In contrast to independent measurements, matched data consist of measurements that should be considered together. For example, matching can be used in clinical studies. Here, patients that exhibit similar characteristics are paired in order to remove confounding effects. Matched data can also arise naturally when multiple measurements are performed on the same entity. For example, matched data can arise when a clinical marker is measured once before and once after a
treatment intervention. Irrespective of how the matched data were generated, their structure should be taken into account through the use of appropriate statistical tests.
The most common type of matched data are paired measurements, which consist of two data points. For this type of data, the following significance tests are available:
McNemar’s test is a non-parametric test for contingency tables that arise from paired measurements. In contrast to the chi-squared test, which is a test for independence, McNemar’s test is a test for symmetry (also called marginal homogeneity). Still, McNemar’s test is related to the chi-squared test because its test static also follows a chi-squared distribution.
In this post, we will explore tests for comparing two groups of dependent (i.e. paired) quantitative data: the Wilcoxon signed rank test and the paired Student’s t-test. The critical difference between these tests is that the test from Wilcoxon is a non-parametric test, while the t-test is a parametric test. In the following, we will explore the ramifications of this difference.