 00:43:57.120 if Mondays happen to be low ridership days 00:43:57.120 --> 00:43:58.420 or high ridership days. 00:43:58.420 --> 00:44:01.630 So if do every sixth day over a year, 00:44:01.630 --> 00:44:04.390 you have a good sample of every week day. 00:44:04.390 --> 00:44:07.510 So that's an example of systematic sampling. 00:44:07.510 --> 00:44:11.830 But you still have that issue of it 00:44:11.830 --> 00:44:13.540 might not be the most efficient. 00:44:13.540 --> 00:44:17.740 Cluster sampling, sometimes it's more efficient 00:44:17.740 --> 00:44:20.110 once you send out a person to collect 00:44:20.110 --> 00:44:22.690 data to do as much as possible. 00:44:22.690 --> 00:44:24.760 And you survey a cluster. 00:44:24.760 --> 00:44:28.510 So one example is, if you're distributing surveys 00:44:28.510 --> 00:44:31.180 to passengers, and you need to distribute 100 surveys. 00:44:31.180 --> 00:44:35.071 If you do 100 simple random sample, 00:44:35.071 --> 00:44:37.570 then those people might be in different parts of the system. 00:44:37.570 --> 00:44:40.570 And one might be the first person 00:44:40.570 --> 00:44:43.000 you see getting off at South Station. 00:44:43.000 --> 00:44:44.920 And then another one by me might be 00:44:44.920 --> 00:44:48.700 the first person you see getting off at the Kendall station. 00:44:48.700 --> 00:44:50.270 So that's very inefficient. 00:44:50.270 --> 00:44:53.070 So a cluster might be everybody on board a bus, 00:44:53.070 --> 00:44:55.690 and that will get a bunch of people together. 00:44:55.690 --> 00:44:59.470 However, it's not as efficient statistically to do that. 00:44:59.470 --> 00:45:01.930 So you can't just add up to 100, and you're 00:45:01.930 --> 00:45:07.360 done because there might be some correlation within the people 00:45:07.360 --> 00:45:09.670 riding that vehicle that they will tend 00:45:09.670 --> 00:45:12.310 to answer in a similar way. 00:45:12.310 --> 00:45:14.410 So you might need to increase your sample size 00:45:14.410 --> 00:45:15.576 when you use this technique. 00:45:15.576 --> 00:45:19.830 But still, you might have a more efficient sampling plan. 00:45:19.830 --> 00:45:21.290 Then, there is the ratio estimation 00:45:21.290 --> 00:45:22.520 and conversion factors. 00:45:22.520 --> 00:45:24.560 We gave examples of this already. 00:45:24.560 --> 00:45:26.820 This is in the context of baseline phase 00:45:26.820 --> 00:45:28.770 and then monitoring phase. 00:45:28.770 --> 00:45:31.930 So you start out with a baseline phase. 00:45:31.930 --> 00:45:33.790 And in the baseline phase, you collect 00:45:33.790 --> 00:45:36.640 the thing you really want and something 00:45:36.640 --> 00:45:40.480 that is very easily collected with lower resources. 00:45:40.480 --> 00:45:42.850 And you make a model of the thing you really 00:45:42.850 --> 00:45:45.910 want as a function of the thing that 00:45:45.910 --> 00:45:47.920 is cheap and easy to collect. 00:45:47.920 --> 00:45:49.420 And then, on the monitoring phase, 00:45:49.420 --> 00:45:54.310 you only measure the thing that is cheap, and easy, and quick. 00:45:54.310 --> 00:45:57.890 And you then use the model to estimate what you really want. 00:45:57.890 --> 00:46:00.790 So converting AFC boarding to passenger miles, 00:46:00.790 --> 00:46:02.320 we give an example of that. 00:46:02.320 --> 00:46:04.090 We're converting loads at checkpoints 00:46:04.090 --> 00:46:05.840 to load somewhere else. 00:46:05.840 --> 00:46:07.840 So maybe only measure loads with a point 00:46:07.840 --> 00:46:09.640 checker at the peak load point. 00:46:09.640 --> 00:46:12.910 And you have some relationship to convert those loads 00:46:12.910 --> 00:46:18.702 to loads at other key transfer stations as an example. 00:46:18.702 --> 00:46:20.160 And then, the stratified sampling-- 00:46:20.160 --> 00:46:23.970 so one of the things that determines how big of a sample 00:46:23.970 --> 00:46:25.830 you need is the variability in the data 00:46:25.830 --> 00:46:26.910 that you're collecting. 00:46:26.910 --> 00:46:30.900 So correlation, when you're looking 00:46:30.900 --> 00:46:35.650 at a whole system with multiple routes or multiple segments-- 00:46:35.650 --> 00:46:37.690 maybe when you look at one route, 00:46:37.690 --> 00:46:42.550 there's some variability of running times. 00:46:42.550 --> 00:46:44.770 But they have a central tendency as well. 00:46:44.770 --> 00:46:46.420 And when you've got a second route, 00:46:46.420 --> 00:46:48.392 you have also some variability and 00:46:48.392 --> 00:46:49.600 a different central tendency. 00:46:49.600 --> 00:46:51.624 So you bunch all the data together, 00:46:51.624 --> 00:46:54.040 some of the variability across data points in our data set 00:46:54.040 --> 00:46:56.980 are going to be the inherent variability of each route. 00:46:56.980 --> 00:46:59.920 And some of it will be systematic-- the differences 00:46:59.920 --> 00:47:01.390 between both routes. 00:47:01.390 --> 00:47:03.340 So if you do a simple random sample, 00:47:03.340 --> 00:47:05.800 and you don't separate the systematic variability 00:47:05.800 --> 00:47:08.560 from the inherent variability, then you're 00:47:08.560 --> 00:47:10.650 going to get a wider variability. 00:47:10.650 --> 00:47:13.270 And you will require a bigger sample size. 00:47:13.270 --> 00:47:14.950 Stratified sampling is an approach 00:47:14.950 --> 00:47:18.790 where you determine sample sizes for each of these separately. 00:47:18.790 --> 00:47:21.790 And it's more efficient if you do it well 00:47:21.790 --> 00:47:25.270 because you eliminate the need, or you at least 00:47:25.270 --> 00:47:28.600 reduce the need, to collect data for the sake 00:47:28.600 --> 00:47:32.380 of the systematic differences between different parts 00:47:32.380 --> 00:47:35.090 of the system. 00:47:35.090 --> 00:47:36.450 Any questions on these methods? 00:47:39.614 --> 00:47:41.066 Yes. 00:47:41.066 --> 00:47:42.518 AUDIENCE: [INAUDIBLE] 00:47:45.034 --> 00:47:46.450 GABRIEL SANCHEZ-MARTINEZ: Yeah, so 00:47:46.450 --> 00:47:47.860 let's maybe pick another example. 00:47:55.330 --> 00:48:01.130 Let's say that you're looking at the proportion of passengers 00:48:01.130 --> 00:48:04.070 in a bus who are students. 00:48:04.070 --> 00:48:05.660 And you're distributing a survey. 00:48:05.660 --> 00:48:11.800 And they tell you whether they're students or not. 00:48:11.800 --> 00:48:13.820 And you want this for the whole system 00:48:13.820 --> 00:48:16.830 or for at least a group of routes. 00:48:16.830 --> 00:48:19.900 And it tends to be that some routes don't serve universities 00:48:19.900 --> 00:48:20.900 and don't serve schools. 00:48:20.900 --> 00:48:24.020 So they have a lower proportion of people. 00:48:24.020 --> 00:48:26.690 And then, some routes that do go through universities, 00:48:26.690 --> 00:48:28.860 and they have a higher proportion of students. 00:48:28.860 --> 00:48:33.290 So if you just want the system-wide proportion 00:48:33.290 --> 00:48:36.890 of people who are students, and you join all these data points 00:48:36.890 --> 00:48:39.320 together, there's going to be a lot of variability 00:48:39.320 --> 00:48:41.630 in what proportion that is across every trip 00:48:41.630 --> 00:48:44.930 that you survey, correct? 00:48:44.930 --> 00:48:49.610 So in some sense, it will indicate 00:48:49.610 --> 00:48:51.290 that because of that variability, 00:48:51.290 --> 00:48:55.260 you're going to need a higher sampling size. 00:48:55.260 --> 00:48:57.830 You're going to have to survey more trips 00:48:57.830 --> 00:49:02.810 to get at your desired accuracy level and tolerance. 00:49:02.810 --> 00:49:06.080 But now, if you say no, I'm going to split routes in two, 00:49:06.080 --> 00:49:07.100 into two stratas. 00:49:07.100 --> 00:49:11.060 One is the routes that serve the universities. 00:49:11.060 --> 00:49:16.700 And these tend to have around 50% proportion. 00:49:16.700 --> 00:49:19.610 And then, there's the routes that don't serve universities. 00:49:19.610 --> 00:49:23.180 And these tend to have proportions near 0. 00:49:23.180 --> 00:49:27.260 So if you're in your 0, you might require a lower sample 00:49:27.260 --> 00:49:28.700 size to cover those. 00:49:28.700 --> 00:49:30.410 And you can just very efficiently 00:49:30.410 --> 00:49:32.480 cover most of your bus routes that way. 00:49:32.480 --> 00:49:35.030 And then, focus your efforts on just the ones 00:49:35.030 --> 00:49:37.160 that have higher proportion. 00:49:37.160 --> 00:49:39.980 And you achieved your system-level tolerance 00:49:39.980 --> 00:49:44.990 requirements with much fewer, with by far fewer resources 00:49:44.990 --> 00:49:47.069 required to collect the data. 00:49:47.069 --> 00:49:48.360 Does that answer your question? 00:49:48.360 --> 00:49:48.942 Yeah. 00:49:48.942 --> 00:49:50.298 AUDIENCE: [INAUDIBLE] 00:49:52.260 --> 00:49:54.510 GABRIEL SANCHEZ-MARTINEZ: So what he meant by inherent 00:49:54.510 --> 00:49:57.600 is that within each bus route or within each strata, 00:49:57.600 --> 00:49:59.130 there will be some variability. 00:49:59.130 --> 00:50:02.130 Even within the trips that are serving universities, 00:50:02.130 --> 00:50:04.530 every trip might have a different proportion. 00:50:04.530 --> 00:50:07.120 So there's going to be a little bit of variability in that. 00:50:07.120 --> 00:50:10.600 But if you mix that with trips that are not serving students, 00:50:10.600 --> 00:50:12.992 then you pull all that data together. 00:50:12.992 --> 00:50:15.450 Then, it's going to look like the variance of that data set 00:50:15.450 --> 00:50:16.170 is much higher. 00:50:20.950 --> 00:50:23.200 All right, so we've tossed these terms 00:50:23.200 --> 00:50:25.430 around-- tolerance, confidence, level accuracy. 00:50:25.430 --> 00:50:27.996 So let's define them more precisely. 00:50:27.996 --> 00:50:29.620 Accuracy-- when we talk about accuracy, 00:50:29.620 --> 00:50:31.960 that has two dimensions. 00:50:31.960 --> 00:50:36.070 So somebody might say, the average boardings per trip 00:50:36.070 --> 00:50:38.032 is 33.1. 00:50:38.032 --> 00:50:39.490 And then, the question that follows 00:50:39.490 --> 00:50:42.070 is, do you mean exactly 33.1? 00:50:42.070 --> 00:50:43.570 How certain are you of that? 00:50:43.570 --> 00:50:45.100 And how accurate is that? 00:50:45.100 --> 00:50:48.970 So when we talk about tolerance, there's relative tolerance, 00:50:48.970 --> 00:50:50.860 and there's absolute tolerance. 00:50:50.860 --> 00:50:52.750 Relative tolerance is expressed in terms 00:50:52.750 --> 00:50:57.760 of a percent of the amount you were collecting or a fraction. 00:50:57.760 --> 00:51:01.660 So you might say mean boardings per trip is 33.1, 00:51:01.660 --> 00:51:03.170 plus or minus 10%. 00:51:03.170 --> 00:51:05.710 And that's the 10% of 33.1. 00:51:05.710 --> 00:51:07.876 That's why it's relative tolerance. 00:51:07.876 --> 00:51:09.250 Then, there's absolute tolerance. 00:51:09.250 --> 00:51:14.240 So mean boarding per trip is 33.1, plus or minus 3.3. 00:51:14.240 --> 00:51:17.630 Now, in this case, these two are equivalent. 00:51:17.630 --> 00:51:20.810 3.3 in absolute terms is 10% of 33.1. 00:51:20.810 --> 00:51:23.600 But this was expressed in absolute terms, 00:51:23.600 --> 00:51:25.820 and the previous one was expressed in relative terms. 00:51:28.766 --> 00:51:32.130 So don't always assume that if you see a percent, 00:51:32.130 --> 00:51:35.190 it's relative because if what you're measuring is in itself 00:51:35.190 --> 00:51:38.850 a percent, unless you're using a percent of a percent, 00:51:38.850 --> 00:51:39.930 then it's absolute. 00:51:39.930 --> 00:51:41.940 So here's an example. 00:51:41.940 --> 00:51:46.740 Mean percentage of students is 23%, plus or minus 5%. 00:51:46.740 --> 00:51:49.785 That's absolute because it's 5%, not 5% of 23%. 00:51:54.660 --> 00:51:57.480 First, we talked about, is that exactly 33.1? 00:51:57.480 --> 00:52:00.010 Or is it something different from 33.1? 00:52:00.010 --> 00:52:02.460 Then, the second question is, how sure are you, 00:52:02.460 --> 00:52:06.310 how confident are you that the number you give, 00:52:06.310 --> 00:52:12.320 plus or minus the tolerance you give, is the right answer? 00:52:12.320 --> 00:52:15.400 So now, you say I'm 95% confident 00:52:15.400 --> 00:52:18.355 that the mean boardings per trip is 33.1, plus or minus 10%. 00:52:18.355 --> 00:52:20.347 So now, you combine the tolerance 00:52:20.347 --> 00:52:21.430 with the confidence level. 00:52:21.430 --> 00:52:24.170 And that's the full expression of your accuracy. 00:52:24.170 --> 00:52:27.740 And that's what you need when we look at the data collection. 00:52:27.740 --> 00:52:30.800 So you have two different things that you could play with. 00:52:30.800 --> 00:52:33.860 And what happens typically is that you choose 00:52:33.860 --> 00:52:35.210 a high confidence level-- 00:52:35.210 --> 00:52:38.150 90%, 95 percent are typical. 00:52:38.150 --> 00:52:39.830 And then, you hold that fixed. 00:52:39.830 --> 00:52:42.830 And you calculate what level of accuracy you need. 00:52:42.830 --> 00:52:45.020 Or rather, you decide what level of accuracy 00:52:45.020 --> 00:52:48.110 you need, depending on the question you want to answer, 00:52:48.110 --> 00:52:51.560 and the impact it could have on the system. 00:52:51.560 --> 00:52:54.350 So if you're looking to [INAUDIBLE] something 00:52:54.350 --> 00:53:01.850 that will have very significant effects on the service plan 00:53:01.850 --> 00:53:04.070 or maybe on investment in the system, 00:53:04.070 --> 00:53:07.430 then you might need a higher accuracy. 00:53:07.430 --> 00:53:10.597 But if you're collecting data just for reporting, 00:53:10.597 --> 00:53:11.930 maybe it doesn't matter as much. 00:53:11.930 --> 00:53:15.830 And you don't need to spend as much money on data collection. 00:53:15.830 --> 00:53:20.540 So as an example here, the National Transit Database-- 00:53:20.540 --> 00:53:23.150 NTD, we call it NTD-- 00:53:23.150 --> 00:53:26.150 for annual boardings and passenger miles, it says, 00:53:26.150 --> 00:53:27.740 you should collect data to achieve 00:53:27.740 --> 00:53:31.890 an accuracy of 10%, relative tolerance at 95% confidence 00:53:31.890 --> 00:53:33.250 level. 00:53:33.250 --> 00:53:36.090 You need both. 00:53:36.090 --> 00:53:38.340 So take home message about this. 00:53:38.340 --> 00:53:40.630 The other thing, the t distribution-- 00:53:40.630 --> 00:53:43.920 so this is a probability distribution that 00:53:43.920 --> 00:53:44.960 is bell-shaped. 00:53:44.960 --> 00:53:47.490 It kind of looks like the normal distribution. 00:53:47.490 --> 00:53:49.440 And it approaches the normal distribution 00:53:49.440 --> 00:53:52.330 as the sample size gets very large. 00:53:52.330 --> 00:53:54.960 This is the distribution that arises naturally 00:53:54.960 --> 00:53:58.110 when you're estimating the mean of a population that 00:53:58.110 --> 00:54:01.950 is normally distributed with unknown mean and variance 00:54:01.950 --> 00:54:04.380 and some known sample size. 00:54:04.380 --> 00:54:08.870 So to the right here, we have your equations 00:54:08.870 --> 00:54:11.990 that I'm sure you've seen before for sample mean, sample 00:54:11.990 --> 00:54:13.880 variance. 00:54:13.880 --> 00:54:15.740 And I guess, what's important to think 00:54:15.740 --> 00:54:18.470 about is that the distribution of what 00:54:18.470 --> 00:54:20.220 you're collecting-- for example, you 00:54:20.220 --> 00:54:23.630 might be collecting data on a number of people boarding route 00:54:23.630 --> 00:54:25.100 1. 00:54:25.100 --> 00:54:29.390 So that might have some distribution. 00:54:29.390 --> 00:54:31.440 As you collect more and more data, 00:54:31.440 --> 00:54:36.350 so as you survey more and more trips, 00:54:36.350 --> 00:54:40.700 the distribution of how many people board each trip 00:54:40.700 --> 00:54:43.400 does not necessarily have to be normal. 00:54:43.400 --> 00:54:45.980 But it turns out from the Central Limit Theorem 00:54:45.980 --> 00:54:52.990 and other laws and properties of statistics and probability 00:54:52.990 --> 00:54:54.920 that the distribution of the estimator-- 00:54:54.920 --> 00:54:58.570 so the distribution of the mean that you calculate based 00:54:58.570 --> 00:55:00.040 on that sample that you collected-- 00:55:00.040 --> 00:55:03.380 is normally distributed as the sample size increases. 00:55:03.380 --> 00:55:06.402 So if you have a lower sample size, 00:55:06.402 --> 00:55:08.110 instead of using the normal distribution, 00:55:08.110 --> 00:55:10.650 use t distribution. 00:55:10.650 --> 00:55:12.730 Sometimes, we call that a student, the t student 00:55:12.730 --> 00:55:13.780 distribution. 00:55:13.780 --> 00:55:20.440 And this distribution gets wider as the variability increases 00:55:20.440 --> 00:55:23.310 and as the sample size gets smaller. 00:55:23.310 --> 00:55:26.090 It has a property called degrees of freedom, 00:55:26.090 --> 00:55:28.360 which is sample size minus 1. 00:55:28.360 --> 00:55:31.294 And you can see from this chart right here when 00:55:31.294 --> 00:55:32.710 you have degrees of freedom equals 00:55:32.710 --> 00:55:35.540 1, which means you collected two data points, 00:55:35.540 --> 00:55:38.870 it's wider than when V approaches infinity. 00:55:38.870 --> 00:55:42.610 And what you have in black here, the thinnest and least variable 00:55:42.610 --> 00:55:46.520 of these, is essentially a normal distribution. 00:55:46.520 --> 00:55:48.990 And this is the distribution not of what you collected. 00:55:48.990 --> 00:55:52.540 It's not the distribution of the number 00:55:52.540 --> 00:55:54.250 of people who boarded route 1. 00:55:54.250 --> 00:55:58.690 It's the distribution of the mean that you estimate. 00:55:58.690 --> 00:55:59.860 AUDIENCE: [INAUDIBLE] 00:55:59.860 --> 00:56:00.550 GABRIEL SANCHEZ-MARTINEZ: Exactly, it's 00:56:00.550 --> 00:56:02.420 a sampling distribution of the mean. 00:56:02.420 --> 00:56:05.980 And if you were to repeat that experiment with the same number 00:56:05.980 --> 00:56:08.680 of trips but different number of trips, 00:56:08.680 --> 00:56:11.320 you might get a slightly different mean. 00:56:11.320 --> 00:56:14.110 So if you were to repeat that many, many times, 00:56:14.110 --> 00:56:19.145 the distribution of those means would be shaped in this manner. 00:56:19.145 --> 00:56:20.020 AUDIENCE: [INAUDIBLE] 00:56:20.020 --> 00:56:22.519 GABRIEL SANCHEZ-MARTINEZ: Yeah, well, student t distributed. 00:56:22.519 --> 00:56:26.700 And as sample size increases to infinity, normally distributed. 00:56:26.700 --> 00:56:27.200 Harry. 00:56:27.200 --> 00:56:32.009 AUDIENCE: So just for V equals 5, I think you [INAUDIBLE].. 00:56:32.009 --> 00:56:33.175 GABRIEL SANCHEZ-MARTINEZ: 4. 00:56:33.175 --> 00:56:33.620 AUDIENCE: 4. 00:56:33.620 --> 00:56:34.460 GABRIEL SANCHEZ-MARTINEZ: Sorry, 6. 00:56:34.460 --> 00:56:35.308 6. 00:56:35.308 --> 00:56:36.955 AUDIENCE: Approximately 5 [INAUDIBLE].. 00:56:36.955 --> 00:56:38.330 GABRIEL SANCHEZ-MARTINEZ: Yes, 6. 00:56:38.330 --> 00:56:39.280 Yeah. 00:56:39.280 --> 00:56:41.950 I mispoke. 00:56:41.950 --> 00:56:43.940 [INAUDIBLE] 00:56:43.940 --> 00:56:47.340 AUDIENCE: When there's a sample variance, sigma x squared 00:56:47.340 --> 00:56:48.320 equals roughly. 00:56:48.320 --> 00:56:50.250 Is that not supposed to be an equals? 00:56:50.250 --> 00:56:52.890 Is that not the way the sample variances define? 00:56:52.890 --> 00:56:56.104 Because I thought it's the-- 00:56:56.104 --> 00:56:57.645 GABRIEL SANCHEZ-MARTINEZ: So-- --it's 00:56:57.645 --> 00:56:59.103 below the variance of distribution. 00:56:59.103 --> 00:57:02.110 But that's roughly [INAUDIBLE]. 00:57:02.110 --> 00:57:05.380 AUDIENCE: Yeah, I guess the issue is that you 00:57:05.380 --> 00:57:10.060 don't know the true mean. 00:57:10.060 --> 00:57:14.530 So you're using an estimate to calculate the sample variance. 00:57:14.530 --> 00:57:17.517 And therefore, it's almost, almost the sample variance. 00:57:17.517 --> 00:57:18.850 GABRIEL SANCHEZ-MARTINEZ: Right. 00:57:18.850 --> 00:57:19.782 But I thought-- 00:57:19.782 --> 00:57:21.240 AUDIENCE: You're using an estimator 00:57:21.240 --> 00:57:23.340 to do the-- that's what you have to do. 00:57:23.340 --> 00:57:24.700 [INTERPOSING VOICES] 00:57:24.700 --> 00:57:26.390 AUDIENCE: He's incorporating the fact 00:57:26.390 --> 00:57:29.350 we're dividing by n minus 1 rather dividing by [INAUDIBLE].. 00:57:29.350 --> 00:57:31.225 GABRIEL SANCHEZ-MARTINEZ: No, so n minus 1, 00:57:31.225 --> 00:57:34.450 that has to do with the degrees of freedom issue. 00:57:34.450 --> 00:57:38.750 And that's to go from population variance to sample variance. 00:57:38.750 --> 00:57:40.630 But the other thing that happens is 00:57:40.630 --> 00:57:43.760 that if you're doing the population, 00:57:43.760 --> 00:57:46.200 then you know exactly what your mean is. 00:57:46.200 --> 00:57:47.295 It's exact, right? 00:57:47.295 --> 00:57:47.920 AUDIENCE: Yeah. 00:57:47.920 --> 00:57:49.920 GABRIEL SANCHEZ-MARTINEZ: And then in that case, 00:57:49.920 --> 00:57:52.500 you would know what the exact variances is as well. 00:57:52.500 --> 00:57:53.080 Yeah. 00:57:53.080 --> 00:57:55.900 So the n minus 1 is just to remove 00:57:55.900 --> 00:57:59.700 a bias that would arise from collecting only a sample. 00:57:59.700 --> 00:58:01.460 AUDIENCE: But here for example, you 00:58:01.460 --> 00:58:03.960 can say this is equals to [INAUDIBLE].. 00:58:03.960 --> 00:58:04.960 GABRIEL SANCHEZ-MARTINEZ: Yeah, yeah, yeah, yeah. 00:58:04.960 --> 00:58:05.792 AUDIENCE: You're working with the sample 00:58:05.792 --> 00:58:07.890 to know it would be an approximate [INAUDIBLE].. 00:58:07.890 --> 00:58:09.310 GABRIEL SANCHEZ-MARTINEZ: Yeah, in practice equal 2. 00:58:09.310 --> 00:58:11.270 AUDIENCE: As your sample distribution 00:58:11.270 --> 00:58:13.377 increases, then obviously, your sample increases-- 00:58:13.377 --> 00:58:14.210 [INTERPOSING VOICES] 00:58:14.210 --> 00:58:14.920 GABRIEL SANCHEZ-MARTINEZ: And therefore, this 00:58:14.920 --> 00:58:16.030 becomes more and more accurate. 00:58:16.030 --> 00:58:16.660 AUDIENCE: [INAUDIBLE] 00:58:16.660 --> 00:58:17.080 GABRIEL SANCHEZ-MARTINEZ: Exactly. 00:58:17.080 --> 00:58:18.640 AUDIENCE: It should be approaching more [INAUDIBLE].. 00:58:18.640 --> 00:58:19.180 GABRIEL SANCHEZ-MARTINEZ: Yeah, so I 00:58:19.180 --> 00:58:20.620 guess what's important to realize 00:58:20.620 --> 00:58:27.430 is that this is an estimate of the population variance, which 00:58:27.430 --> 00:58:30.260 in itself uses another estimate. 00:58:30.260 --> 00:58:32.200 And I guess, that's why that's there. 00:58:32.200 --> 00:58:33.530 But it's a very small detail. 00:58:33.530 --> 00:58:37.496 I didn't mean to distract you. 00:58:37.496 --> 00:58:42.046 AUDIENCE: So for the n, is it the sum of all the different 00:58:42.046 --> 00:58:43.730 samples of [INAUDIBLE] or is it just-- 00:58:43.730 --> 00:58:44.070 [INTERPOSING VOICES] 00:58:44.070 --> 00:58:45.630 GABRIEL SANCHEZ-MARTINEZ: So you don't ever 00:58:45.630 --> 00:58:47.160 repeat the experiment like this. 00:58:47.160 --> 00:58:49.800 This is more of a theoretical explanation 00:58:49.800 --> 00:58:52.420 to why there is a distribution to the mean, 00:58:52.420 --> 00:58:53.850 even though you only have one. 00:58:53.850 --> 00:58:55.380 You only have one mean, right? 00:58:55.380 --> 00:58:57.340 Because you're going to collect data. 00:58:57.340 --> 00:58:59.100 And once you finish collecting data, 00:58:59.100 --> 00:59:01.680 you're going to calculate the mean of all that data. 00:59:01.680 --> 00:59:04.020 So you only have one mean. 00:59:04.020 --> 00:59:08.160 If you were hypothetically to repeat that experiment, 00:59:08.160 --> 00:59:10.656 and you calculated separate means for each one, 00:59:10.656 --> 00:59:12.030 then you would get a distribution 00:59:12.030 --> 00:59:14.220 that would look like this. 00:59:14.220 --> 00:59:17.100 In practice, you would just increase your sample size 00:59:17.100 --> 00:59:21.554 and still compute one mean, which would be more accurate. 00:59:21.554 --> 00:59:22.054 Yeah. 00:59:24.910 --> 00:59:27.010 OK, let's move on. 00:59:27.010 --> 00:59:28.629 So tolerance and confidence level-- 00:59:28.629 --> 00:59:29.920 so we have these distributions. 00:59:29.920 --> 00:59:33.760 These are the distributions of the statistics, 00:59:33.760 --> 00:59:35.310 of the mean in this case. 00:59:35.310 --> 00:59:36.640 They are bell-shaped. 00:59:36.640 --> 00:59:41.977 As your sample size increases, the degrees of freedom goes up. 00:59:41.977 --> 00:59:43.060 And your accuracy goes up. 00:59:43.060 --> 00:59:45.790 And the variance of that statistic distribution 00:59:45.790 --> 00:59:46.370 decreases. 00:59:46.370 --> 00:59:47.770 So it gets thinner. 00:59:47.770 --> 00:59:52.240 So here in red, you have a distribution with a smaller 00:59:52.240 --> 00:59:55.570 sample, and therefore, less accuracy or less confidence 00:59:55.570 --> 00:59:56.590 would look like. 00:59:56.590 --> 00:59:59.260 And then as you increase your sample size, 00:59:59.260 --> 01:00:04.120 you see that it becomes more peaky. 01:00:04.120 --> 01:00:09.130 So when we talk about tolerance, and let's 01:00:09.130 --> 01:00:11.170 come back to the concept of absolute tolerance 01:00:11.170 --> 01:00:13.330 in particular, we're talking about the distance 01:00:13.330 --> 01:00:16.000 between the center of that distribution, which 01:00:16.000 --> 01:00:20.020 is a symmetrical distribution, and some limit. 01:00:20.020 --> 01:00:24.460 So we're saying, if you have a tolerance of plus/minus 10. 01:00:24.460 --> 01:00:28.390 Then, you're going to measure 10, say 10 boardings, 01:00:28.390 --> 01:00:32.270 from the center to the right and from the center to the left. 01:00:32.270 --> 01:00:35.590 And that's your absolute tolerance. 01:00:35.590 --> 01:00:38.410 So when you calculate absolute tolerance, 01:00:38.410 --> 01:00:40.750 you can express that tolerance as a function 01:00:40.750 --> 01:00:46.210 of the variance and/or the standard deviation, 01:00:46.210 --> 01:00:48.790 rather of your mean. 01:00:48.790 --> 01:00:52.750 So instead of saying 10, you could say 2 times 01:00:52.750 --> 01:00:57.010 the standard deviation of that distribution using the equation 01:00:57.010 --> 01:00:58.496 that we just calculated. 01:00:58.496 --> 01:00:59.620 And that's very convenient. 01:00:59.620 --> 01:01:02.100 Why would we do that? 01:01:02.100 --> 01:01:04.170 Why would I want to complicate things that way? 01:01:07.068 --> 01:01:09.075 AUDIENCE: [? Outside ?] [? of ?] a cumulative 01:01:09.075 --> 01:01:10.950 GABRIEL SANCHEZ-MARTINEZ: No, I mean, there's 01:01:10.950 --> 01:01:12.690 a mathematical convenience here. 01:01:12.690 --> 01:01:15.420 What is this a function of? 01:01:15.420 --> 01:01:18.510 It's a function of the standard deviation 01:01:18.510 --> 01:01:22.490 of the thing you were collecting and your sample size, right? 01:01:22.490 --> 01:01:23.670 And what do we want to do? 01:01:23.670 --> 01:01:25.470 We want to determine how many things we 01:01:25.470 --> 01:01:26.670 need to collect, right? 01:01:26.670 --> 01:01:27.570 So here we go-- 01:01:27.570 --> 01:01:28.650 we have n. 01:01:28.650 --> 01:01:32.280 And now we can solve for n, we have the sample size 01:01:32.280 --> 01:01:34.380 that we require for a given tolerance. 01:01:34.380 --> 01:01:37.560 So we're going to decide what the tolerance is 01:01:37.560 --> 01:01:41.100 and calculate sample size, a minimum required sample size. 01:01:41.100 --> 01:01:44.030 You can always collect more data. 01:01:44.030 --> 01:01:44.810 All right. 01:01:44.810 --> 01:01:46.790 So again, to review, this is the same equation 01:01:46.790 --> 01:01:48.200 I had in the last slide. 01:01:48.200 --> 01:01:51.020 You have absolutely tolerance. 01:01:51.020 --> 01:01:54.740 You can express that as a multiplier 01:01:54.740 --> 01:01:59.270 times the standard deviation of the mean. 01:01:59.270 --> 01:02:02.330 And then you solve for n, and you get this equation 01:02:02.330 --> 01:02:03.260 right here. 01:02:03.260 --> 01:02:06.170 t is your tolerance and you can-- 01:02:06.170 --> 01:02:09.980 oh, sorry. t is the number of standard deviations 01:02:09.980 --> 01:02:11.690 from the mean. 01:02:11.690 --> 01:02:14.600 d is your tolerance, which you choose. 01:02:14.600 --> 01:02:17.090 And this is something that you know, or collect, 01:02:17.090 --> 01:02:18.410 or approximate. 01:02:18.410 --> 01:02:20.210 So these are all given. 01:02:20.210 --> 01:02:21.510 Where does t come from? 01:02:21.510 --> 01:02:24.050 Well, we said that we're going to use the t 01:02:24.050 --> 01:02:24.890 distribution, right? 01:02:24.890 --> 01:02:28.220 So the t distribution has a table-- 01:02:28.220 --> 01:02:30.230 or it has a certain shape, rather. 01:02:30.230 --> 01:02:32.870 And using Excel or looking up at some table, 01:02:32.870 --> 01:02:38.030 you can figure out what t is for two times 01:02:38.030 --> 01:02:40.890 the standard deviation from the center. 01:02:40.890 --> 01:02:43.820 So you can just plug it in from Excel or from-- 01:02:43.820 --> 01:02:46.040 it's a property of the distribution, essentially. 01:02:46.040 --> 01:02:48.890 Once you pick a confidence interval, you know t. 01:02:48.890 --> 01:02:51.470 If you want to go to 95, it's a certain value. 01:02:51.470 --> 01:02:54.320 If you want to go to 90, it's a different value. 01:02:54.320 --> 01:02:55.460 OK. 01:02:55.460 --> 01:02:57.050 When we look at relative tolerance, 01:02:57.050 --> 01:03:00.740 relative tolerance is just absolute tolerance 01:03:00.740 --> 01:03:03.890 divided by the mean that you are collecting, correct? 01:03:03.890 --> 01:03:06.890 Because instead of saying plus or minus 10 boardings, 01:03:06.890 --> 01:03:09.380 we're saying plus or minus 5% of the mean. 01:03:09.380 --> 01:03:13.730 So we just take absolute tolerance and divide by x bar, 01:03:13.730 --> 01:03:17.240 the sampling mean, the sample mean. 01:03:17.240 --> 01:03:19.040 And we solve for n again. 01:03:19.040 --> 01:03:23.690 So what we have now, it looks very similar as to the question 01:03:23.690 --> 01:03:24.570 right here. 01:03:24.570 --> 01:03:27.660 But now we have the mean and the denominator. 01:03:27.660 --> 01:03:30.860 OK, this quantity, standard deviation 01:03:30.860 --> 01:03:34.040 divided by mean, sample standard deviation divided 01:03:34.040 --> 01:03:38.200 by sampling mean, is called the coefficient of variation. 01:03:38.200 --> 01:03:40.930 And there's a convenience to this. 01:03:40.930 --> 01:03:44.192 And there's actually a reason why 01:03:44.192 --> 01:03:45.900 sometimes relative tolerance is preferred 01:03:45.900 --> 01:03:46.820 to absolute tolerance. 01:03:46.820 --> 01:03:48.361 It's because of this, because there's 01:03:48.361 --> 01:03:52.620 a mathematically convenient characteristic of property 01:03:52.620 --> 01:03:53.760 coming out of this-- 01:03:53.760 --> 01:03:57.270 that you don't need to know the standard deviation of what 01:03:57.270 --> 01:04:00.300 you're collecting to figure out your sample size. 01:04:00.300 --> 01:04:02.310 We're kind of running in circles here, right? 01:04:02.310 --> 01:04:04.101 We're saying that to determine sample size, 01:04:04.101 --> 01:04:05.829 you need to know the standard deviation. 01:04:05.829 --> 01:04:07.120 Well, I haven't collected data. 01:04:07.120 --> 01:04:09.009 So I don't know how variable the data is. 01:04:09.009 --> 01:04:09.800 So that's an issue. 01:04:09.800 --> 01:04:11.820 Now I have to estimate what that is. 01:04:11.820 --> 01:04:15.510 It tends to happen that the coefficient of variation 01:04:15.510 --> 01:04:19.230 is a more stable property than the variation in itself, 01:04:19.230 --> 01:04:22.410 than the variance or the standard deviation itself. 01:04:22.410 --> 01:04:26.670 So you're more likely to get away 01:04:26.670 --> 01:04:29.640 with using default values for the coefficient of variation 01:04:29.640 --> 01:04:34.260 than you are with assuming a specific standard deviation. 01:04:34.260 --> 01:04:37.480 AUDIENCE: It should be noted that it's unitless, coefficient 01:04:37.480 --> 01:04:38.410 of variation. 01:04:38.410 --> 01:04:40.326 GABRIEL SANCHEZ-MARTINEZ: Yes, it is unitless. 01:04:40.326 --> 01:04:41.980 Thank you. 01:04:41.980 --> 01:04:42.480 OK. 01:04:42.480 --> 01:04:45.210 So what happens is that relative tolerances are typically 01:04:45.210 --> 01:04:46.080 used for averages. 01:04:46.080 --> 01:04:47.310 So here's an example-- 01:04:47.310 --> 01:04:51.760 you measured 5720 boardings plus minus 5%. 01:04:51.760 --> 01:04:54.494 So if you were to get the absolute equivalent 01:04:54.494 --> 01:04:55.910 of the absolute tolerance of that. 01:04:55.910 --> 01:04:58.890 That would be 5% of 5720. 01:04:58.890 --> 01:05:01.180 That would be 286 passengers. 01:05:01.180 --> 01:05:03.600 That's a weird thing to report. 01:05:03.600 --> 01:05:06.000 5% is more understandable, right? 01:05:06.000 --> 01:05:07.630 And it kind of makes more sense. 01:05:07.630 --> 01:05:11.700 So that's what we want naturally, anyway. 01:05:11.700 --> 01:05:14.360 So as I said, the coefficient variation 01:05:14.360 --> 01:05:17.310 is typically easier to guess than the mean and the variance 01:05:17.310 --> 01:05:18.690 separately. 01:05:18.690 --> 01:05:20.820 So we use that. 01:05:20.820 --> 01:05:23.070 Here's an example using the t distribution, 01:05:23.070 --> 01:05:26.070 where the sample is not large enough 01:05:26.070 --> 01:05:30.280 to assume a normal distribution. 01:05:30.280 --> 01:05:33.550 So we say, let's have a relative tolerance of plus minus 5%, 01:05:33.550 --> 01:05:36.120 a confidence level of 95%, and a coefficient 01:05:36.120 --> 01:05:37.650 of variation of 0.3. 01:05:37.650 --> 01:05:39.660 So we start out assuming large sample, 01:05:39.660 --> 01:05:42.210 and therefore degrees of freedom is infinity. 01:05:42.210 --> 01:05:44.140 We can use the normal distribution. 01:05:44.140 --> 01:05:46.860 If we look at the normal distribution, 01:05:46.860 --> 01:05:52.920 with plus minus 5%, confidence level 95%, the t is 1.96. 01:05:52.920 --> 01:05:57.030 So we look that up on a table, or we use Excel norm dist, 01:05:57.030 --> 01:05:58.440 or-- yeah. 01:05:58.440 --> 01:06:02.110 t dist for t and norm dist for normal. 01:06:02.110 --> 01:06:04.860 We got 1.96. 01:06:04.860 --> 01:06:06.870 We plug in the relative tolerance, 01:06:06.870 --> 01:06:08.366 the 0.3-- we get 140. 01:06:08.366 --> 01:06:11.460 140 is not quite infinity, right? 01:06:11.460 --> 01:06:14.190 So if we look at 140 as a sample size, 01:06:14.190 --> 01:06:16.980 that would imply that all the degrees of freedom is 139. 01:06:16.980 --> 01:06:19.410 Now we go back and look at the t dist, 01:06:19.410 --> 01:06:23.730 and we change 1.96 to the value from the t distribution 01:06:23.730 --> 01:06:26.680 for that degree of freedoms. 01:06:26.680 --> 01:06:28.710 And we get 140.73. 01:06:28.710 --> 01:06:32.010 So you're sort of seeing that you were almost right. 01:06:32.010 --> 01:06:35.160 140 is very large. 01:06:35.160 --> 01:06:37.380 In practice, you would just round up a little bit 01:06:37.380 --> 01:06:40.800 and get a nice round number, and you would even play with this 01:06:40.800 --> 01:06:43.860 once you're looking at planning who you're going to send out 01:06:43.860 --> 01:06:45.780 and how many hours you're going to collect. 01:06:45.780 --> 01:06:48.974 You want to get at least 141, but if you're 01:06:48.974 --> 01:06:51.390 going to have people in units of eight hours, for example, 01:06:51.390 --> 01:06:54.560 or units of four hours, then you might as well finish the batch 01:06:54.560 --> 01:06:56.250 for four hours, the last one. 01:06:56.250 --> 01:07:00.500 Maybe you'll get 150, 160 from that. 01:07:00.500 --> 01:07:02.740 Here's an example of that equation 01:07:02.740 --> 01:07:08.260 with different assumptions of confidence and tolerance. 01:07:08.260 --> 01:07:11.320 And so we're using 90% confidence, 01:07:11.320 --> 01:07:15.410 and we're assuming a certain sample size here. 01:07:15.410 --> 01:07:19.000 So you can see that, as the tolerance decreases, which 01:07:19.000 --> 01:07:22.150 means that you require a greater accuracy 01:07:22.150 --> 01:07:25.060 for different coefficients of variation, 01:07:25.060 --> 01:07:26.670 the sample size can get really large. 01:07:26.670 --> 01:07:29.200 So if your data is not very variable, 01:07:29.200 --> 01:07:31.160 then you can sample just a few trips. 01:07:31.160 --> 01:07:33.490 And you know because they don't vary 01:07:33.490 --> 01:07:35.440 that much what the mean is. 01:07:35.440 --> 01:07:37.540 But if there's a lot of variability across strips, 01:07:37.540 --> 01:07:38.440 then you need more. 01:07:38.440 --> 01:07:43.630 So that's what you see as you go down the rows on this table. 01:07:43.630 --> 01:07:44.860 Here we have tolerance. 01:07:44.860 --> 01:07:51.850 If you only have to be 50% accurate, plus minus 50%, 01:07:51.850 --> 01:07:54.160 then you don't have to collect that much data. 01:07:54.160 --> 01:07:56.410 If you want to be more precise, and you 01:07:56.410 --> 01:08:00.860 want to say plus minus 5%, then you need a bigger sample size, 01:08:00.860 --> 01:08:01.870 right? 01:08:01.870 --> 01:08:03.720 OK. 01:08:03.720 --> 01:08:05.940 Proportions-- and the homework, actually, 01:08:05.940 --> 01:08:08.871 is based on proportions, so this is important. 01:08:08.871 --> 01:08:10.620 Consider something, a group of passengers, 01:08:10.620 --> 01:08:13.740 to estimate the proportion of passengers who are students. 01:08:13.740 --> 01:08:16.109 So from probability, when you are 01:08:16.109 --> 01:08:17.880 looking at an event that can either 01:08:17.880 --> 01:08:20.830 be 0 or 1, or black or white-- 01:08:20.830 --> 01:08:24.540 in this case, students or non-students-- 01:08:24.540 --> 01:08:27.240 there's a certain probability that that person is a student, 01:08:27.240 --> 01:08:27.739 right? 01:08:27.739 --> 01:08:29.850 And what you want to estimate is that probability 01:08:29.850 --> 01:08:31.920 or, in other words, what percent of the things 01:08:31.920 --> 01:08:34.290 you observe are students. 01:08:37.020 --> 01:08:40.229 So from the properties of the Bernoulli distribution, 01:08:40.229 --> 01:08:43.200 the variance is p times 1 minus p. 01:08:43.200 --> 01:08:47.160 So if everybody is a student, or nobody is a student, 01:08:47.160 --> 01:08:49.800 either way there's no variability, right? 01:08:49.800 --> 01:08:55.319 So you would have 1 times 1 minus 1, 1 times 0, 0-- no 01:08:55.319 --> 01:08:56.430 variability. 01:08:56.430 --> 01:08:59.609 Though at the peak variability, the highest variance 01:08:59.609 --> 01:09:02.910 of this distribution, is when 50% of your people 01:09:02.910 --> 01:09:08.340 are students, so 0.5 times 1 minus 0.5, 0.25. 01:09:08.340 --> 01:09:10.859 That's the highest variance, OK? 01:09:10.859 --> 01:09:12.792 So the tolerance is typically specified 01:09:12.792 --> 01:09:15.000 in absolute terms when you're estimating proportions, 01:09:15.000 --> 01:09:18.420 because the proportion is in itself a percent. 01:09:18.420 --> 01:09:22.470 So you use absolute tolerance. 01:09:22.470 --> 01:09:28.859 And you just substitute, essentially, this variance. 01:09:28.859 --> 01:09:31.710 You put in the variance of the Bernoulli distribution, 01:09:31.710 --> 01:09:33.300 which is p times 1 minus p. 01:09:33.300 --> 01:09:36.205 And that's how you get the sampling equation, sample size 01:09:36.205 --> 01:09:37.080 requirement equation. 01:09:41.950 --> 01:09:43.180 Here's a problem. 01:09:43.180 --> 01:09:47.899 We don't know in advance what the proportion will be, right? 01:09:47.899 --> 01:09:50.415 And we need that to know how many people we need to survey 01:09:50.415 --> 01:09:52.540 to figure out-- or how many trips we need to survey 01:09:52.540 --> 01:09:53.649 to figure out-- 01:09:53.649 --> 01:09:55.066 sorry, how many students we need-- 01:09:55.066 --> 01:09:56.440 how many riders we need to survey 01:09:56.440 --> 01:09:58.760 to figure out what the average number of students are. 01:09:58.760 --> 01:09:59.963 OK, so-- 01:09:59.963 --> 01:10:03.414 AUDIENCE: And it's also a [INAUDIBLE] p times 1 01:10:03.414 --> 01:10:05.248 minus p [INAUDIBLE] is a constrained number. 01:10:05.248 --> 01:10:07.455 GABRIEL SANCHEZ-MARTINEZ: It is a constrained number, 01:10:07.455 --> 01:10:09.417 and that's exactly where we're going. 01:10:09.417 --> 01:10:11.750 So we use something called absolute equivalent tolerance 01:10:11.750 --> 01:10:13.340 instead of absolute tolerance. 01:10:13.340 --> 01:10:15.950 We assume that p is 0.5-- 01:10:15.950 --> 01:10:18.090 that's the maximum it could be. 01:10:18.090 --> 01:10:20.750 So let's go ahead with a worst case scenario. 01:10:20.750 --> 01:10:22.830 And then what happens with p itself? 01:10:22.830 --> 01:10:27.260 Well, if your percent is high, then you 01:10:27.260 --> 01:10:29.960 can tolerate a bigger number, right? 01:10:29.960 --> 01:10:35.600 So if it's 32%, you're probably OK with plus minus 5%. 01:10:35.600 --> 01:10:39.320 If your average were 1.2, plus minus 5% 01:10:39.320 --> 01:10:40.970 is not that good, right? 01:10:40.970 --> 01:10:42.170 You need a higher-- 01:10:42.170 --> 01:10:46.220 you need a much stricter, tighter confidence 01:10:46.220 --> 01:10:47.700 interval for that. 01:10:47.700 --> 01:10:51.259 So probably not good to do plus minus 5% in that case. 01:10:51.259 --> 01:10:53.550 AUDIENCE: [? Well, do ?] [? you mean ?] you have a plus 01:10:53.550 --> 01:10:55.730 minus 5% absolutely percentage? 01:10:55.730 --> 01:10:56.040 GABRIEL SANCHEZ-MARTINEZ: Absolute, yeah. 01:10:56.040 --> 01:10:57.530 AUDIENCE: And you'd be going negative [INAUDIBLE] 01:10:57.530 --> 01:10:57.800 GABRIEL SANCHEZ-MARTINEZ: Negative, 01:10:57.800 --> 01:11:00.590 which is possible but difficult to interpret. 01:11:00.590 --> 01:11:04.320 AUDIENCE: Sorry, so this isn't actually 32% plus or minus 5% 01:11:04.320 --> 01:11:06.020 of 32 [INAUDIBLE] 01:11:06.020 --> 01:11:06.610 GABRIEL SANCHEZ-MARTINEZ: It is not-- yeah, 01:11:06.610 --> 01:11:09.110 it's absolute tolerance, not relative tolerance, right. 01:11:09.110 --> 01:11:12.500 So what's convenient about this is that these two factors work 01:11:12.500 --> 01:11:13.490 in opposite directions. 01:11:13.490 --> 01:11:19.490 So as you get bigger, as the proportion gets closer to 50%, 01:11:19.490 --> 01:11:20.690 the variance increases. 01:11:20.690 --> 01:11:23.150 So oh, well, we need a bigger sample. 01:11:23.150 --> 01:11:26.630 But your tolerance increases as well, 01:11:26.630 --> 01:11:28.670 so you don't need as big of a sample. 01:11:28.670 --> 01:11:30.050 And so it's convenient. 01:11:30.050 --> 01:11:33.500 And the practical solution is assume p is 0.5 01:11:33.500 --> 01:11:37.070 and work in terms of absolute equivalent tolerance. 01:11:37.070 --> 01:11:40.160 So you pick a tolerance under the assumption 01:11:40.160 --> 01:11:43.670 that our proportion is 50%. 01:11:43.670 --> 01:11:46.170 And here's what happens. 01:11:46.170 --> 01:11:48.800 Yeah, if the expected proportion is 50%, 01:11:48.800 --> 01:11:51.890 and you say plus minus 5 percent, what you would get 01:11:51.890 --> 01:11:56.520 is this 5%, if it turns out that p is 5%. 01:11:56.520 --> 01:12:01.400 But if it worked more to the extremes, like 5% or 95%, 01:12:01.400 --> 01:12:04.970 what you would actually achieve from having planned the survey, 01:12:04.970 --> 01:12:07.580 assuming 50%, is 2.2-- 01:12:07.580 --> 01:12:11.690 so much better, much more acceptable 01:12:11.690 --> 01:12:14.840 to say 5% plus minus 2.2%, right? 01:12:14.840 --> 01:12:16.370 So it works out. 01:12:16.370 --> 01:12:20.030 And there's a convenient equation 01:12:20.030 --> 01:12:22.640 if you assume a very large sample, or large enough sample, 01:12:22.640 --> 01:12:26.570 and you pick 95%, 0.25, which is the variance 01:12:26.570 --> 01:12:30.320 times the normal distribution t squared 01:12:30.320 --> 01:12:32.280 is 0.96, which is almost 1. 01:12:32.280 --> 01:12:33.530 So then you get this equation. 01:12:33.530 --> 01:12:35.654 You take 1, you divide it by the tolerance 01:12:35.654 --> 01:12:37.820 that you want, your equivalent tolerance, and that's 01:12:37.820 --> 01:12:38.940 your sample size. 01:12:38.940 --> 01:12:42.950 So it doesn't depend on anything about the data in itself. 01:12:42.950 --> 01:12:46.490 You just say if I want, on whatever I'm collecting, 01:12:46.490 --> 01:12:48.270 whatever proportion I'm collecting, 01:12:48.270 --> 01:12:51.620 a 5% absolute equivalent tolerance, 01:12:51.620 --> 01:12:57.190 then I need 400 surveys to be answered. 01:12:57.190 --> 01:12:58.296 Yeah? 01:12:58.296 --> 01:13:03.152 AUDIENCE: So this assumes a random-- 01:13:03.152 --> 01:13:05.110 GABRIEL SANCHEZ-MARTINEZ: Simple random sample. 01:13:05.110 --> 01:13:05.750 AUDIENCE: [INAUDIBLE] 01:13:05.750 --> 01:13:07.190 GABRIEL SANCHEZ-MARTINEZ: Yes, a simple random sample. 01:13:07.190 --> 01:13:08.648 So you would increase these numbers 01:13:08.648 --> 01:13:11.050 if you are using cluster sampling 01:13:11.050 --> 01:13:13.330 to account for correlation. 01:13:13.330 --> 01:13:16.830 You would have to increase them if you're giving people 01:13:16.830 --> 01:13:19.330 a survey, and not all of them answer the survey, because you 01:13:19.330 --> 01:13:22.240 need 400 surveys answered. 01:13:22.240 --> 01:13:24.610 So if only half of the people answer the survey, 01:13:24.610 --> 01:13:27.010 then you need to distribute 800 surveys. 01:13:27.010 --> 01:13:28.962 AUDIENCE: Do you recommend calculating also 01:13:28.962 --> 01:13:32.070 that the standard error after this so that [INAUDIBLE] 01:13:32.070 --> 01:13:32.570 make sure? 01:13:32.570 --> 01:13:33.530 GABRIEL SANCHEZ-MARTINEZ: Absolutely, yeah. 01:13:33.530 --> 01:13:35.810 You want to go back and check with the standard error 01:13:35.810 --> 01:13:38.330 and when your confidence interval is and see 01:13:38.330 --> 01:13:39.830 if you meet it or if you need to add 01:13:39.830 --> 01:13:41.570 a few days of data collection. 01:13:41.570 --> 01:13:42.360 AUDIENCE: Right. 01:13:42.360 --> 01:13:43.651 GABRIEL SANCHEZ-MARTINEZ: Yeah. 01:13:43.651 --> 01:13:48.740 OK, so with proportions, you need a very large sample size 01:13:48.740 --> 01:13:51.590 to estimate a proportion if you want accuracy. 01:13:51.590 --> 01:13:54.800 If you say absolutely equivalent intolerance of 4%, 01:13:54.800 --> 01:13:56.900 then you need 600. 01:13:56.900 --> 01:14:00.020 That's a big number, so it just gives you an idea of that. 01:14:00.020 --> 01:14:02.390 If you get greedy with the tolerance, 01:14:02.390 --> 01:14:08.580 you have to pay for the surveyors to go out. 01:14:08.580 --> 01:14:11.090 OK. 01:14:11.090 --> 01:14:14.510 So the process is you determine the needed sample size 01:14:14.510 --> 01:14:18.140 just with the discussion of the equations that we discussed. 01:14:18.140 --> 01:14:19.850 Then you multiply the sample sizes. 01:14:23.675 --> 01:14:25.550 If you're using stratified sampling or if you 01:14:25.550 --> 01:14:28.280 have questions that have multiple variables, 01:14:28.280 --> 01:14:30.920 you need to then make sure that you achieve that sample 01:14:30.920 --> 01:14:34.200 size for each combination of things that you're measuring. 01:14:34.200 --> 01:14:36.830 So if you're, for example, looking at not just 01:14:36.830 --> 01:14:42.880 boardings, but proportion of passengers that are car-owning, 01:14:42.880 --> 01:14:43.810 who are pleased. 01:14:43.810 --> 01:14:46.990 So you could just independently measure pleased, independently 01:14:46.990 --> 01:14:52.840 measure passengers who own a car. 01:14:52.840 --> 01:14:55.960 And you might have the tolerance you need on each one, 01:14:55.960 --> 01:14:57.910 but if you want the combination of that, 01:14:57.910 --> 01:14:59.650 now you need a higher sample, because you 01:14:59.650 --> 01:15:03.610 need that number for the combination of those things. 01:15:03.610 --> 01:15:05.230 Then there's a clustering effect, 01:15:05.230 --> 01:15:06.862 so a typical thing if you're doing 01:15:06.862 --> 01:15:08.820 the clustering of a whole vehicle of passengers 01:15:08.820 --> 01:15:12.190 is to multiply by 4. 01:15:12.190 --> 01:15:15.010 And then for things like OD matrices, the rule of thumb 01:15:15.010 --> 01:15:17.927 is 20 times the number of cells. 01:15:17.927 --> 01:15:18.760 What does that mean? 01:15:18.760 --> 01:15:20.554 That if your OD matrix is quite aggregate, 01:15:20.554 --> 01:15:21.970 and it's at the segment level-- so 01:15:21.970 --> 01:15:24.700 say you divide a root into two segments, 01:15:24.700 --> 01:15:27.190 then your OD matrix has four cells. 01:15:27.190 --> 01:15:30.310 Four cells times 20, that's how many people you have to survey. 01:15:30.310 --> 01:15:33.269 If you do error at the stop level, 01:15:33.269 --> 01:15:35.560 then you have many more stops and, therefore, many more 01:15:35.560 --> 01:15:39.465 cells and, therefore, a much higher sample size. 01:15:39.465 --> 01:15:41.090 If you have a response rate that is not 01:15:41.090 --> 01:15:43.360 100%, which is always the case, then you 01:15:43.360 --> 01:15:46.480 have to expand by 1 minus that in the reciprocal-- sorry, 1 01:15:46.480 --> 01:15:48.080 over that in the reciprocal. 01:15:48.080 --> 01:15:49.760 And then you get a very large number, 01:15:49.760 --> 01:15:51.860 and you say I don't have the budget for that. 01:15:51.860 --> 01:15:57.460 And you have to make tradeoffs and figure out what you can do. 01:15:57.460 --> 01:15:59.590 And maybe you have to-- 01:15:59.590 --> 01:16:01.750 maybe you can't collect this combination 01:16:01.750 --> 01:16:03.160 and know that accurately, right? 01:16:03.160 --> 01:16:07.500 So you revise your expectations. 01:16:07.500 --> 01:16:11.265 OK, with response rates, you are concerned 01:16:11.265 --> 01:16:12.640 with getting the correct answers. 01:16:12.640 --> 01:16:14.740 You also want to be getting a high response rate. 01:16:14.740 --> 01:16:17.281 If you don't get a high response rate, there might be a bias. 01:16:17.281 --> 01:16:19.730 So you have to worry about that. 01:16:19.730 --> 01:16:21.250 If you have low response rates, that 01:16:21.250 --> 01:16:23.000 means you need to distribute more surveys, 01:16:23.000 --> 01:16:24.190 and that costs money. 01:16:24.190 --> 01:16:26.240 And there's the bias that I just mentioned, 01:16:26.240 --> 01:16:29.980 so people who don't respond may not be responding for a reason. 01:16:29.980 --> 01:16:32.560 And then done that might bias your results. 01:16:32.560 --> 01:16:34.990 And that might make you decide something in planning 01:16:34.990 --> 01:16:38.570 that is not the right decision based on what actually happens. 01:16:38.570 --> 01:16:41.410 So we call that the non-response bias. 01:16:41.410 --> 01:16:43.099 OK, so what happens? 01:16:43.099 --> 01:16:44.890 People who don't respond might be different 01:16:44.890 --> 01:16:47.015 or might have responded differently to the question 01:16:47.015 --> 01:16:47.950 had they responded. 01:16:47.950 --> 01:16:50.120 So here's some examples. 01:16:50.120 --> 01:16:52.660 If you're surveying people who are standing, 01:16:52.660 --> 01:16:54.220 they are less comfortable. 01:16:54.220 --> 01:16:57.280 And maybe it's a crowded bus-- they are less comfortable. 01:16:57.280 --> 01:17:00.100 Or maybe they're getting off one of those stops that 01:17:00.100 --> 01:17:03.250 is coming up, so they are less likely to have the time 01:17:03.250 --> 01:17:05.020 to respond to your survey. 01:17:05.020 --> 01:17:07.570 People with low literacy, teenagers, 01:17:07.570 --> 01:17:10.420 people who don't speak the language, 01:17:10.420 --> 01:17:11.870 are less likely to respond. 01:17:11.870 --> 01:17:14.720 And they might have different travel patterns. 01:17:14.720 --> 01:17:16.710 So if you understand those things, 01:17:16.710 --> 01:17:18.392 and you get lower samples for them, 01:17:18.392 --> 01:17:20.350 you might be able to do some sort of correction 01:17:20.350 --> 01:17:21.670 to those biases. 01:17:21.670 --> 01:17:23.740 But you have to pay attention. 01:17:23.740 --> 01:17:25.390 How do you improve your response rate? 01:17:25.390 --> 01:17:28.150 Well you can make your questions shorter. 01:17:28.150 --> 01:17:29.950 You can do a quick oral survey. 01:17:29.950 --> 01:17:32.890 That's what we're going to do for this homework. 01:17:32.890 --> 01:17:36.550 You can try to get information from automatic sources whenever 01:17:36.550 --> 01:17:37.100 possible. 01:17:37.100 --> 01:17:42.100 So if you have an AFC system, let's not collect boardings, 01:17:42.100 --> 01:17:45.100 because we know that. 01:17:45.100 --> 01:17:47.650 And then of course some training, and just being kind, 01:17:47.650 --> 01:17:51.610 and having supervision helps a lot. 01:17:51.610 --> 01:17:53.650 OK, here's some suggested tolerances 01:17:53.650 --> 01:17:55.340 for different things. 01:17:55.340 --> 01:17:58.420 So we're looking here at boardings or the peak load. 01:17:58.420 --> 01:18:00.580 And you see here that the suggested tolerance 01:18:00.580 --> 01:18:05.290 is 30%, plus minus 30%, when you have a route with one 01:18:05.290 --> 01:18:05.980 to three buses. 01:18:05.980 --> 01:18:07.270 And then as you have more and more buses, 01:18:07.270 --> 01:18:08.380 the tolerance decreases. 01:18:08.380 --> 01:18:11.920 That means you require a larger sample. 01:18:11.920 --> 01:18:14.670 Why is that? 01:18:14.670 --> 01:18:16.530 Why do you need a bigger sample if you 01:18:16.530 --> 01:18:20.238 have a route with more buses? 01:18:20.238 --> 01:18:23.560 AUDIENCE: You're less likely to sample a different bus. 01:18:23.560 --> 01:18:26.830 GABRIEL SANCHEZ-MARTINEZ: Yes, and when you have higher-- 01:18:26.830 --> 01:18:30.112 when you have more buses, you tend to have higher frequency. 01:18:30.112 --> 01:18:30.820 There's bunching. 01:18:30.820 --> 01:18:35.260 OK, so if you then survey loads, for example, 01:18:35.260 --> 01:18:38.590 and you only get a few because of the bunching effect 01:18:38.590 --> 01:18:40.380 and because there are more buses, 01:18:40.380 --> 01:18:42.910 and you're observing a smaller percentage of them 01:18:42.910 --> 01:18:45.490 for a given time period, say, you're 01:18:45.490 --> 01:18:48.760 less likely to have observed the bus that was really crowded, 01:18:48.760 --> 01:18:49.330 right? 01:18:49.330 --> 01:18:52.390 So that means that you need to decrease your tolerance. 01:18:52.390 --> 01:18:55.490 And therefore, it's more expensive to survey that. 01:18:55.490 --> 01:18:56.350 OK, good. 01:18:56.350 --> 01:19:00.220 Trip time-- 10% for routes with less than 20 minutes, 01:19:00.220 --> 01:19:03.490 5% with routes of greater than 20 minutes. 01:19:03.490 --> 01:19:06.100 Similar concept if you have greater than 20 minutes-- 01:19:09.540 --> 01:19:11.170 there can be just more variability, 01:19:11.170 --> 01:19:14.860 and you really want to get that right. 01:19:14.860 --> 01:19:16.900 When you have less than 20 minutes, 01:19:16.900 --> 01:19:20.080 your decision on cycle times and things 01:19:20.080 --> 01:19:22.960 like this are not going to have as much impact on the fleet 01:19:22.960 --> 01:19:24.550 size that you require. 01:19:24.550 --> 01:19:31.720 As you get bigger running times, a small percentage change 01:19:31.720 --> 01:19:34.600 in the mean could influence how many buses 01:19:34.600 --> 01:19:37.750 you need to dedicate to that and the cost of running 01:19:37.750 --> 01:19:39.990 that service. 01:19:39.990 --> 01:19:43.610 On-time performance-- 10% absolute equivalent tolerance. 01:19:43.610 --> 01:19:47.260 These are typical values-- don't take them as gospel, please. 01:19:47.260 --> 01:19:49.530 And these are for reporting, not for anything that's 01:19:49.530 --> 01:19:51.750 very critical for operations. 01:19:51.750 --> 01:19:53.560 Some of them are. 01:19:53.560 --> 01:19:56.820 Yeah, 30% at least, I would say, is for reporting. 01:19:56.820 --> 01:20:00.840 I wouldn't make any critical decisions with 30%. 01:20:00.840 --> 01:20:04.410 On-time performance-- we're talking here about whether 01:20:04.410 --> 01:20:07.060 a trip is on time or not on time-- 01:20:07.060 --> 01:20:08.970 so Bernoulli trials, right? 01:20:08.970 --> 01:20:10.650 And there's a proportion of trips 01:20:10.650 --> 01:20:15.120 that are on time, and what we do is that, we essentially 01:20:15.120 --> 01:20:19.710 say plus-- if we say plus minus 10%, then we're saying 01:20:19.710 --> 01:20:22.980 that the sample size should be 1 over 0.1. 01:20:22.980 --> 01:20:23.480 Yeah. 01:20:26.330 --> 01:20:28.160 All right, default coefficient-- these 01:20:28.160 --> 01:20:29.576 are default values for coefficient 01:20:29.576 --> 01:20:30.950 of variation of key data items. 01:20:30.950 --> 01:20:33.170 Ideally, you have your own data that you look at, 01:20:33.170 --> 01:20:34.790 and you don't resort to this. 01:20:34.790 --> 01:20:37.910 But if you ever find yourself in a situation 01:20:37.910 --> 01:20:40.470 where you need to start out with something. 01:20:40.470 --> 01:20:45.440 Here are some based on studies that previous [AUDIO OUT] They 01:20:45.440 --> 01:20:48.590 took different routes and looked at loads 01:20:48.590 --> 01:20:51.440 and running times for different time periods 01:20:51.440 --> 01:20:53.570 and found what the coefficients of variations were. 01:20:53.570 --> 01:20:56.420 And here they are on a table for you to use. 01:21:00.947 --> 01:21:03.530 In the interest of time, since I want to discuss the homework, 01:21:03.530 --> 01:21:05.750 I'm going to stop here with slide 25. 01:21:05.750 --> 01:21:11.480 And I'm going to not cover the whole process, which 01:21:11.480 --> 01:21:14.880 includes the monitoring phase. 01:21:14.880 --> 01:21:17.790 And in this slide here, we have how you 01:21:17.790 --> 01:21:20.010 establish conversion factor. 01:21:20.010 --> 01:21:23.870 The conversion factor in itself has a variance. 01:21:23.870 --> 01:21:26.130 So there's some uncertainty about the relationship 01:21:26.130 --> 01:21:31.380 that you estimate between your baseline data item 01:21:31.380 --> 01:21:33.550 and your auxiliary data item. 01:21:33.550 --> 01:21:37.210 So you need to consider that in your sample size. 01:21:37.210 --> 01:21:39.720 And here are some tables with some examples of what 01:21:39.720 --> 01:21:44.130 happens when you require different-- well, when you're 01:21:44.130 --> 01:21:47.940 variability of or your coefficient 01:21:47.940 --> 01:21:52.650 of variation of your relationship increases 01:21:52.650 --> 01:21:54.390 or decreases. 01:21:54.390 --> 01:21:56.430 OK, let's look at the homework. 01:21:56.430 --> 01:21:59.893 I really want to use these last five minutes for that. 01:21:59.893 --> 01:22:07.560 So please take one and pass. 01:22:07.560 --> 01:22:12.300 OK, so the MBTA, there's a proposal here in Boston 01:22:12.300 --> 01:22:14.850 of taking Route 70 and 70A-- 01:22:14.850 --> 01:22:17.370 they run through Waltham, and they 01:22:17.370 --> 01:22:20.130 go into around Central Square. 01:22:20.130 --> 01:22:23.690 And some people are saying those two routes should be extended 01:22:23.690 --> 01:22:28.430 to Kendall Square, because a lot of people 01:22:28.430 --> 01:22:31.700 are actually going to MIT, or Kendall Square, or the Kendall 01:22:31.700 --> 01:22:33.890 Square area-- 01:22:33.890 --> 01:22:37.280 not just Kendall Square Station, but the whole area around. 01:22:37.280 --> 01:22:39.350 So if it's true, A lot of people could 01:22:39.350 --> 01:22:40.670 benefit from that extension. 01:22:40.670 --> 01:22:41.670 And we don't know. 01:22:41.670 --> 01:22:43.140 So what are you going to do? 01:22:43.140 --> 01:22:45.620 You're going to go to a specific stop 01:22:45.620 --> 01:22:48.620 where it is very likely that the people who would be going 01:22:48.620 --> 01:22:52.430 to MIT or those areas of Kendall Square that would benefit 01:22:52.430 --> 01:22:55.040 from this extension would alight, 01:22:55.040 --> 01:22:57.140 and you're going to ask people, would you 01:22:57.140 --> 01:23:01.250 have stayed on your bus if this bus had continued 01:23:01.250 --> 01:23:02.960 to MIT and Kendall Square? 01:23:02.960 --> 01:23:06.635 It's a simple oral survey, yes or no question, one question. 01:23:06.635 --> 01:23:08.510 You're going to work in teams of four people. 01:23:13.130 --> 01:23:16.670 The stop that you're going to station yourself in 01:23:16.670 --> 01:23:18.296 is shown in figure 3. 01:23:21.230 --> 01:23:23.360 And you're going to collect data for the AM peak, 01:23:23.360 --> 01:23:25.760 from 7:30 to 9:30. 01:23:25.760 --> 01:23:27.320 You pick the day. 01:23:27.320 --> 01:23:29.090 The teams are assigned on Stellar, 01:23:29.090 --> 01:23:32.150 so please log into Stellar and see what your team is 01:23:32.150 --> 01:23:34.910 and coordinate with them to pick a day. 01:23:34.910 --> 01:23:37.580 And tell me what that day is, because-- 01:23:37.580 --> 01:23:39.410 actually, right after class, I'm going 01:23:39.410 --> 01:23:43.370 to set up a shared spreadsheet that you can all access. 01:23:43.370 --> 01:23:46.519 And just go into that spreadsheet and pick a day. 01:23:46.519 --> 01:23:48.560 I'm going to put all the days that are available, 01:23:48.560 --> 01:23:51.170 and you can say team 1, team 2, et cetera. 01:23:51.170 --> 01:23:54.410 Make sure that two teams don't go on the same day. 01:23:54.410 --> 01:23:56.400 We want data from different days. 01:23:56.400 --> 01:23:58.400 And you're going to all bring that data together 01:23:58.400 --> 01:24:00.650 in that same spreadsheet, and there 01:24:00.650 --> 01:24:03.650 are some questions for you to analyze 01:24:03.650 --> 01:24:06.230 the data that you collected, all of the class collected 01:24:06.230 --> 01:24:08.540 together. 01:24:08.540 --> 01:24:12.980 You're measuring the percent of people who would 01:24:12.980 --> 01:24:14.450 have stayed on the bus, right? 01:24:14.450 --> 01:24:18.730 So it's a proportion. 01:24:18.730 --> 01:24:22.960 And one submission per team in PDF format to Stellar. 01:24:22.960 --> 01:24:26.410 This is due March 7, but in order 01:24:26.410 --> 01:24:28.830 to leave you enough time to do the analysis, 01:24:28.830 --> 01:24:31.590 the data collection efforts should be done by February 28. 01:24:31.590 --> 01:24:37.150 So please submit your data by the end of Tuesday, February 28 01:24:37.150 --> 01:24:41.230 at midnight, say, or sometime before the beginning of March 01:24:41.230 --> 01:24:43.300 in the morning, where a person would 01:24:43.300 --> 01:24:45.100 be trying to analyze your data. 01:24:48.510 --> 01:24:51.280 OK, if you have questions, let me know. 01:24:51.280 --> 01:24:56.250 And if not, have fun. 01:24:56.250 --> 01:24:58.910 Remember that assignment 1 is due Thursday. 01:25:01.531 --> 01:25:02.030 Eric? 01:25:02.030 --> 01:25:03.822 AUDIENCE: Just the one question: [? is that ?] [? this is ?] 01:25:03.822 --> 01:25:06.140 going to miss anyone who is transferred to the Red Line 01:25:06.140 --> 01:25:07.746 to then go to Kendall Square. 01:25:07.746 --> 01:25:09.620 GABRIEL SANCHEZ-MARTINEZ: And going back to-- 01:25:09.620 --> 01:25:10.120 let's see. 01:25:14.430 --> 01:25:17.660 I forget where I had it. 01:25:17.660 --> 01:25:20.630 Well, I guess what I-- there was a point I made earlier 01:25:20.630 --> 01:25:23.730 where we can measure that from automatically collected data, 01:25:23.730 --> 01:25:24.230 right? 01:25:24.230 --> 01:25:24.950 AUDIENCE: OK. 01:25:24.950 --> 01:25:25.610 GABRIEL SANCHEZ-MARTINEZ: Does that make sense? 01:25:25.610 --> 01:25:27.860 AUDIENCE: Yeah, people who [? car up ?] come from 70. 01:25:27.860 --> 01:25:29.235 GABRIEL SANCHEZ-MARTINEZ: So if I 01:25:29.235 --> 01:25:32.410 see you tapping of the 70 or the 70A, 01:25:32.410 --> 01:25:35.480 and then I see you tapping at Central Square, 01:25:35.480 --> 01:25:37.790 I can infer that you were using the service 01:25:37.790 --> 01:25:40.790 to transfer to Central Square. 01:25:40.790 --> 01:25:42.950 And then we'll cover ODX, which is 01:25:42.950 --> 01:25:44.480 an inference model for destinations 01:25:44.480 --> 01:25:46.210 later in this course. 01:25:46.210 --> 01:25:51.170 But looking at the sequence of taps, I can infer-- 01:25:51.170 --> 01:25:53.420 we can infer-- what the destination of that bus trip 01:25:53.420 --> 01:25:53.919 was. 01:25:53.919 --> 01:25:55.720 We can infer that it was the stop that 01:25:55.720 --> 01:25:57.440 was closest to Central. 01:25:57.440 --> 01:26:00.710 And later that day, presumably the person 01:26:00.710 --> 01:26:04.310 who might be going to Kendall Square Station after work taps 01:26:04.310 --> 01:26:05.199 to Kendall Square. 01:26:05.199 --> 01:26:07.490 So I might think, oh, he took the Red Line from Central 01:26:07.490 --> 01:26:09.500 to Kendall. 01:26:09.500 --> 01:26:12.320 So I don't need to ask those people where they're going. 01:26:12.320 --> 01:26:14.880 And anyway, they might not care about this extension. 01:26:14.880 --> 01:26:17.570 So we're going to stand on the bus stop that 01:26:17.570 --> 01:26:21.590 is after Central Square and see where those people are going 01:26:21.590 --> 01:26:25.350 and whether they would have stayed on that bus. 01:26:25.350 --> 01:26:28.119 AUDIENCE: Is this an actual [INAUDIBLE] 01:26:28.119 --> 01:26:30.410 GABRIEL SANCHEZ-MARTINEZ: Some people are proposing it. 01:26:30.410 --> 01:26:33.060 It is a real proposal. 01:26:33.060 --> 01:26:35.230 The MBTA is a big organization. 01:26:35.230 --> 01:26:41.490 So I can't say that the MBTA wants to do this 01:26:41.490 --> 01:26:43.210 or doesn't want to do this. 01:26:43.210 --> 01:26:45.090 But some people are interested. 01:26:45.090 --> 01:26:48.630 And it will get looked into. 01:26:48.630 --> 01:26:50.770 So it's useful. 01:26:50.770 --> 01:26:53.195 AUDIENCE: [? Can ?] [? we ?] [? share ?] [INAUDIBLE] 01:26:53.195 --> 01:26:56.105 GABRIEL SANCHEZ-MARTINEZ: Yeah, why not? 01:26:56.105 --> 01:26:58.045 AUDIENCE: [INAUDIBLE] 01:26:58.045 --> 01:27:00.470 GABRIEL SANCHEZ-MARTINEZ: Yeah. 01:27:00.470 --> 01:27:03.320 And I guess one other thing that I-- yeah, 01:27:03.320 --> 01:27:06.250 so we're going to probably make of this 01:27:06.250 --> 01:27:08.594 like a theme of assignments. 01:27:08.594 --> 01:27:10.760 So there's going to be another assignment on surface 01:27:10.760 --> 01:27:12.510 planning, operations planning. 01:27:12.510 --> 01:27:15.160 So we're going to start looking at this combination of Route 70 01:27:15.160 --> 01:27:19.760 and 70A, and we're going to essentially make 01:27:19.760 --> 01:27:22.520 a thread of this and do some serious planning 01:27:22.520 --> 01:27:26.300 on some scenarios where the 70 and the 70A could be merged. 01:27:26.300 --> 01:27:29.860 And they could maybe be terminated a little-- 01:27:29.860 --> 01:27:32.810 yeah, we'll make some changes to the service plan 01:27:32.810 --> 01:27:34.440 under some hypothetical scenarios. 01:27:34.440 --> 01:27:38.840 And you'll get a chance to do an operations plan on these. 01:27:38.840 --> 01:27:41.550 And then the last homework will be on policy, 01:27:41.550 --> 01:27:44.170 so there might be some policy questions 01:27:44.170 --> 01:27:47.930 that I have in mind about what we could do about 01:27:47.930 --> 01:27:52.640 service outside, on the outer parts of the 70 and 70A. 01:27:57.440 --> 01:27:59.290 All right?