Hypothesis Tests with Related Samples

Difference scores Calculate difference between first and second score e. g. Difference = After (X2) – Before (X1) OR X1 – X2 Base subsequent analysis on difference scores

Example Industrial psychologist is concerned that a recent round of layoffs at a plant may have increased the stress felt by employees who retained their positions Hypothesis: Employees will report more stress after layoffs occurred

Participant n = 7 XBEFORE XAFTER 1 21 23 2 24 26 3 15 4 18 22 5 19 20 6 7

The question to answer: Is the mean difference significantly different from what we would expect it to be if Ho was true (i.e., 0)? t = MD - μD sMD

Sums of squares:

Effect size

Effect size r2 = Percentage of variance accounted for by the effect r2= t2 t2 + df

Assumptions 1. Observations within each treatment condition must be independent 2. Population of difference scores must be normally distributed