__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.__