ABSTRACT
An important feature of the ANOVA model in chapter eight is that the J treatment groups are independent. In chapter seven it was noted that for J=2 groups it can be advantageous to test H0: μ1= μ2 using dependent groups. For example, suppose you conduct an experiment on mice in which the goal is to determine whether two different conditions affect learning. You could randomly assign some mice to one condition and randomly assign a different (independent) sample of mice to the other and test H0: μ1 = μ2, where μj is the average learning occurring under the jth condition. Alternatively, you could randomly sample n pairs of litter mates and assign one litter mate to each of the two treatment groups. If Xij(i=1,…,n; j=1,2) are the n pairs of observations, you can test H0: μ1=μ2 with https://www.w3.org/1998/Math/MathML"> T = ( J n ) ( x ^ 1 − x ˙ 2 ) / s D https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203767757/a38c2774-0749-41c9-a2e1-e80a84258bc7/content/math11_0_1_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
