### Chapter 2 highlights

#### Chapter 2

Assumptions for the usual two sample t test

Enumerating a small permutation distribution

Example: 2 students were randomly assigned to a new reading program, 3 were randomly assigned to the usual reading program.  Over winter break, the number of books read were 7 and 15 from the new group, versus 2, 4, and 8 from the old group.   What were all the possible ways that their books read could have been distributed among the two groups?

 New group Old group New group mean Old group mean Mean difference 7,15 2,4,8 11 4.67 6.33 8,15 2,4,7 11.5 4.33 7.17 2,15 4,7,8 8.5 6.33 2.17 4,15 2,7,8 9.5 5.67 3.83 7,8 2,4,15 7.5 7 .5 2,7 4,8,15 4.5 9 -4.5 4,7 2,8,15 5.5 8.33 -2.83 2,8 4,7,15 5 8.67 -3.67 4,8 2,7,15 6 8 -2 2,4 7,8,15 3 10 -7

Let's examine the permutation distribution of the mean differences.

The permutation principle: The permutation distribution is an appropriate reference distribution for conducting inference (calculating p values, determining the significance of tests). Permutation distributions lead to exact tests.

Equivalence of other statistics, summary of steps in a permutation test.

Hypotheses tested in a two sample permutation test

Basing a permutation test on other sample statistics, such as the median or trimmed mean.