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# File: MIT18_05S22_in-class18-script.txt
# Author: Jeremy Orloff
#
# MIT OpenCourseWare: https://ocw.mit.edu
# 18.05 Introduction to Probability and Statistics
# Spring 2022
# For information about citing these materials or our Terms of Use, visit:
# https://ocw.mit.edu/terms.
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Class 18 NHST: significance, power, t-tests
Jerry
Slide 1
Slide 2: Announcements/Agenda (2 minutes)
Slide 3: Understand this figure (4 minutes)
We use this figure all the time.
It turns out that many students don't really understand it
This is an attempt tackle this problem head on.
Slide 4: Simple and composite hypotheses (2 minutes)
Key point: simple: the sampling distribution well-defined;
composite: sampling distribution depends on which value of parameter
Slides 5 --Outlines pieces of NHST (3 minutes)
Slides 6-7: Meaning of p-values --one sided (3 minutes)
Many paused slides
Slide 8: Critical values (2 minutes)
Slide 9: Meaning of p-value: two-sided (4 minutes)
Key point min(left prob, right prob) < alpha/2 --> reject
Slides 10abc CONCEPT questions (8 minutes)
Computing critical values and p values
Draw some pictures
10c. We obviously don't reject because
z = 1.8 and the test is LEFT-sided
Slide 11: Error, significance, power (3 minutes)
Key: power and significance, both prob(test stat in rej. region)
Jen
Slide 12 TABLE QUESTION significance and power (3 minutes work, 3 minutes discussion)
DISCUSSION: KEY POINT: both are probabilities of
rejection region for the correct hypothesis.
Prob. of type II depends on H_A = 1 - power
Slide 13 CONCEPT question power is given by what area (5 minutes)
key explanation: power = P(x in rejection region | H_A)
Slide 14 CONCEPT question which has higher power (5 minutes)
-- Have test statistic, null distribution, rejection region
-- Have alternative distrtribution
-- Power = area under alt. distr above rejection region
Slide 15 Discussion (6 minutes)
SKIP THIS IF NOT ENOUGH TIME TO GET TO THE BOARD QUESTION
Give them a chance to discuss without any hints.
Rejection region > 2\sigma, so alpha \approx 0.025
Trick question: Can't compute power without specificying H_A
Slide 16: reminder z test (2 minutes)
Key --use a specific known value of mu_0
Slide 17 One sample t-test (2 minutes)
Just like z-test except: use sample variance instead of true variance.
So get a different null distribution
Slide 18 BOARD Question: z and 1-sample t (Work 8 minutes, discussion 4 minutes)
Discussion: brief. Compute stat, use known null distribution to compute p-value.
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Probably won't get to here
If a little bit of time left, skip to discussion on slides 21-23
Slide 19 Two sample t-test review of formulas (1 minutes)
Jerry
Slide 20 BOARD question: 2-sample t-test (Work: 8 minutes, discussion: 4 minutes)
BRIEF DISCUSSION: No computation. You compute the test stat and use
the known null distribution to compute the p-value
Point them to posted solutions
Slides 21-23 Discussion: effect of base rate (6 minutes)
Key: these asks for prob. of a hypothesis
Use board to write prob. being referred to
Q1: P(H0 is true | published) = P(H0 | rejection) --can't answer
Q2: (b) Same --given baserates so can answer: 100 %
Q3: (b) Same --given baserates so can answer: 0 %