1. Psychology 202a Advanced Psychological Statistics October 1, 2015

2. The Plan for Today What if we don’t know the sampling distribution of a statistic? The Z test Assumptions The two-sample Z test The t test

3. What if we don’t know the sampling distribution? The bootstrap Bradley Efron Illustration in R

4. Using the central limit theorem for inference The one-sample Z test Example:  = 10, n = 25, M = 105

5. Assumptions of the Z test Independent observations.  is known. Distribution is normal or sample is sufficiently large. Problem: those assumptions are virtually never actually met.

6. The two-sample Z test Example:    =    = 10, n 1 = n 2 = 25, M 1 = 103, M 2 = 108.

7. Two-sample Z test (cont.)

8. Assumptions of the two-sample Z test Independent observations within groups. Independent observations between groups.  is known for both populations. Distribution is normal or sample is sufficiently large in both populations.

9. The one-sample t test Solution to not knowing  : substitute an estimate of the standard deviation. Class example. The t test in SAS.