WEBVTT 00:00:00.000 --> 00:00:01.943 align:middle line:90% [SQUEAKING] 00:00:01.943 --> 00:00:03.386 align:middle line:90% [RUSTLING] 00:00:03.386 --> 00:00:06.272 align:middle line:90% [CLICKING] 00:00:06.272 --> 00:00:09.057 align:middle line:90% 00:00:09.057 --> 00:00:10.140 align:middle line:90% JOSH MCDERMOTT: All right. 00:00:10.140 --> 00:00:10.720 align:middle line:90% Fantastic. 00:00:10.720 --> 00:00:16.560 align:middle line:84% So last time we started talking about sound localization. 00:00:16.560 --> 00:00:19.800 align:middle line:84% And so what I'm going to do today is wrap that up. 00:00:19.800 --> 00:00:21.360 align:middle line:84% We're going to have a brief interlude 00:00:21.360 --> 00:00:23.840 align:middle line:84% to discuss psychophysical methods. 00:00:23.840 --> 00:00:26.220 align:middle line:84% Everybody's going to learn how to measure a threshold. 00:00:26.220 --> 00:00:29.600 align:middle line:84% And then we're going to talk about pitch perception 00:00:29.600 --> 00:00:31.800 align:middle line:84% And then following on that, next time, 00:00:31.800 --> 00:00:34.160 align:middle line:84% we'll get into auditory scene analysis 00:00:34.160 --> 00:00:37.100 align:middle line:90% and then speech perception 00:00:37.100 --> 00:00:40.440 align:middle line:84% So we talked about the fact that sound localization 00:00:40.440 --> 00:00:42.100 align:middle line:84% is this really interesting problem 00:00:42.100 --> 00:00:45.320 align:middle line:84% because location information is not made explicit 00:00:45.320 --> 00:00:47.800 align:middle line:90% in the sensory input. 00:00:47.800 --> 00:00:50.200 align:middle line:84% And we discussed the sources of information 00:00:50.200 --> 00:00:52.340 align:middle line:84% that we get about sound localization, 00:00:52.340 --> 00:00:55.098 align:middle line:84% these different kinds of cues that 00:00:55.098 --> 00:00:56.640 align:middle line:84% are informative about where something 00:00:56.640 --> 00:00:58.440 align:middle line:90% is coming from in the world. 00:00:58.440 --> 00:01:01.160 align:middle line:84% So there are two that are binaural, interaural intensity 00:01:01.160 --> 00:01:03.960 align:middle line:84% or level differences and interaural time differences. 00:01:03.960 --> 00:01:06.480 align:middle line:84% And then spectral cues that come from the filtering 00:01:06.480 --> 00:01:09.000 align:middle line:90% of the pinna that are monaural. 00:01:09.000 --> 00:01:13.160 align:middle line:84% So the binaural cues, they originate from the fact 00:01:13.160 --> 00:01:15.460 align:middle line:84% that the ears are in different locations, 00:01:15.460 --> 00:01:17.493 align:middle line:84% and so there are differences in the path length. 00:01:17.493 --> 00:01:19.160 align:middle line:84% And then there's also an acoustic shadow 00:01:19.160 --> 00:01:21.280 align:middle line:90% that is cast by the head. 00:01:21.280 --> 00:01:23.408 align:middle line:84% We looked at the magnitude of these cues, 00:01:23.408 --> 00:01:25.200 align:middle line:84% in particular for the time differences that 00:01:25.200 --> 00:01:27.575 align:middle line:84% exist between the two ears, they're really, really small, 00:01:27.575 --> 00:01:30.080 align:middle line:90% but they're reliable. 00:01:30.080 --> 00:01:33.000 align:middle line:84% We talked about the idea that time differences 00:01:33.000 --> 00:01:36.103 align:middle line:84% are arguably most useful for low frequencies, 00:01:36.103 --> 00:01:37.520 align:middle line:84% because for high frequencies, they 00:01:37.520 --> 00:01:40.200 align:middle line:84% are ambiguous, and potentially also limited 00:01:40.200 --> 00:01:43.200 align:middle line:84% by the upper cutoff of phase locking. 00:01:43.200 --> 00:01:46.680 align:middle line:84% Conversely, level differences are 00:01:46.680 --> 00:01:49.092 align:middle line:84% largest for high frequencies, and they get smaller 00:01:49.092 --> 00:01:50.800 align:middle line:84% for low frequencies, just due to the fact 00:01:50.800 --> 00:01:53.040 align:middle line:84% that the low frequencies pass over the head. 00:01:53.040 --> 00:01:54.760 align:middle line:84% And so there's this classical kind 00:01:54.760 --> 00:01:58.630 align:middle line:84% of cartoon story of binaural hearing 00:01:58.630 --> 00:02:01.133 align:middle line:84% called the duplex theory, where for low frequencies, 00:02:01.133 --> 00:02:03.550 align:middle line:84% we can rely on time differences, and for high frequencies, 00:02:03.550 --> 00:02:05.530 align:middle line:84% we can use intensity differences. 00:02:05.530 --> 00:02:07.350 align:middle line:84% And then we talked about some evidence that 00:02:07.350 --> 00:02:10.729 align:middle line:84% was taken as being consistent with duplex theory, 00:02:10.729 --> 00:02:13.838 align:middle line:84% namely that localization is best for low frequencies 00:02:13.838 --> 00:02:15.630 align:middle line:84% and high frequencies, and gets a little bit 00:02:15.630 --> 00:02:17.750 align:middle line:84% worse for medium frequencies when you test people 00:02:17.750 --> 00:02:21.222 align:middle line:90% with pure tones. 00:02:21.222 --> 00:02:24.070 align:middle line:84% And then we talked a little bit about something 00:02:24.070 --> 00:02:26.350 align:middle line:84% that might be useful for the problem set. 00:02:26.350 --> 00:02:29.270 align:middle line:84% We then discussed the kind of classical model 00:02:29.270 --> 00:02:33.270 align:middle line:84% for how you might detect timing differences between the two 00:02:33.270 --> 00:02:37.150 align:middle line:84% ears, namely the Jeffress model for ITD detection, where 00:02:37.150 --> 00:02:39.350 align:middle line:84% the idea is that you have neurons that can 00:02:39.350 --> 00:02:41.130 align:middle line:90% act as coincidence detectors. 00:02:41.130 --> 00:02:44.510 align:middle line:84% They get inputs from the two ears, but with a time delay-- 00:02:44.510 --> 00:02:46.570 align:middle line:84% a different time delay for the two ears, 00:02:46.570 --> 00:02:49.765 align:middle line:84% and that causes them to respond most 00:02:49.765 --> 00:02:52.390 align:middle line:84% when there's a particular time difference between the two ears. 00:02:52.390 --> 00:02:55.630 align:middle line:84% So really like possibly, I think the first model 00:02:55.630 --> 00:02:57.790 align:middle line:84% in the history of computational neuroscience, which 00:02:57.790 --> 00:02:59.408 align:middle line:90% is kind of cool. 00:02:59.408 --> 00:03:00.950 align:middle line:84% And we talked about how this has been 00:03:00.950 --> 00:03:03.710 align:middle line:84% found in the brainstem of some species. 00:03:03.710 --> 00:03:06.630 align:middle line:84% And then how there's this kind of remarkable segregation 00:03:06.630 --> 00:03:08.990 align:middle line:84% of function, where two different parts of the brainstem 00:03:08.990 --> 00:03:11.610 align:middle line:84% have sensitivity to these two main binaural cues. 00:03:11.610 --> 00:03:14.110 align:middle line:84% So the intensity differences are believed 00:03:14.110 --> 00:03:16.540 align:middle line:84% to be detected in a different part of the superior olive. 00:03:16.540 --> 00:03:18.290 align:middle line:84% So you've got the segregation of function. 00:03:18.290 --> 00:03:21.770 align:middle line:84% The medial superior olive contains ITD detectors, 00:03:21.770 --> 00:03:25.750 align:middle line:84% and the lateral superior olive contains ILD detectors. 00:03:25.750 --> 00:03:28.310 align:middle line:84% And we talked about how when you get to the cortex, 00:03:28.310 --> 00:03:30.990 align:middle line:84% the coding changes, and that the neurons tend 00:03:30.990 --> 00:03:33.070 align:middle line:84% to be cue independent and broadly tuned 00:03:33.070 --> 00:03:35.910 align:middle line:90% to one side or the other. 00:03:35.910 --> 00:03:38.570 align:middle line:84% And then got into the issue with these binaural cues, 00:03:38.570 --> 00:03:40.045 align:middle line:84% which is that they're informative, 00:03:40.045 --> 00:03:41.170 align:middle line:90% but they're also ambiguous. 00:03:41.170 --> 00:03:43.130 align:middle line:84% So there's the cone of confusion, 00:03:43.130 --> 00:03:45.390 align:middle line:84% which is this region of space that 00:03:45.390 --> 00:03:47.870 align:middle line:84% is consistent with particular binaural cues, 00:03:47.870 --> 00:03:51.470 align:middle line:84% just due to the symmetry of the situation. 00:03:51.470 --> 00:03:53.860 align:middle line:84% And so to resolve that ambiguity, 00:03:53.860 --> 00:03:56.350 align:middle line:84% we're believed to rely on these pinna cues. 00:03:56.350 --> 00:03:58.100 align:middle line:84% And the pinna cue is derived from the fact 00:03:58.100 --> 00:03:59.740 align:middle line:84% that the ears have these folds such 00:03:59.740 --> 00:04:02.680 align:middle line:84% that depending on the direction that the sound is coming from, 00:04:02.680 --> 00:04:04.960 align:middle line:84% it will bounce off the ears in a particular pattern, 00:04:04.960 --> 00:04:08.380 align:middle line:84% and that causes it to be filtered differently. 00:04:08.380 --> 00:04:11.000 align:middle line:84% Everybody's ears filter the sound slightly differently, 00:04:11.000 --> 00:04:13.280 align:middle line:84% so this is a graph showing you two different ears. 00:04:13.280 --> 00:04:15.613 align:middle line:84% And the point is there are these transfer functions that 00:04:15.613 --> 00:04:17.300 align:middle line:84% changes a function of the direction 00:04:17.300 --> 00:04:19.980 align:middle line:84% from which the sound comes from, whether it's up or down. 00:04:19.980 --> 00:04:23.860 align:middle line:84% And here's the concept where there's a transfer 00:04:23.860 --> 00:04:25.240 align:middle line:90% function in your ears. 00:04:25.240 --> 00:04:27.460 align:middle line:90% That's the filter of your ear. 00:04:27.460 --> 00:04:30.520 align:middle line:84% That colors the spectrum of the sound that comes in, 00:04:30.520 --> 00:04:33.180 align:middle line:84% and so you get some altered spectrum. 00:04:33.180 --> 00:04:35.060 align:middle line:84% And so in principle, you might be 00:04:35.060 --> 00:04:37.140 align:middle line:84% able to detect the transfer function 00:04:37.140 --> 00:04:40.000 align:middle line:84% and use that to localize sounds in elevation. 00:04:40.000 --> 00:04:42.640 align:middle line:84% Now, we discussed some evidence that people actually use this. 00:04:42.640 --> 00:04:46.540 align:middle line:84% Namely, when you put plastic molds in somebody's ears, 00:04:46.540 --> 00:04:49.920 align:middle line:84% their ability to localize in elevation collapses. 00:04:49.920 --> 00:04:52.260 align:middle line:84% They preserve their ability to localize in azimuth. 00:04:52.260 --> 00:04:53.832 align:middle line:84% And then we talked about evidence 00:04:53.832 --> 00:04:56.040 align:middle line:84% that people actually learn the cues from their pinna, 00:04:56.040 --> 00:04:58.498 align:middle line:84% because if you make people go home with these plastic molds 00:04:58.498 --> 00:05:00.680 align:middle line:84% and walk around with them for several weeks, 00:05:00.680 --> 00:05:05.280 align:middle line:84% they slowly regain the ability to localize in elevation. 00:05:05.280 --> 00:05:07.460 align:middle line:84% And I showed you very briefly an example 00:05:07.460 --> 00:05:10.100 align:middle line:84% of a computational model that is optimized 00:05:10.100 --> 00:05:12.220 align:middle line:84% to localize sounds that reproduces 00:05:12.220 --> 00:05:13.420 align:middle line:90% a lot of these effects. 00:05:13.420 --> 00:05:14.900 align:middle line:84% So systems that learn to localize 00:05:14.900 --> 00:05:19.260 align:middle line:84% sounds end up behaving a lot like humans. 00:05:19.260 --> 00:05:21.680 align:middle line:84% And then at the end of the lecture last time, 00:05:21.680 --> 00:05:24.380 align:middle line:84% we talked about stereo reproduction of audio, 00:05:24.380 --> 00:05:26.660 align:middle line:84% and how it's imperfect because it can't completely 00:05:26.660 --> 00:05:29.980 align:middle line:84% reproduce the spatial cues that actually happen in the world, 00:05:29.980 --> 00:05:32.700 align:middle line:84% but nonetheless, kind of does help you to distinguish 00:05:32.700 --> 00:05:34.512 align:middle line:90% different sounds in music. 00:05:34.512 --> 00:05:35.720 align:middle line:90% And that's where we left off. 00:05:35.720 --> 00:05:39.180 align:middle line:84% And so the last topic that we'll talk about in sound localization 00:05:39.180 --> 00:05:40.395 align:middle line:90% is distance perception. 00:05:40.395 --> 00:05:42.020 align:middle line:84% So so far, we've been talking about how 00:05:42.020 --> 00:05:44.720 align:middle line:84% you tell the direction that a sound is coming from, 00:05:44.720 --> 00:05:46.940 align:middle line:84% whether it's here, or here, or here, or here, 00:05:46.940 --> 00:05:50.570 align:middle line:84% but obviously, another dimension to location in the world 00:05:50.570 --> 00:05:53.850 align:middle line:90% is how far away something is. 00:05:53.850 --> 00:05:55.610 align:middle line:84% And one of the main ways in which 00:05:55.610 --> 00:05:58.050 align:middle line:84% we determine how far away something is actually 00:05:58.050 --> 00:05:59.210 align:middle line:90% reverberation. 00:05:59.210 --> 00:06:05.530 align:middle line:84% And so here's-- you'll just be able to hear the effect here. 00:06:05.530 --> 00:06:08.870 align:middle line:84% So here's somebody who's real close. 00:06:08.870 --> 00:06:09.827 align:middle line:90% [AUDIO PLAYBACK] 00:06:09.827 --> 00:06:13.490 align:middle line:90% - [INAUDIBLE] 00:06:13.490 --> 00:06:15.630 align:middle line:84% JOSH MCDERMOTT: And here's somebody who's far. 00:06:15.630 --> 00:06:18.730 align:middle line:90% - [INAUDIBLE] 00:06:18.730 --> 00:06:19.370 align:middle line:90% [END PLAYBACK] 00:06:19.370 --> 00:06:21.450 align:middle line:84% JOSH MCDERMOTT: It's supposed to sound further away. 00:06:21.450 --> 00:06:23.783 align:middle line:84% These reverb demos are always challenging in a classroom 00:06:23.783 --> 00:06:25.695 align:middle line:84% because they're played out of speakers 00:06:25.695 --> 00:06:27.570 align:middle line:84% and are subject to all the reverberation that 00:06:27.570 --> 00:06:28.672 align:middle line:90% happens in the room. 00:06:28.672 --> 00:06:29.630 align:middle line:90% But here's the concept. 00:06:29.630 --> 00:06:35.890 align:middle line:84% So sound attenuates with distance. 00:06:35.890 --> 00:06:40.050 align:middle line:84% So if somebody is right next to you, there is sound-- 00:06:40.050 --> 00:06:42.290 align:middle line:84% so let's suppose you're this person, 00:06:42.290 --> 00:06:45.070 align:middle line:84% and there's this person in back of you who's talking. 00:06:45.070 --> 00:06:48.130 align:middle line:84% So there's sound that reaches you from that person 00:06:48.130 --> 00:06:49.730 align:middle line:90% directly to your ears. 00:06:49.730 --> 00:06:52.930 align:middle line:84% And that sound will typically be pretty high in intensity 00:06:52.930 --> 00:06:56.290 align:middle line:90% because they're close. 00:06:56.290 --> 00:07:00.970 align:middle line:84% This person up here is much further away. 00:07:00.970 --> 00:07:03.150 align:middle line:84% And so the sound will attenuate over distance. 00:07:03.150 --> 00:07:05.530 align:middle line:84% And so the direct sound that reaches you 00:07:05.530 --> 00:07:08.370 align:middle line:84% straight from the sound source will be lower in amplitude 00:07:08.370 --> 00:07:10.170 align:middle line:84% when the person's further away compared 00:07:10.170 --> 00:07:11.770 align:middle line:90% to when the person's here. 00:07:11.770 --> 00:07:15.090 align:middle line:84% Now, the reverberation will tend to be pretty constant. 00:07:15.090 --> 00:07:16.210 align:middle line:90% And the idea behind-- 00:07:16.210 --> 00:07:18.725 align:middle line:84% so reverberation, that's the term 00:07:18.725 --> 00:07:20.850 align:middle line:84% that we use to refer to all of the reflections that 00:07:20.850 --> 00:07:22.810 align:middle line:90% can occur in the world. 00:07:22.810 --> 00:07:25.690 align:middle line:84% So most surfaces in the world, they reflect sound. 00:07:25.690 --> 00:07:28.750 align:middle line:84% And so when a sound source is producing sound, 00:07:28.750 --> 00:07:30.930 align:middle line:84% the sound will reach you directly 00:07:30.930 --> 00:07:32.590 align:middle line:90% on a kind of a straight line. 00:07:32.590 --> 00:07:35.570 align:middle line:84% But also after reflecting off of all the different surfaces 00:07:35.570 --> 00:07:36.870 align:middle line:90% in the environment. 00:07:36.870 --> 00:07:39.490 align:middle line:84% And so the sum total of all those reflections 00:07:39.490 --> 00:07:41.770 align:middle line:90% is what we call reverberation. 00:07:41.770 --> 00:07:46.230 align:middle line:84% And you can recognize that when you go into a big space. 00:07:46.230 --> 00:07:48.740 align:middle line:84% You walk out into the atrium, it's a big space. 00:07:48.740 --> 00:07:50.800 align:middle line:84% There's like lots of echoes and the path lengths 00:07:50.800 --> 00:07:54.640 align:middle line:84% are kind of long, whereas like if you're in your car, 00:07:54.640 --> 00:07:58.840 align:middle line:84% the path lengths are very short, so it sounds different. 00:07:58.840 --> 00:08:02.120 align:middle line:84% But the key concept here is that the path lengths 00:08:02.120 --> 00:08:04.460 align:middle line:84% for reverberation, if you're in a space, 00:08:04.460 --> 00:08:05.720 align:middle line:90% they all kind average out. 00:08:05.720 --> 00:08:07.840 align:middle line:84% So some of them are short and some are long. 00:08:07.840 --> 00:08:10.520 align:middle line:84% And so the overall level of reverberation 00:08:10.520 --> 00:08:12.720 align:middle line:84% will be pretty similar irrespective of 00:08:12.720 --> 00:08:15.700 align:middle line:84% whether the person is close to you or far from you. 00:08:15.700 --> 00:08:19.760 align:middle line:84% But what will change is the amplitude of the direct sound. 00:08:19.760 --> 00:08:22.600 align:middle line:84% So if the person's really close, that direct component 00:08:22.600 --> 00:08:25.300 align:middle line:84% of the sound will be very high in level, 00:08:25.300 --> 00:08:28.480 align:middle line:84% whereas if they're far away, it will be lower in level. 00:08:28.480 --> 00:08:32.960 align:middle line:84% So that's kind of one of the main cues to sound distance. 00:08:32.960 --> 00:08:35.299 align:middle line:84% So this is just kind of a diagram that shows that. 00:08:35.299 --> 00:08:38.280 align:middle line:84% So what it's attempting to depict 00:08:38.280 --> 00:08:40.600 align:middle line:84% is a situation where the source is near, 00:08:40.600 --> 00:08:44.159 align:middle line:84% that's on top, a situation where the source is more distant. 00:08:44.159 --> 00:08:49.142 align:middle line:84% And this is like all of the different reflections 00:08:49.142 --> 00:08:50.100 align:middle line:90% that you would receive. 00:08:50.100 --> 00:08:52.860 align:middle line:84% So imagine you play a clip from the sound source. 00:08:52.860 --> 00:08:54.960 align:middle line:84% So this is the sound that reaches you 00:08:54.960 --> 00:08:56.030 align:middle line:90% from the direct path. 00:08:56.030 --> 00:08:57.780 align:middle line:84% And then these are all of the reflections, 00:08:57.780 --> 00:08:59.960 align:middle line:84% and they arrive later because the path length 00:08:59.960 --> 00:09:02.720 align:middle line:84% that they have to take in order to reach you is longer. 00:09:02.720 --> 00:09:06.100 align:middle line:84% So they arrive later, but their amplitude is also a bit lower. 00:09:06.100 --> 00:09:09.620 align:middle line:84% And so the idea is that if something is close, 00:09:09.620 --> 00:09:12.800 align:middle line:84% that direct sound is high in amplitude. 00:09:12.800 --> 00:09:14.820 align:middle line:84% If it's further away, it's lower in amplitude, 00:09:14.820 --> 00:09:16.700 align:middle line:84% but the reverberation is pretty similar. 00:09:16.700 --> 00:09:20.160 align:middle line:84% And so the ratio direct to reverberant sound 00:09:20.160 --> 00:09:22.960 align:middle line:84% gives you information about how far away something is. 00:09:22.960 --> 00:09:24.960 align:middle line:84% Also, another thing that you can use 00:09:24.960 --> 00:09:26.560 align:middle line:84% to tell how far away something is 00:09:26.560 --> 00:09:32.440 align:middle line:84% if the sound source is familiar and has a characteristic level. 00:09:32.440 --> 00:09:34.220 align:middle line:84% So for instance, like dogs barking, 00:09:34.220 --> 00:09:36.400 align:middle line:84% they typically bark at a certain SPL level of-- 00:09:36.400 --> 00:09:38.880 align:middle line:84% I don't know-- 70 dB or something, right? 00:09:38.880 --> 00:09:41.040 align:middle line:84% And if you're familiar with that sound source, 00:09:41.040 --> 00:09:44.450 align:middle line:84% then that can tell you how far away they are, potentially. 00:09:44.450 --> 00:09:47.523 align:middle line:84% So if the sound that arrives at your ears is low in level, 00:09:47.523 --> 00:09:49.190 align:middle line:84% and you realize that it's a sound that's 00:09:49.190 --> 00:09:51.398 align:middle line:84% normally high in level, that tells you it's far away. 00:09:51.398 --> 00:09:57.110 align:middle line:84% So those are two different kinds of cues that you can use. 00:09:57.110 --> 00:10:00.810 align:middle line:84% So that's all that I got to tell you about sound localization. 00:10:00.810 --> 00:10:03.570 align:middle line:84% What questions do you have before we move on? 00:10:03.570 --> 00:10:12.070 align:middle line:90% 00:10:12.070 --> 00:10:13.010 align:middle line:90% Yeah. 00:10:13.010 --> 00:10:15.910 align:middle line:84% AUDIENCE: So let's say it's an unfamiliar sound. 00:10:15.910 --> 00:10:20.470 align:middle line:84% If there were just like, no walls at all or [INAUDIBLE] 00:10:20.470 --> 00:10:22.930 align:middle line:84% would it just be hard to perceive distance? 00:10:22.930 --> 00:10:23.110 align:middle line:90% JOSH MCDERMOTT: Yeah. 00:10:23.110 --> 00:10:25.152 align:middle line:84% You would have no idea how far away the thing is. 00:10:25.152 --> 00:10:25.830 align:middle line:90% Yeah. 00:10:25.830 --> 00:10:26.870 align:middle line:90% Yeah. 00:10:26.870 --> 00:10:29.830 align:middle line:84% And in fact, yeah, you could go into an anechoic room 00:10:29.830 --> 00:10:30.970 align:middle line:90% and try to test this. 00:10:30.970 --> 00:10:31.790 align:middle line:90% Yeah. 00:10:31.790 --> 00:10:34.450 align:middle line:90% Yeah. 00:10:34.450 --> 00:10:34.950 align:middle line:90% Yeah. 00:10:34.950 --> 00:10:35.450 align:middle line:90% Yeah. 00:10:35.450 --> 00:10:37.000 align:middle line:90% And I should say the-- 00:10:37.000 --> 00:10:39.630 align:middle line:84% so reverberation is one of these things that it-- 00:10:39.630 --> 00:10:42.390 align:middle line:84% I mean, it's everywhere in the world. 00:10:42.390 --> 00:10:44.170 align:middle line:84% It's also everywhere in music production. 00:10:44.170 --> 00:10:48.270 align:middle line:84% It's maybe the most commonly employed method 00:10:48.270 --> 00:10:50.650 align:middle line:84% in music production to change the way things sound. 00:10:50.650 --> 00:10:55.790 align:middle line:84% And so if you pay attention to recorded music, 00:10:55.790 --> 00:10:59.110 align:middle line:84% like the production engineer is often 00:10:59.110 --> 00:11:01.630 align:middle line:84% manipulating the reverberation to make certain things sound 00:11:01.630 --> 00:11:03.005 align:middle line:84% like they're in different places. 00:11:03.005 --> 00:11:05.390 align:middle line:84% So sometimes a lead vocal will actually 00:11:05.390 --> 00:11:08.090 align:middle line:84% be pretty dry, so it kind of sounds like it's very close. 00:11:08.090 --> 00:11:10.590 align:middle line:84% Like the backing vocals will have more reverberation on them 00:11:10.590 --> 00:11:12.465 align:middle line:84% to make them sound like they're further away. 00:11:12.465 --> 00:11:16.390 align:middle line:84% So it's a very common kind of production trick. 00:11:16.390 --> 00:11:19.550 align:middle line:84% And you're leveraging the fact that your brain 00:11:19.550 --> 00:11:21.430 align:middle line:84% kind of understands the statistics of reverb 00:11:21.430 --> 00:11:24.830 align:middle line:90% from growing up in the world. 00:11:24.830 --> 00:11:27.710 align:middle line:84% Any other questions about sound localization or distance 00:11:27.710 --> 00:11:28.610 align:middle line:90% or reverb? 00:11:28.610 --> 00:11:31.910 align:middle line:90% 00:11:31.910 --> 00:11:40.350 align:middle line:84% So let's talk about psychophysical methods. 00:11:40.350 --> 00:11:45.230 align:middle line:84% So oftentimes, when we are studying perception, 00:11:45.230 --> 00:11:47.810 align:middle line:90% we deal with thresholds. 00:11:47.810 --> 00:11:51.250 align:middle line:84% So we've talked about the idea of a just-noticeable difference. 00:11:51.250 --> 00:11:53.190 align:middle line:84% So that's kind of like the smallest amount 00:11:53.190 --> 00:11:55.230 align:middle line:90% that you can discriminate. 00:11:55.230 --> 00:11:57.730 align:middle line:84% So we encountered this when we were talking about intensity. 00:11:57.730 --> 00:12:00.990 align:middle line:84% So remember like we talked about how one reason why it's often 00:12:00.990 --> 00:12:03.870 align:middle line:84% convenient to describe sounds with the decibel scale 00:12:03.870 --> 00:12:06.950 align:middle line:84% is that the just-noticeable difference is usually 00:12:06.950 --> 00:12:08.170 align:middle line:90% about one decibel. 00:12:08.170 --> 00:12:10.470 align:middle line:84% And that's true irrespective of whether the sound is 00:12:10.470 --> 00:12:14.450 align:middle line:84% pretty low in level, say, 40 db SPL, or pretty high in level, 00:12:14.450 --> 00:12:16.348 align:middle line:90% say, 90 dB SPL. 00:12:16.348 --> 00:12:17.890 align:middle line:84% So that's just noticeable difference. 00:12:17.890 --> 00:12:18.990 align:middle line:90% It's a threshold. 00:12:18.990 --> 00:12:21.430 align:middle line:84% And so what I want to talk about now 00:12:21.430 --> 00:12:24.550 align:middle line:84% is how you would go about-- is really what we mean by threshold 00:12:24.550 --> 00:12:26.550 align:middle line:84% and how you would go about measuring that, 00:12:26.550 --> 00:12:29.850 align:middle line:84% because it ends up being pretty broadly relevant. 00:12:29.850 --> 00:12:32.470 align:middle line:90% 00:12:32.470 --> 00:12:34.870 align:middle line:84% Historically, there's two types of thresholds 00:12:34.870 --> 00:12:37.180 align:middle line:90% that people talk about. 00:12:37.180 --> 00:12:39.380 align:middle line:84% One is what's called an absolute threshold. 00:12:39.380 --> 00:12:42.620 align:middle line:84% So in the context of sound, this is the minimum audible signal. 00:12:42.620 --> 00:12:45.485 align:middle line:84% So this is what is measured when you get your audiogram measured. 00:12:45.485 --> 00:12:46.860 align:middle line:84% So remember, when we were talking 00:12:46.860 --> 00:12:49.200 align:middle line:84% about hearing impairment, we showed the audiogram. 00:12:49.200 --> 00:12:51.960 align:middle line:84% That's the detection threshold for different frequencies. 00:12:51.960 --> 00:12:53.335 align:middle line:84% It's the thing that kind of looks 00:12:53.335 --> 00:12:56.620 align:middle line:84% a U. Worse at low frequencies and high frequencies, best 00:12:56.620 --> 00:12:57.980 align:middle line:90% at medium frequencies. 00:12:57.980 --> 00:13:00.180 align:middle line:90% So that's an absolute threshold. 00:13:00.180 --> 00:13:02.740 align:middle line:84% The other kind of threshold is a differential threshold 00:13:02.740 --> 00:13:04.160 align:middle line:90% or a discrimination threshold. 00:13:04.160 --> 00:13:07.700 align:middle line:84% And this is the minimum perceptible change. 00:13:07.700 --> 00:13:10.220 align:middle line:84% I like to refer to this as the Just-Noticeable Difference, 00:13:10.220 --> 00:13:11.240 align:middle line:90% or JND. 00:13:11.240 --> 00:13:13.820 align:middle line:84% I like it because it's self-explanatory. 00:13:13.820 --> 00:13:16.900 align:middle line:84% The more classical term in hearing research 00:13:16.900 --> 00:13:18.267 align:middle line:90% is difference limen. 00:13:18.267 --> 00:13:20.600 align:middle line:84% I don't really like it because it's sort of inscrutable, 00:13:20.600 --> 00:13:22.683 align:middle line:84% but that's just what people classically call that, 00:13:22.683 --> 00:13:25.740 align:middle line:84% and so you'll often read papers that talk about the DL. 00:13:25.740 --> 00:13:27.360 align:middle line:84% It's just a discrimination threshold. 00:13:27.360 --> 00:13:31.420 align:middle line:84% So that's what they called it in the old days. 00:13:31.420 --> 00:13:38.020 align:middle line:84% So naively, a threshold is a stimulus value 00:13:38.020 --> 00:13:39.700 align:middle line:90% that you can detect. 00:13:39.700 --> 00:13:42.560 align:middle line:84% So let's say we're talking about the absolute threshold. 00:13:42.560 --> 00:13:45.125 align:middle line:84% So I'm going to play you a 1-kilohertz tone, 00:13:45.125 --> 00:13:47.000 align:middle line:84% and I want to determine your threshold right. 00:13:47.000 --> 00:13:49.460 align:middle line:84% So we're going to vary the intensity of that 1-kilohertz 00:13:49.460 --> 00:13:49.960 align:middle line:90% tone. 00:13:49.960 --> 00:13:51.980 align:middle line:90% And the naive notion is that-- 00:13:51.980 --> 00:13:54.860 align:middle line:84% let's suppose this is a graph where this is the stimulus 00:13:54.860 --> 00:13:57.700 align:middle line:84% level, and this is the proportion of time 00:13:57.700 --> 00:13:59.580 align:middle line:90% that you will detect things. 00:13:59.580 --> 00:14:01.460 align:middle line:84% Naively, the idea of the threshold 00:14:01.460 --> 00:14:04.220 align:middle line:84% is that there is this special value here, 00:14:04.220 --> 00:14:06.920 align:middle line:84% where if the stimulus is below the threshold, 00:14:06.920 --> 00:14:09.680 align:middle line:84% you don't hear it, so you're at 0%. 00:14:09.680 --> 00:14:11.800 align:middle line:84% And if the stimulus is above the threshold, 00:14:11.800 --> 00:14:15.260 align:middle line:84% you hear it, meaning 100% of the time you can detect it. 00:14:15.260 --> 00:14:19.300 align:middle line:84% This is what is known as a psychometric function. 00:14:19.300 --> 00:14:21.195 align:middle line:90% So it plots performance. 00:14:21.195 --> 00:14:22.820 align:middle line:84% In this case, it's the percent of times 00:14:22.820 --> 00:14:25.700 align:middle line:84% you detect the signal as a function of a stimulus 00:14:25.700 --> 00:14:28.500 align:middle line:84% parameter, for instance, the stimulus level. 00:14:28.500 --> 00:14:33.160 align:middle line:84% So that's kind of like the naive idea of what might happen 00:14:33.160 --> 00:14:35.267 align:middle line:84% and what might be associated with the threshold. 00:14:35.267 --> 00:14:36.850 align:middle line:84% Now, in practice, anytime you actually 00:14:36.850 --> 00:14:39.610 align:middle line:84% do an experiment to try to measure this, what you get 00:14:39.610 --> 00:14:42.130 align:middle line:84% is something that looks more like a sigmoid. 00:14:42.130 --> 00:14:46.330 align:middle line:84% So when the stimulus level is very, very low, 00:14:46.330 --> 00:14:48.150 align:middle line:90% people will never hear it. 00:14:48.150 --> 00:14:50.005 align:middle line:84% When you get to these intermediate values, 00:14:50.005 --> 00:14:51.630 align:middle line:84% sometimes people will say they hear it, 00:14:51.630 --> 00:14:53.930 align:middle line:84% sometimes they will say they don't. 00:14:53.930 --> 00:14:56.010 align:middle line:84% And then you'll get into this regime 00:14:56.010 --> 00:14:59.390 align:middle line:84% where people will always say that they hear it. 00:14:59.390 --> 00:15:03.690 align:middle line:84% So in practice, when we are talking about a threshold, 00:15:03.690 --> 00:15:05.690 align:middle line:84% and you're dealing with real data, 00:15:05.690 --> 00:15:08.890 align:middle line:84% you assume some kind of arbitrary level of performance, 00:15:08.890 --> 00:15:11.350 align:middle line:84% and you just define that as the threshold. 00:15:11.350 --> 00:15:13.710 align:middle line:84% So maybe 75% correct, for instance. 00:15:13.710 --> 00:15:16.662 align:middle line:90% 00:15:16.662 --> 00:15:18.370 align:middle line:84% But the threshold is typically associated 00:15:18.370 --> 00:15:19.870 align:middle line:90% with the psychometric function. 00:15:19.870 --> 00:15:22.730 align:middle line:90% So how would you measure this? 00:15:22.730 --> 00:15:26.970 align:middle line:84% So maybe like the simplest type of experiment that you might do 00:15:26.970 --> 00:15:28.810 align:middle line:84% is the one that they often do when 00:15:28.810 --> 00:15:31.150 align:middle line:84% they will measure an audiogram in a doctor's office. 00:15:31.150 --> 00:15:35.170 align:middle line:84% And that's what would be called a one-interval, two-alternative 00:15:35.170 --> 00:15:37.390 align:middle line:90% task, or a yes-no task. 00:15:37.390 --> 00:15:40.570 align:middle line:84% So we're always playing you a tone, 00:15:40.570 --> 00:15:43.050 align:middle line:84% and you have to say whether you hear the tone or not. 00:15:43.050 --> 00:15:46.358 align:middle line:90% 00:15:46.358 --> 00:15:48.110 align:middle line:90% So is there a signal present? 00:15:48.110 --> 00:15:50.258 align:middle line:84% So we could be presenting tones and noise. 00:15:50.258 --> 00:15:52.550 align:middle line:84% That's what we were doing when we talked about masking, 00:15:52.550 --> 00:15:55.453 align:middle line:84% and we were trying to infer auditory filters. 00:15:55.453 --> 00:15:57.370 align:middle line:84% But there's lots of other kind of applications 00:15:57.370 --> 00:15:58.370 align:middle line:90% with this kind of thing. 00:15:58.370 --> 00:16:00.450 align:middle line:84% So for instance, you might want to measure 00:16:00.450 --> 00:16:03.850 align:middle line:84% how well are air traffic controllers can detect aircraft 00:16:03.850 --> 00:16:05.730 align:middle line:84% on a radar screen, or you might want 00:16:05.730 --> 00:16:08.870 align:middle line:84% to measure how well doctors can detect tumors on X-ray images. 00:16:08.870 --> 00:16:12.090 align:middle line:84% These detection tasks are very widespread. 00:16:12.090 --> 00:16:14.530 align:middle line:84% And so the framework that we will talk about 00:16:14.530 --> 00:16:17.270 align:middle line:84% for thinking about them is very broadly relevant. 00:16:17.270 --> 00:16:21.050 align:middle line:84% And the framework is known as signal detection theory. 00:16:21.050 --> 00:16:24.290 align:middle line:84% And so the key idea is that this kind of very simple experiment 00:16:24.290 --> 00:16:28.730 align:middle line:84% that you might naturally think to do is affected by bias. 00:16:28.730 --> 00:16:33.280 align:middle line:84% And what I mean by that is that the results of the experiment 00:16:33.280 --> 00:16:37.960 align:middle line:84% will vary depending on how inclined the observer is 00:16:37.960 --> 00:16:42.600 align:middle line:84% to say yes, independent of how well they actually hear or see 00:16:42.600 --> 00:16:44.740 align:middle line:84% or whatever it is you're trying to measure. 00:16:44.740 --> 00:16:48.160 align:middle line:84% So here, we have observer 1 and observer 2. 00:16:48.160 --> 00:16:50.040 align:middle line:84% We've done the classic experiment 00:16:50.040 --> 00:16:51.840 align:middle line:84% to try to measure an audiogram, which 00:16:51.840 --> 00:16:54.500 align:middle line:84% is we have all these trials where the signal is present. 00:16:54.500 --> 00:16:58.880 align:middle line:84% So let's say it's a 1-kilohertz tone at 10 dB SPL, 00:16:58.880 --> 00:17:00.480 align:middle line:84% pretty close to people's threshold. 00:17:00.480 --> 00:17:04.240 align:middle line:84% So observer 1 says yes to 90% of the tones. 00:17:04.240 --> 00:17:07.960 align:middle line:84% Observer 2 says yes only 65% of the time. 00:17:07.960 --> 00:17:10.400 align:middle line:90% Looks like observer 1 is better. 00:17:10.400 --> 00:17:13.760 align:middle line:84% But the problem here is that observer 1 just 00:17:13.760 --> 00:17:14.980 align:middle line:90% really likes to say yes. 00:17:14.980 --> 00:17:18.160 align:middle line:84% And this is revealed when we also include trials 00:17:18.160 --> 00:17:19.760 align:middle line:90% where the signal is absent. 00:17:19.760 --> 00:17:22.790 align:middle line:84% So you can see that the response proportions for observer 1 00:17:22.790 --> 00:17:25.040 align:middle line:84% are exactly the same when the signal is absent as when 00:17:25.040 --> 00:17:26.560 align:middle line:90% the signal is present. 00:17:26.560 --> 00:17:28.800 align:middle line:90% They're just biased. 00:17:28.800 --> 00:17:31.400 align:middle line:84% Whereas observer 2, these response proportions 00:17:31.400 --> 00:17:32.115 align:middle line:90% change a lot. 00:17:32.115 --> 00:17:33.740 align:middle line:84% So when the signal is actually present, 00:17:33.740 --> 00:17:35.560 align:middle line:84% they say yes a lot more of the time 00:17:35.560 --> 00:17:38.080 align:middle line:90% than when the signal is absent. 00:17:38.080 --> 00:17:40.280 align:middle line:84% So it's kind of clear from looking at these numbers 00:17:40.280 --> 00:17:42.530 align:middle line:84% that you actually have no evidence that observer 1 can 00:17:42.530 --> 00:17:45.862 align:middle line:84% hear anything, whereas you have a fair bit of evidence 00:17:45.862 --> 00:17:48.320 align:middle line:84% that observer 2 is actually sensitive to whether the signal 00:17:48.320 --> 00:17:49.340 align:middle line:90% is there or not. 00:17:49.340 --> 00:17:55.240 align:middle line:90% 00:17:55.240 --> 00:17:57.920 align:middle line:84% So the key concept here is that if you 00:17:57.920 --> 00:17:59.920 align:middle line:84% are doing an experiment like this, 00:17:59.920 --> 00:18:04.460 align:middle line:84% where there is a single interval and the person either says, 00:18:04.460 --> 00:18:06.720 align:middle line:84% yes, I hear it, or no, I don't, you 00:18:06.720 --> 00:18:11.160 align:middle line:84% have to consider both what are called hits and false alarms. 00:18:11.160 --> 00:18:15.900 align:middle line:84% So in this kind of experiment, there are two types of trials. 00:18:15.900 --> 00:18:19.200 align:middle line:84% The first type of trial is where the signal is present. 00:18:19.200 --> 00:18:20.640 align:middle line:90% So we play the beep. 00:18:20.640 --> 00:18:23.200 align:middle line:84% The second type of trial is where there is no signal, 00:18:23.200 --> 00:18:24.920 align:middle line:90% so the beep doesn't get played. 00:18:24.920 --> 00:18:27.610 align:middle line:84% Now, there are two types of responses. 00:18:27.610 --> 00:18:29.750 align:middle line:84% The person can say, yes, I hear something, 00:18:29.750 --> 00:18:31.710 align:middle line:90% or no, I didn't hear anything. 00:18:31.710 --> 00:18:39.430 align:middle line:84% And so that gives us four types of trial-response combinations 00:18:39.430 --> 00:18:42.190 align:middle line:84% A hit is a trial where the signal is present 00:18:42.190 --> 00:18:45.790 align:middle line:84% and the person correctly says, yes, I heard something. 00:18:45.790 --> 00:18:48.390 align:middle line:84% A miss is a trial where the signal is present 00:18:48.390 --> 00:18:52.130 align:middle line:84% and the person says, no, I didn't hear anything. 00:18:52.130 --> 00:18:54.490 align:middle line:84% And if we are computing proportions, 00:18:54.490 --> 00:18:57.070 align:middle line:84% if you know the hit rate-- so that's the proportion 00:18:57.070 --> 00:18:59.790 align:middle line:84% of the signal trials that the person said yes on-- 00:18:59.790 --> 00:19:02.990 align:middle line:84% you also know the miss rate because these two things 00:19:02.990 --> 00:19:06.550 align:middle line:90% have to add up to 1. 00:19:06.550 --> 00:19:08.790 align:middle line:84% When there is not a signal present 00:19:08.790 --> 00:19:10.630 align:middle line:84% and the person incorrectly says, yes, I 00:19:10.630 --> 00:19:13.310 align:middle line:84% heard something, that's called a false alarm. 00:19:13.310 --> 00:19:16.725 align:middle line:84% And if the signal is not present and the person correctly 00:19:16.725 --> 00:19:18.350 align:middle line:84% says no, I didn't hear anything, that's 00:19:18.350 --> 00:19:20.877 align:middle line:90% called a correct rejection. 00:19:20.877 --> 00:19:22.710 align:middle line:84% So again, the proportion of the false alarms 00:19:22.710 --> 00:19:24.970 align:middle line:84% and the correct rejections have to add up to 1, 00:19:24.970 --> 00:19:27.530 align:middle line:84% so you really only need to worry about one of them. 00:19:27.530 --> 00:19:31.390 align:middle line:84% And so the performance of a person in this experiment 00:19:31.390 --> 00:19:34.870 align:middle line:84% can be summarized by these two numbers, the hit 00:19:34.870 --> 00:19:36.490 align:middle line:90% rate and the false alarm rate. 00:19:36.490 --> 00:19:39.030 align:middle line:84% And so the key idea is that if you actually 00:19:39.030 --> 00:19:42.030 align:middle line:84% want to measure how sensitive the person is to the signal, 00:19:42.030 --> 00:19:44.908 align:middle line:84% you have to measure both hits and false alarms. 00:19:44.908 --> 00:19:46.950 align:middle line:84% One of them on their own is not going to tell you 00:19:46.950 --> 00:19:48.230 align:middle line:90% how sensitive they are. 00:19:48.230 --> 00:19:51.005 align:middle line:90% 00:19:51.005 --> 00:19:53.510 align:middle line:84% And this is because subjects or participants 00:19:53.510 --> 00:19:56.350 align:middle line:84% with the same sensitivity can have different biases. 00:19:56.350 --> 00:19:58.110 align:middle line:84% So one subject may err in the direction 00:19:58.110 --> 00:20:00.610 align:middle line:84% of saying the signal is there more often than it is, 00:20:00.610 --> 00:20:03.010 align:middle line:84% while another subject may err in the other direction. 00:20:03.010 --> 00:20:05.750 align:middle line:90% 00:20:05.750 --> 00:20:09.510 align:middle line:84% So the framework that we use to understand this stuff, 00:20:09.510 --> 00:20:11.350 align:middle line:84% as I alluded to earlier, is what's 00:20:11.350 --> 00:20:13.310 align:middle line:90% called signal detection theory. 00:20:13.310 --> 00:20:16.710 align:middle line:84% And this picture here, this is kind of the classical picture 00:20:16.710 --> 00:20:18.982 align:middle line:84% that is associated with signal detection theory, 00:20:18.982 --> 00:20:21.190 align:middle line:84% and it's really worth spending some time to make sure 00:20:21.190 --> 00:20:23.390 align:middle line:90% that you understand this. 00:20:23.390 --> 00:20:27.830 align:middle line:84% So the central assumption of signal detection theory 00:20:27.830 --> 00:20:32.930 align:middle line:84% is that a stimulus elicits a response in the nervous system, 00:20:32.930 --> 00:20:35.430 align:middle line:84% and you base your decisions on that response. 00:20:35.430 --> 00:20:39.170 align:middle line:84% And that response, it is a function of the stimulus, 00:20:39.170 --> 00:20:42.070 align:middle line:90% but it also contains noise. 00:20:42.070 --> 00:20:44.990 align:middle line:84% So the internal response x to a stimulus 00:20:44.990 --> 00:20:48.030 align:middle line:84% can be represented thus as a random variable. 00:20:48.030 --> 00:20:50.550 align:middle line:84% Now, typically we will assume that random variable has 00:20:50.550 --> 00:20:52.590 align:middle line:84% a Gaussian distribution because it kind of just 00:20:52.590 --> 00:20:55.150 align:middle line:90% makes the math simpler. 00:20:55.150 --> 00:20:57.950 align:middle line:84% And because of the central limit theorem, lots of things 00:20:57.950 --> 00:20:59.790 align:middle line:84% are often Gaussian, so it's probably 00:20:59.790 --> 00:21:02.150 align:middle line:90% not a terrible assumption. 00:21:02.150 --> 00:21:06.990 align:middle line:84% But the key consequence of this assumption of internal noise 00:21:06.990 --> 00:21:09.990 align:middle line:84% is that two presentations of the same stimulus 00:21:09.990 --> 00:21:12.970 align:middle line:84% will not necessarily result in identical percepts. 00:21:12.970 --> 00:21:16.490 align:middle line:84% So especially when we get close to threshold, 00:21:16.490 --> 00:21:18.250 align:middle line:84% we can play the exact same stimulus, 00:21:18.250 --> 00:21:19.875 align:middle line:84% sometimes you'll feel like you hear it, 00:21:19.875 --> 00:21:21.160 align:middle line:90% sometimes you might not. 00:21:21.160 --> 00:21:24.700 align:middle line:90% 00:21:24.700 --> 00:21:28.940 align:middle line:84% So the consequence of this is that all 00:21:28.940 --> 00:21:32.460 align:middle line:84% of the trials where the signal is absent 00:21:32.460 --> 00:21:35.660 align:middle line:84% are associated with some particular distribution 00:21:35.660 --> 00:21:37.540 align:middle line:90% of internal responses. 00:21:37.540 --> 00:21:39.560 align:middle line:84% So these are probability distributions. 00:21:39.560 --> 00:21:42.180 align:middle line:84% The y-axis here is probability, the x-axis 00:21:42.180 --> 00:21:43.780 align:middle line:90% is the internal response. 00:21:43.780 --> 00:21:46.740 align:middle line:84% And then all the trials that are associated with the signal being 00:21:46.740 --> 00:21:49.580 align:middle line:84% present also give rise to a distribution 00:21:49.580 --> 00:21:51.980 align:middle line:90% of internal response. 00:21:51.980 --> 00:21:54.845 align:middle line:84% So these are these Gaussian bumps 00:21:54.845 --> 00:21:57.220 align:middle line:84% So this is like the distribution of the internal response 00:21:57.220 --> 00:21:59.980 align:middle line:84% over lots of trials where the signal is present, 00:21:59.980 --> 00:22:05.200 align:middle line:84% and over lots of other trials where the signal is absent. 00:22:05.200 --> 00:22:08.060 align:middle line:84% And you can see that the distributions overlap, 00:22:08.060 --> 00:22:10.060 align:middle line:84% and that's just because of noise. 00:22:10.060 --> 00:22:13.940 align:middle line:90% 00:22:13.940 --> 00:22:17.240 align:middle line:84% So you could think of the task of the observer. 00:22:17.240 --> 00:22:19.740 align:middle line:84% So let's suppose that we're just doing the detection task. 00:22:19.740 --> 00:22:22.140 align:middle line:84% You're trying to determine whether the signal was present 00:22:22.140 --> 00:22:23.060 align:middle line:90% or not. 00:22:23.060 --> 00:22:26.960 align:middle line:84% So your brain gives you a particular value on this axis. 00:22:26.960 --> 00:22:29.340 align:middle line:90% That's the internal response. 00:22:29.340 --> 00:22:32.300 align:middle line:84% You don't know whether that came from the red distribution 00:22:32.300 --> 00:22:33.640 align:middle line:90% or the blue distribution. 00:22:33.640 --> 00:22:35.980 align:middle line:84% Only the experimenter knows that because they're 00:22:35.980 --> 00:22:38.820 align:middle line:84% the person who determined whether the stimulus was present 00:22:38.820 --> 00:22:39.820 align:middle line:90% or not. 00:22:39.820 --> 00:22:43.000 align:middle line:84% And so as the observer, as the participant in this experiment, 00:22:43.000 --> 00:22:46.038 align:middle line:84% you get a value on this axis, and you have to decide, 00:22:46.038 --> 00:22:47.580 align:middle line:84% did it come from the red distribution 00:22:47.580 --> 00:22:49.420 align:middle line:90% or the blue distribution? 00:22:49.420 --> 00:22:52.600 align:middle line:84% And because these distributions overlap, 00:22:52.600 --> 00:22:54.800 align:middle line:84% it will not be possible to do this perfectly. 00:22:54.800 --> 00:22:56.680 align:middle line:84% You're going to get some things wrong. 00:22:56.680 --> 00:23:01.220 align:middle line:90% 00:23:01.220 --> 00:23:08.580 align:middle line:84% So a key quantity in signal detection theory 00:23:08.580 --> 00:23:13.500 align:middle line:84% is this measure of how separated these distributions are. 00:23:13.500 --> 00:23:17.610 align:middle line:84% And so the intuition here is that if a signal is very 00:23:17.610 --> 00:23:20.450 align:middle line:84% detectable-- so let's suppose we're presenting a tone 00:23:20.450 --> 00:23:24.410 align:middle line:84% that's like at 70 dB SPL, so way above threshold-- 00:23:24.410 --> 00:23:28.170 align:middle line:84% these distributions will be very far apart. 00:23:28.170 --> 00:23:30.050 align:middle line:90% So they won't overlap very much. 00:23:30.050 --> 00:23:32.690 align:middle line:84% And that means that you won't have to make very many errors. 00:23:32.690 --> 00:23:35.130 align:middle line:84% But as you get close to threshold, 00:23:35.130 --> 00:23:38.370 align:middle line:84% those distributions will get closer and closer together. 00:23:38.370 --> 00:23:41.690 align:middle line:84% So the measure of how sensitive you 00:23:41.690 --> 00:23:44.210 align:middle line:84% are to the presence of the stimulus 00:23:44.210 --> 00:23:47.090 align:middle line:84% is given by d prime, which is the difference 00:23:47.090 --> 00:23:49.850 align:middle line:84% in the means of these two distributions divided 00:23:49.850 --> 00:23:51.030 align:middle line:90% by the standard deviation. 00:23:51.030 --> 00:23:52.890 align:middle line:84% And for simplicity, we typically assume 00:23:52.890 --> 00:23:55.610 align:middle line:84% that the standard deviation is the same for the signal 00:23:55.610 --> 00:23:57.470 align:middle line:84% present and the signal absent distribution. 00:23:57.470 --> 00:23:59.470 align:middle line:84% So there's some constant level of internal noise 00:23:59.470 --> 00:24:03.330 align:middle line:84% that just gets added to all responses. 00:24:03.330 --> 00:24:05.063 align:middle line:84% But the difficulty of distinguishing 00:24:05.063 --> 00:24:06.730 align:middle line:84% whether the stimulus is presented or not 00:24:06.730 --> 00:24:09.070 align:middle line:84% is determined by how much the distributions overlap. 00:24:09.070 --> 00:24:11.770 align:middle line:90% 00:24:11.770 --> 00:24:15.470 align:middle line:84% So here's a situation where they're separated by a fair bit. 00:24:15.470 --> 00:24:20.430 align:middle line:84% Here's a situation where they are closer. 00:24:20.430 --> 00:24:22.590 align:middle line:84% So if you're doing an experiment, 00:24:22.590 --> 00:24:24.010 align:middle line:84% I said we've got to pay attention 00:24:24.010 --> 00:24:25.390 align:middle line:90% to both hits and false alarms. 00:24:25.390 --> 00:24:28.570 align:middle line:84% And so this quantity, d prime, that 00:24:28.570 --> 00:24:32.130 align:middle line:84% is a measure of how separated these distributions are, 00:24:32.130 --> 00:24:35.090 align:middle line:84% can be estimated by taking the hit rate and the false alarm 00:24:35.090 --> 00:24:38.250 align:middle line:84% rate passing them through z, which 00:24:38.250 --> 00:24:41.290 align:middle line:84% is the inverse of the standard normal cumulative distribution 00:24:41.290 --> 00:24:42.970 align:middle line:84% function-- and that's because we assume 00:24:42.970 --> 00:24:44.750 align:middle line:84% that the internal noise is Gaussian-- 00:24:44.750 --> 00:24:46.450 align:middle line:90% and then taking the difference. 00:24:46.450 --> 00:24:48.860 align:middle line:84% But conceptually, you can think of this 00:24:48.860 --> 00:24:50.610 align:middle line:84% as like this is a function of the hit rate 00:24:50.610 --> 00:24:52.443 align:middle line:84% and it's a function of the false alarm rate, 00:24:52.443 --> 00:24:53.810 align:middle line:90% and we're taking the difference. 00:24:53.810 --> 00:24:54.790 align:middle line:90% So what does that mean? 00:24:54.790 --> 00:24:56.832 align:middle line:84% Well, it means when the hit rate is a lot greater 00:24:56.832 --> 00:24:59.950 align:middle line:84% than the false alarm rate, you're more sensitive. 00:24:59.950 --> 00:25:02.073 align:middle line:84% And as those two things become more similar, 00:25:02.073 --> 00:25:02.990 align:middle line:90% you're less sensitive. 00:25:02.990 --> 00:25:04.890 align:middle line:84% And if they're equal, so if the hit rate is 00:25:04.890 --> 00:25:06.970 align:middle line:84% the same as the false alarm rate, then really, 00:25:06.970 --> 00:25:11.490 align:middle line:84% we have no evidence that you can detect the signal at all. 00:25:11.490 --> 00:25:13.620 align:middle line:84% So if you're actually doing this task, 00:25:13.620 --> 00:25:17.800 align:middle line:84% though, you have to set a criterion So remember, 00:25:17.800 --> 00:25:20.660 align:middle line:84% as an observer performing this experiment, 00:25:20.660 --> 00:25:23.440 align:middle line:84% your nervous system is giving you an internal response, so 00:25:23.440 --> 00:25:26.820 align:middle line:84% some value on this axis And you got to make a decision. 00:25:26.820 --> 00:25:30.280 align:middle line:90% Is the signal there or not? 00:25:30.280 --> 00:25:33.480 align:middle line:84% And that requires setting a criterion, 00:25:33.480 --> 00:25:38.000 align:middle line:84% C, where if the response exceeds the criterion, you say, 00:25:38.000 --> 00:25:39.560 align:middle line:90% yes, I heard something. 00:25:39.560 --> 00:25:42.540 align:middle line:84% And if the response is below the criterion you say, no, 00:25:42.540 --> 00:25:50.000 align:middle line:90% I didn't hear something 00:25:50.000 --> 00:25:54.880 align:middle line:84% And so the key concept here is that your sensitivity does not 00:25:54.880 --> 00:25:57.460 align:middle line:84% depend on where you put the criterion. 00:25:57.460 --> 00:26:01.680 align:middle line:84% So here's a situation where the criterion is up a lot 00:26:01.680 --> 00:26:04.680 align:middle line:84% higher So that corresponds to somebody 00:26:04.680 --> 00:26:06.660 align:middle line:90% being very conservative. 00:26:06.660 --> 00:26:09.880 align:middle line:84% This means that you only say that you heard something 00:26:09.880 --> 00:26:12.620 align:middle line:84% when that internal response is very, very high. 00:26:12.620 --> 00:26:16.960 align:middle line:90% 00:26:16.960 --> 00:26:21.960 align:middle line:84% Whereas back here, you're more liberal, 00:26:21.960 --> 00:26:23.960 align:middle line:84% and you're going to say yes to everything 00:26:23.960 --> 00:26:26.960 align:middle line:90% that exceeds this value. 00:26:26.960 --> 00:26:30.200 align:middle line:84% So how do the hit rate and the false alarm rate 00:26:30.200 --> 00:26:32.560 align:middle line:84% relate to this particular diagram? 00:26:32.560 --> 00:26:36.600 align:middle line:84% Well, the hit rate, remember, is the proportion 00:26:36.600 --> 00:26:40.200 align:middle line:84% of trials where the signal is actually present, where you say, 00:26:40.200 --> 00:26:41.920 align:middle line:90% yes, I heard something. 00:26:41.920 --> 00:26:45.578 align:middle line:84% Now, what we're positing here is that you're 00:26:45.578 --> 00:26:47.120 align:middle line:84% going to say that you heard something 00:26:47.120 --> 00:26:50.540 align:middle line:84% any time the internal response exceeds the criterion. 00:26:50.540 --> 00:26:53.540 align:middle line:84% So that's any time the response is above here. 00:26:53.540 --> 00:26:57.400 align:middle line:90% 00:26:57.400 --> 00:27:00.580 align:middle line:84% Now, for the trials where the signal is present, 00:27:00.580 --> 00:27:02.560 align:middle line:84% we've got the red distribution here. 00:27:02.560 --> 00:27:04.840 align:middle line:84% And so the proportion of trials where 00:27:04.840 --> 00:27:07.780 align:middle line:84% the target is present for which you will respond yes 00:27:07.780 --> 00:27:09.870 align:middle line:84% is going to be going to be the integral 00:27:09.870 --> 00:27:12.890 align:middle line:84% of this red distribution from the criterion 00:27:12.890 --> 00:27:14.432 align:middle line:84% all the way up to positive infinity. 00:27:14.432 --> 00:27:15.890 align:middle line:84% So that's going to be the hit rate. 00:27:15.890 --> 00:27:17.910 align:middle line:84% It's the area under the red curve. 00:27:17.910 --> 00:27:20.790 align:middle line:84% And similarly, the false alarm rate 00:27:20.790 --> 00:27:22.910 align:middle line:84% will be the area under the blue curve that 00:27:22.910 --> 00:27:24.710 align:middle line:90% exceeds that same criterion. 00:27:24.710 --> 00:27:28.150 align:middle line:84% And you can see here, that this area under the red curve 00:27:28.150 --> 00:27:30.972 align:middle line:84% is a lot bigger than this area under the blue curve. 00:27:30.972 --> 00:27:32.430 align:middle line:84% And so the person was going to have 00:27:32.430 --> 00:27:33.930 align:middle line:90% a positive value of d prime. 00:27:33.930 --> 00:27:35.070 align:middle line:90% Yeah? 00:27:35.070 --> 00:27:37.230 align:middle line:84% AUDIENCE: Is this criterion always constant 00:27:37.230 --> 00:27:43.310 align:middle line:84% or is this a Fourier line that it's been shown on? 00:27:43.310 --> 00:27:45.030 align:middle line:84% JOSH MCDERMOTT: That's a great question. 00:27:45.030 --> 00:27:46.950 align:middle line:90% So it could be constant. 00:27:46.950 --> 00:27:50.550 align:middle line:84% But really, this is a function of the observer. 00:27:50.550 --> 00:27:53.430 align:middle line:84% And the criterion could, in practice, drift around. 00:27:53.430 --> 00:27:55.950 align:middle line:84% And in practice, one of the things 00:27:55.950 --> 00:28:00.130 align:middle line:84% that is challenging about running an experiment like this, 00:28:00.130 --> 00:28:02.070 align:middle line:84% where there's just a single interval, 00:28:02.070 --> 00:28:04.190 align:middle line:84% is the fact that the observer has to figure out 00:28:04.190 --> 00:28:05.810 align:middle line:90% where to set their criterion. 00:28:05.810 --> 00:28:08.430 align:middle line:84% And they may initially not be very sure, 00:28:08.430 --> 00:28:10.550 align:middle line:84% and it may change from trial to trial. 00:28:10.550 --> 00:28:12.385 align:middle line:84% And so that's one of the messy things 00:28:12.385 --> 00:28:14.510 align:middle line:84% that you sometimes have to deal with with this type 00:28:14.510 --> 00:28:16.470 align:middle line:90% of experiment. 00:28:16.470 --> 00:28:19.970 align:middle line:84% But this particular framework here, we are, for the moment, 00:28:19.970 --> 00:28:22.130 align:middle line:84% assuming that the criterion is a fixed value. 00:28:22.130 --> 00:28:26.410 align:middle line:84% So if you want to compute a hit rate and false alarm rate, 00:28:26.410 --> 00:28:28.290 align:middle line:84% you're assuming a fixed criterion. 00:28:28.290 --> 00:28:28.790 align:middle line:90% Yeah. 00:28:28.790 --> 00:28:33.230 align:middle line:90% 00:28:33.230 --> 00:28:40.350 align:middle line:84% So there's an alternative way of doing the experiment where 00:28:40.350 --> 00:28:43.780 align:middle line:90% life gets a little bit simpler. 00:28:43.780 --> 00:28:46.430 align:middle line:84% And that's called a two-interval, 00:28:46.430 --> 00:28:48.810 align:middle line:84% two alternative forced choice experiment. 00:28:48.810 --> 00:28:52.310 align:middle line:84% And so in this type of experiment, on a given trial, 00:28:52.310 --> 00:28:55.270 align:middle line:84% there are two intervals, interval 1 and interval 2. 00:28:55.270 --> 00:28:58.230 align:middle line:84% This is an example experiment where 00:28:58.230 --> 00:29:02.350 align:middle line:84% the task is to detect a tone that is being played in noise. 00:29:02.350 --> 00:29:04.350 align:middle line:84% So this is like one of these masking experiments 00:29:04.350 --> 00:29:06.920 align:middle line:84% that we talked about a couple lectures ago. 00:29:06.920 --> 00:29:10.500 align:middle line:84% So we've got the signal here and the noise. 00:29:10.500 --> 00:29:13.640 align:middle line:84% One of the intervals-- here, it's depicted as interval 1, 00:29:13.640 --> 00:29:15.420 align:middle line:84% but it would randomly be assigned 00:29:15.420 --> 00:29:16.600 align:middle line:90% to interval 1 or interval 2. 00:29:16.600 --> 00:29:18.440 align:middle line:84% One of the intervals will contain the tone. 00:29:18.440 --> 00:29:22.980 align:middle line:84% The other interval will just contain the noise. 00:29:22.980 --> 00:29:25.380 align:middle line:84% And now the task is just to determine which 00:29:25.380 --> 00:29:26.520 align:middle line:90% interval the signal is in. 00:29:26.520 --> 00:29:30.726 align:middle line:90% Is it the first or the second? 00:29:30.726 --> 00:29:34.200 align:middle line:84% So the advantage of this type of task is that as a participant, 00:29:34.200 --> 00:29:37.380 align:middle line:84% you don't have to figure out where to set your criterion. 00:29:37.380 --> 00:29:39.060 align:middle line:84% You're just comparing the two intervals 00:29:39.060 --> 00:29:41.780 align:middle line:84% and trying to decide which one contains the tone. 00:29:41.780 --> 00:29:45.120 align:middle line:84% And that reduces the effects of subject bias, 00:29:45.120 --> 00:29:47.620 align:middle line:84% and it reduces this issue with the criterion possibly moving 00:29:47.620 --> 00:29:51.340 align:middle line:84% around and the person having to figure out where to set it. 00:29:51.340 --> 00:29:53.140 align:middle line:84% But you can map this kind of experiment 00:29:53.140 --> 00:29:56.580 align:middle line:84% onto the signal detection framework just as well. 00:29:56.580 --> 00:30:01.180 align:middle line:84% So now the task is to decide which of the intervals 00:30:01.180 --> 00:30:02.840 align:middle line:90% actually contains your signal. 00:30:02.840 --> 00:30:06.160 align:middle line:84% And so the idea is that on every trial, 00:30:06.160 --> 00:30:08.983 align:middle line:84% you're getting one sample from the red distribution and one 00:30:08.983 --> 00:30:10.400 align:middle line:84% sample from the blue distribution, 00:30:10.400 --> 00:30:13.540 align:middle line:84% because one of the intervals has your signal and the other 00:30:13.540 --> 00:30:14.680 align:middle line:90% interval doesn't. 00:30:14.680 --> 00:30:17.300 align:middle line:84% And the decision rule is just going 00:30:17.300 --> 00:30:19.660 align:middle line:84% to be whether the internal response is 00:30:19.660 --> 00:30:23.580 align:middle line:84% greater in the first interval compared to the second interval. 00:30:23.580 --> 00:30:26.660 align:middle line:84% Now, in this particular trial, you can see that the red 00:30:26.660 --> 00:30:29.860 align:middle line:84% sample-- so the internal response from the interval where 00:30:29.860 --> 00:30:31.460 align:middle line:90% the signal was present-- 00:30:31.460 --> 00:30:33.940 align:middle line:84% is greater than the blue sample, the interval 00:30:33.940 --> 00:30:35.440 align:middle line:90% where the signal was absent. 00:30:35.440 --> 00:30:39.460 align:middle line:84% And so here, you would get the trial correct because this 00:30:39.460 --> 00:30:40.660 align:middle line:90% is higher than this. 00:30:40.660 --> 00:30:42.500 align:middle line:84% But that doesn't always have to be 00:30:42.500 --> 00:30:45.640 align:middle line:84% the case because these responses are, to some extent, random. 00:30:45.640 --> 00:30:47.980 align:middle line:84% So here would be a case where you got unlucky 00:30:47.980 --> 00:30:51.420 align:middle line:84% and your brain gave you a bigger response on the interval where 00:30:51.420 --> 00:30:56.120 align:middle line:90% the signal was absent. 00:30:56.120 --> 00:30:59.563 align:middle line:84% But in this particular case, over time, over lots of trials, 00:30:59.563 --> 00:31:01.980 align:middle line:84% you'd get things right more than you would get them wrong. 00:31:01.980 --> 00:31:08.020 align:middle line:84% And so your proportion correct would be above chance. 00:31:08.020 --> 00:31:12.620 align:middle line:84% So you can use this 2AFC task, and the advantage here is you 00:31:12.620 --> 00:31:15.200 align:middle line:84% don't have to-- there's no hits, there's no false alarms. 00:31:15.200 --> 00:31:17.260 align:middle line:84% You just measure percent correct, 00:31:17.260 --> 00:31:19.700 align:middle line:84% and that's the measure of sensitivity Whereas 00:31:19.700 --> 00:31:22.140 align:middle line:84% for the one-interval tasks, percent correct 00:31:22.140 --> 00:31:23.660 align:middle line:84% is vulnerable to bias, so you have 00:31:23.660 --> 00:31:26.160 align:middle line:84% to measure both hits and false alarms and compute d prime. 00:31:26.160 --> 00:31:27.820 align:middle line:84% And then the person has to figure out 00:31:27.820 --> 00:31:30.040 align:middle line:90% where to put their criterion 00:31:30.040 --> 00:31:32.540 align:middle line:84% So we've got these two types of psychophysical tasks, 00:31:32.540 --> 00:31:35.420 align:middle line:84% one-interval tasks and two-interval, 00:31:35.420 --> 00:31:37.940 align:middle line:84% two alternative forced choice tasks. 00:31:37.940 --> 00:31:41.020 align:middle line:84% There are various advantages to the 2AFC task. 00:31:41.020 --> 00:31:43.380 align:middle line:84% Now, how do you measure a threshold? 00:31:43.380 --> 00:31:45.620 align:middle line:84% So the simplest way to do this is 00:31:45.620 --> 00:31:48.000 align:middle line:84% to generate a psychometric function 00:31:48.000 --> 00:31:50.220 align:middle line:84% And the way that you do that is what is called 00:31:50.220 --> 00:31:53.100 align:middle line:90% the method of constant stimuli. 00:31:53.100 --> 00:31:55.220 align:middle line:84% I've always found this to be a confusing way 00:31:55.220 --> 00:31:57.348 align:middle line:84% to describe this because it somehow 00:31:57.348 --> 00:31:59.140 align:middle line:84% makes me feel like it's an experiment where 00:31:59.140 --> 00:32:00.765 align:middle line:84% the stimuli never changed or something, 00:32:00.765 --> 00:32:02.190 align:middle line:90% which is not what it means. 00:32:02.190 --> 00:32:06.242 align:middle line:84% What it means is that you have to decide beforehand 00:32:06.242 --> 00:32:08.450 align:middle line:84% what all the stimuli are going to be that you present 00:32:08.450 --> 00:32:09.930 align:middle line:90% in the experiment. 00:32:09.930 --> 00:32:11.690 align:middle line:84% And then you run a bunch of trials of each 00:32:11.690 --> 00:32:13.170 align:middle line:84% because this is what's going to be 00:32:13.170 --> 00:32:14.427 align:middle line:90% the outcome of the experiment. 00:32:14.427 --> 00:32:16.510 align:middle line:84% You're going to generate a psychometric function-- 00:32:16.510 --> 00:32:20.130 align:middle line:84% remember, the psychometric function plots performance. 00:32:20.130 --> 00:32:22.890 align:middle line:84% So if this is a 2AFC task, the performance here would be 00:32:22.890 --> 00:32:26.330 align:middle line:84% percent correct If it was a one-interval task, 00:32:26.330 --> 00:32:30.545 align:middle line:84% this would be d prime versus some stimulus parameter. 00:32:30.545 --> 00:32:32.170 align:middle line:84% In this case, the signal level if we're 00:32:32.170 --> 00:32:35.090 align:middle line:90% measuring a detection threshold 00:32:35.090 --> 00:32:39.450 align:middle line:84% So for a 2AFC task, chance performance is 50% So when 00:32:39.450 --> 00:32:41.250 align:middle line:84% the signal level is below your threshold, 00:32:41.250 --> 00:32:44.250 align:middle line:84% you'll just be guessing, and you'll get 50% right on average. 00:32:44.250 --> 00:32:46.210 align:middle line:84% And then as the signal level increases, 00:32:46.210 --> 00:32:47.630 align:middle line:90% you get better and better. 00:32:47.630 --> 00:32:49.810 align:middle line:84% And so you get this kind of sigmoid-like curve. 00:32:49.810 --> 00:32:52.090 align:middle line:84% And then, typically we define the threshold 00:32:52.090 --> 00:32:55.710 align:middle line:84% as being the point that gives you 75% correct, for instance. 00:32:55.710 --> 00:33:00.570 align:middle line:84% And that would be about 57 dB in this particular case. 00:33:00.570 --> 00:33:03.750 align:middle line:84% So it's called the method of constant stimuli 00:33:03.750 --> 00:33:05.630 align:middle line:84% because before you do the experiment, 00:33:05.630 --> 00:33:10.010 align:middle line:84% you have to decide what values on the x-axis you're 00:33:10.010 --> 00:33:11.530 align:middle line:90% going to present. 00:33:11.530 --> 00:33:14.530 align:middle line:84% So you're going to have a whole bunch of trials 00:33:14.530 --> 00:33:18.010 align:middle line:84% where the signal is 51 dB, maybe 100 of those. 00:33:18.010 --> 00:33:20.827 align:middle line:84% And then you measure how many of those people get correct. 00:33:20.827 --> 00:33:22.410 align:middle line:84% And then a whole bunch of trials where 00:33:22.410 --> 00:33:28.010 align:middle line:84% it's 52, 53, 54, so on and so forth, all the way up to 63. 00:33:28.010 --> 00:33:31.815 align:middle line:84% So the experimenter decides that ahead of time, you 00:33:31.815 --> 00:33:33.690 align:middle line:84% run all those trials, you measure performance 00:33:33.690 --> 00:33:36.270 align:middle line:84% as a function of the stimulus level. 00:33:36.270 --> 00:33:37.770 align:middle line:84% You get your psychometric function, 00:33:37.770 --> 00:33:42.052 align:middle line:84% and you estimate your threshold from the psychometric function. 00:33:42.052 --> 00:33:43.510 align:middle line:84% And that can be a fine thing to do. 00:33:43.510 --> 00:33:45.052 align:middle line:84% Psychometric functions are beautiful. 00:33:45.052 --> 00:33:47.105 align:middle line:90% They look nice in papers. 00:33:47.105 --> 00:33:48.730 align:middle line:84% It can often be a good way to make sure 00:33:48.730 --> 00:33:50.772 align:middle line:84% that things make sense, that performance actually 00:33:50.772 --> 00:33:53.850 align:middle line:84% goes up as you increase the stimulus parameter. 00:33:53.850 --> 00:33:57.800 align:middle line:84% On the other hand, you have to know beforehand what 00:33:57.800 --> 00:34:00.100 align:middle line:90% the relevant dynamic range is. 00:34:00.100 --> 00:34:01.485 align:middle line:84% If you want to hit the threshold, 00:34:01.485 --> 00:34:03.360 align:middle line:84% and you happen to choose stimulus values that 00:34:03.360 --> 00:34:06.520 align:middle line:84% are out here, or down here, you're not 00:34:06.520 --> 00:34:08.620 align:middle line:84% going to get a very useful result. 00:34:08.620 --> 00:34:11.360 align:middle line:84% And the other thing that's kind of suboptimal about it 00:34:11.360 --> 00:34:14.280 align:middle line:84% is that you spend quite a lot of trials 00:34:14.280 --> 00:34:16.822 align:middle line:84% on this region of the curve, and on this region of the curve, 00:34:16.822 --> 00:34:18.905 align:middle line:84% which really are not very relevant to constraining 00:34:18.905 --> 00:34:19.739 align:middle line:90% the threshold. 00:34:19.739 --> 00:34:21.156 align:middle line:84% The threshold is mostly determined 00:34:21.156 --> 00:34:25.159 align:middle line:84% by these kinds of values, so it's sort of inefficient. 00:34:25.159 --> 00:34:27.679 align:middle line:84% So to address these issues there's 00:34:27.679 --> 00:34:29.760 align:middle line:84% an alternative way to measure thresholds, which 00:34:29.760 --> 00:34:32.120 align:middle line:84% is what is called an adaptive procedure, 00:34:32.120 --> 00:34:35.600 align:middle line:84% also sometimes referred to as a staircase. 00:34:35.600 --> 00:34:38.480 align:middle line:84% And so the idea of the adaptive procedure 00:34:38.480 --> 00:34:41.212 align:middle line:84% is that you start people off with kind 00:34:41.212 --> 00:34:44.040 align:middle line:90% of a easy version of the task. 00:34:44.040 --> 00:34:46.613 align:middle line:84% So you set the stimulus parameter to a value 00:34:46.613 --> 00:34:48.280 align:middle line:84% that you're pretty confident everybody's 00:34:48.280 --> 00:34:50.760 align:middle line:90% going to be able to detect. 00:34:50.760 --> 00:34:53.199 align:middle line:84% And if they get things-- if they get things right, 00:34:53.199 --> 00:34:55.320 align:middle line:90% then you make the task harder. 00:34:55.320 --> 00:34:58.465 align:middle line:84% If they continue to get it right, you make it even harder. 00:34:58.465 --> 00:35:00.340 align:middle line:84% And then once they start to get things wrong, 00:35:00.340 --> 00:35:02.080 align:middle line:90% you make it a little bit easier. 00:35:02.080 --> 00:35:04.460 align:middle line:84% And what happens if you do this is, in theory, 00:35:04.460 --> 00:35:06.840 align:middle line:84% you should converge to a value that 00:35:06.840 --> 00:35:08.880 align:middle line:90% corresponds to the threshold. 00:35:08.880 --> 00:35:12.880 align:middle line:84% So that's the kind of intuitive picture. 00:35:12.880 --> 00:35:14.720 align:middle line:84% One kind of classic way to do this 00:35:14.720 --> 00:35:18.620 align:middle line:84% is what's called an X-down Y-up adaptive procedure. 00:35:18.620 --> 00:35:21.640 align:middle line:84% So for instance, two down, one up. 00:35:21.640 --> 00:35:22.820 align:middle line:90% So what does that mean? 00:35:22.820 --> 00:35:25.400 align:middle line:84% That means if you get two in a row correct, 00:35:25.400 --> 00:35:29.520 align:middle line:84% you move the stimulus level down one step. 00:35:29.520 --> 00:35:32.280 align:middle line:84% If you get something wrong, you move the stimulus level 00:35:32.280 --> 00:35:33.440 align:middle line:90% up one step. 00:35:33.440 --> 00:35:36.720 align:middle line:90% So here's how this would work. 00:35:36.720 --> 00:35:39.560 align:middle line:84% So you start out your experiment with some pretty high stimulus 00:35:39.560 --> 00:35:40.600 align:middle line:90% level. 00:35:40.600 --> 00:35:43.340 align:middle line:84% Person does two trials, they get both of them correct, 00:35:43.340 --> 00:35:46.120 align:middle line:84% so the stimulus level is lowered by the experimenter. 00:35:46.120 --> 00:35:49.520 align:middle line:84% The person gets another two correct, it's lowered. 00:35:49.520 --> 00:35:51.380 align:middle line:84% Get another two correct, it's lowered. 00:35:51.380 --> 00:35:53.650 align:middle line:84% They get one correct, oh, they get one wrong. 00:35:53.650 --> 00:35:55.662 align:middle line:84% So that means that the stimulus level goes up. 00:35:55.662 --> 00:35:57.370 align:middle line:84% They get two correct, so it gets lowered. 00:35:57.370 --> 00:35:58.890 align:middle line:84% They get two correct, it gets lowered. 00:35:58.890 --> 00:36:00.182 align:middle line:90% They get one wrong, it goes up. 00:36:00.182 --> 00:36:01.550 align:middle line:90% They get one wrong, it goes up. 00:36:01.550 --> 00:36:02.710 align:middle line:90% Two correct, it goes down. 00:36:02.710 --> 00:36:04.270 align:middle line:90% Two correct, it goes down. 00:36:04.270 --> 00:36:06.570 align:middle line:84% One wrong, it goes up, and so on and so forth. 00:36:06.570 --> 00:36:09.810 align:middle line:84% And so what happens is that you kind of, in theory, 00:36:09.810 --> 00:36:11.390 align:middle line:84% find your way to this regime where 00:36:11.390 --> 00:36:13.890 align:middle line:84% people are getting some of the trials right and some of them 00:36:13.890 --> 00:36:15.190 align:middle line:90% wrong. 00:36:15.190 --> 00:36:18.910 align:middle line:84% And so for instance, this particular adaptive procedure 00:36:18.910 --> 00:36:21.590 align:middle line:84% rule, the two down, one up rule will 00:36:21.590 --> 00:36:26.730 align:middle line:84% converge to a stimulus value that will give you 70.7% 00:36:26.730 --> 00:36:27.530 align:middle line:90% correct. 00:36:27.530 --> 00:36:31.610 align:middle line:84% And you can work out exactly why that is. 00:36:31.610 --> 00:36:33.990 align:middle line:84% So what are the advantages of this? 00:36:33.990 --> 00:36:36.710 align:middle line:84% Well, in theory, it should be more efficient 00:36:36.710 --> 00:36:38.310 align:middle line:84% because you don't spend a ton of time 00:36:38.310 --> 00:36:40.830 align:middle line:84% with trials that are super easy or super hard. 00:36:40.830 --> 00:36:43.190 align:middle line:84% You find your way to the relevant part 00:36:43.190 --> 00:36:45.070 align:middle line:90% of the stimulus space. 00:36:45.070 --> 00:36:47.390 align:middle line:84% It also has the nice advantage that you can start out 00:36:47.390 --> 00:36:49.430 align:middle line:84% the experiment really easy, so the person 00:36:49.430 --> 00:36:51.710 align:middle line:84% can figure out what they're supposed to be doing. 00:36:51.710 --> 00:36:53.130 align:middle line:84% So you give them a bunch of easy trials, 00:36:53.130 --> 00:36:54.838 align:middle line:84% they build up their confidence and stuff, 00:36:54.838 --> 00:37:00.630 align:middle line:84% and then you move down into the more difficult regime. 00:37:00.630 --> 00:37:02.230 align:middle line:84% The disadvantage of this is that you 00:37:02.230 --> 00:37:04.710 align:middle line:84% don't end up with the full psychometric function. 00:37:04.710 --> 00:37:07.290 align:middle line:84% You just get a threshold estimate to come out of this. 00:37:07.290 --> 00:37:09.190 align:middle line:84% And so sometimes you might want to know 00:37:09.190 --> 00:37:13.590 align:middle line:84% what the actual psychometric function kind of looks like. 00:37:13.590 --> 00:37:19.710 align:middle line:84% So just to summarize, I talked about the distinction between 00:37:19.710 --> 00:37:25.830 align:middle line:84% one-interval yes/no tasks and two-interval 2AFC tasks. 00:37:25.830 --> 00:37:27.630 align:middle line:84% So key thing to take away from this 00:37:27.630 --> 00:37:29.630 align:middle line:84% is that with one-interval tasks, you 00:37:29.630 --> 00:37:32.190 align:middle line:84% have to measure both hits and false alarms 00:37:32.190 --> 00:37:35.830 align:middle line:84% and compute d prime as a measure of sensitivity. 00:37:35.830 --> 00:37:37.470 align:middle line:90% You can't use percent correct. 00:37:37.470 --> 00:37:40.090 align:middle line:84% And the challenge is that the observer has to set a criterion. 00:37:40.090 --> 00:37:42.730 align:middle line:84% And as we discussed, maybe that would move around, 00:37:42.730 --> 00:37:45.790 align:middle line:84% maybe they wouldn't know where to put it. 00:37:45.790 --> 00:37:48.490 align:middle line:84% If you use a 2AFC task, you can just measure percent correct, 00:37:48.490 --> 00:37:51.620 align:middle line:84% and that gives you a bias-free measure of sensitivity. 00:37:51.620 --> 00:37:53.980 align:middle line:84% And then we discussed two ways to measure a threshold. 00:37:53.980 --> 00:37:56.540 align:middle line:84% One is the method of constant stimuli, where 00:37:56.540 --> 00:37:58.220 align:middle line:84% you decide on a bunch of stimulus values 00:37:58.220 --> 00:37:59.887 align:middle line:84% that you want to measure performance at, 00:37:59.887 --> 00:38:01.973 align:middle line:90% you get a psychometric function. 00:38:01.973 --> 00:38:04.140 align:middle line:84% The other is an adaptive procedure, sometimes called 00:38:04.140 --> 00:38:07.480 align:middle line:84% a staircase, where you converge on a stimulus value 00:38:07.480 --> 00:38:09.980 align:middle line:84% where people are getting some of them right and some of them 00:38:09.980 --> 00:38:10.460 align:middle line:90% wrong. 00:38:10.460 --> 00:38:12.752 align:middle line:84% That will just give you a threshold estimate as opposed 00:38:12.752 --> 00:38:14.340 align:middle line:90% to the psychometric function. 00:38:14.340 --> 00:38:15.900 align:middle line:84% And the threshold in both cases is 00:38:15.900 --> 00:38:18.340 align:middle line:84% defined as the stimulus parameter that 00:38:18.340 --> 00:38:21.480 align:middle line:84% is needed to achieve some criterion level of performance, 00:38:21.480 --> 00:38:23.990 align:middle line:90% like 75% correct. 00:38:23.990 --> 00:38:26.240 align:middle line:84% That is the whirlwind guide to psychophysical methods. 00:38:26.240 --> 00:38:28.260 align:middle line:84% That's how you measure thresholds. 00:38:28.260 --> 00:38:31.620 align:middle line:84% Next time, we will talk about pitch perception and pitch 00:38:31.620 --> 00:38:33.500 align:middle line:90% discrimination thresholds. 00:38:33.500 --> 00:38:35.730 align:middle line:90% So I will see you then. 00:38:35.730 --> 00:38:48.000 align:middle line:90%