Stat 301 Day 24 Fishers Exact Test Announcements

Announcements n n Project 2 proposals HW 6 q q n First problem extends

This week n n n What about an exact p-value? What about random sampling

Finding the p-value n Fix the success/failure outcomes q Simulation: Model the random shuffling

Investigation 3. 7 (p. 216) (g) C(50, 16) (h) C(14, 10) x C(36, 24)

Fisher’s Exact Test n Let X count the number of successes in a sample

Yawning study M N n Let X represent the number of yawners in the

Yawning study (o) Let X represent the number of non-yawners in the no-yawn-seed group

Fisher’s Exact Test n Once have the two-way table, are multiple equivalent ways to

To Do n n n Quiz 20 Submit project 2 proposal Review Investigation 3.

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Stat 301 – Day 24 Fisher’s Exact Test

Announcements n n Project 2 proposals HW 6 q q n First problem extends from class tomorrow Other problems can do most of the pieces after today (will discuss relative risk and odds ratio on Thursday) Exam 2 next Tuesday

Last Time – Normal approximation n

Quiz 21

This week n n n What about an exact p-value? What about random sampling rather than random assignment? What about statistics other than the difference in the sample proportions?

Investigation 3. 7 (p. 214)

Finding the p-value n Fix the success/failure outcomes q Simulation: Model the random shuffling of the outcomes to the two treatment groups (of the same size) Blue cards Green cards How many ways are there to deal 50 cards into piles of 34 and 16? How many of these end up with 10 or more blue cards in group A?

Investigation 3. 7 (p. 216) (g) C(50, 16) (h) C(14, 10) x C(36, 24) (i) P(X = 10) = C(14, 10) C(26, 24)/ C(50, 16)

Fisher’s Exact Test n Let X count the number of successes in a sample of n objects selected from a population of N objects consisting of M successes n Two-way table applet, JMP, R

JMP

Yawning study M N n Let X represent the number of yawners in the yawn seed group p-value = P(X > 10) with N = 50, M = 14, n = 34 (n) Success = “not yawning” M N n p-value = P(X < 24) with N = 50, M = 36, n = 34

Yawning study (o) Let X represent the number of non-yawners in the no-yawn-seed group M N n p-value = P(X > 12) with M = 36, n = 16, N = 50

Fisher’s Exact Test n Once have the two-way table, are multiple equivalent ways to calculate the p-value. q q q Identifying values of M, n, and N and writing out P(X ? ? )… Include detail on how you carried out the calculation (which inputs, which technology) Interpretation of p-value: X% of “random shuffles” would have a difference in proportions at least as extreme (larger or smaller? ) as XX assuming no treatment effect (null hypothesis is true)

Investigation 3. 1 (p. 183)

To Do n n n Quiz 20 Submit project 2 proposal Review Investigation 3. 1 (a)-(j)