AP Stats - Ch. 25

data are paired when observations are collected in pairs or the observations in one group are naturally related to observations in the other. The simplest form of pairing is to measure each subject twice---often before and after a treatment is applied. More sophisticated forms are paring in experiments are a form of blocking and arise in other contexts. Pairing in observational and survey data is a form of matching

A hypothesis test for the mean of the pairwise difference (or the mean difference of the pairs) of two groups. It tests the null hypothesis

H0: mued = delta 0

where the hypothesised difference is almost always 0, using the statistic

t= ((bar d) - delta 0)/ SE(d)

with n-1 degrees of freedom where the SE((bar)d)= sd/(root)n and n is the number of pairs.

a confidence interval for the mean of the pairwise differences between paired groups found as

(bar)d +/- t*(n-1) xSE((bar)d), where SE(bar d) is the same as previously stated.

a/n

n