Monday, December 7, 2009

Tests for comparing two related samples

Dependent samples, also called related samples or correlated samples, occur when the response of the nth person in the second sample is partly a function of the response of the nth person in the first sample. There are several common forms of sample dependency . (1) Before-after and other studies in which the same people are surveyed at different points in time, including panel studies. (2) Matched-pairs studies in which each of the subjects of the study is paired with each of those in a comparison group on the basis matching factors (e.g. age, sex, income, etc.). (3) The pairs can simply be inherent in the situation we are trying to analyze. For instance, one tries to compare the time spent watching television by the man and woman within a couple. The blocks are naturally households. Men and women should not be considered as independent observations.

The aim of tests for related samples is to exclude from the analysis the within-group variation. The calculation of the differences is realized within each pair of subjects. In this tutorial, we show how to implement 3 tests for two related samples. Two of them are non-parametric (sign test and Wilcoxon matched-pairs ranks test), the last one is the parametric t-test for related samples.

Keywords: parametric test, non-parametric test, paired samples, sign test, wilcoxon signed rank test, paired samples t-test, normality test
Tutorial: en_Tanagra_Nonparametric_Test_for_Two_Related_Samples.pdf
Dataset : comparison_2_related_samples.xls
References :
R. Lowry, « Concepts and Applications of Inferential Statistics », SubChapter 12a. The Wilcoxon Signed-Rank Test.