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.