Question

Discuss the type of data required for both the paired t-test and the Wilcoxon matched  pairs signed-rank test.

Answer 1

Paired t test:

The paired sample t-test, sometimes called the dependent sample t-test, is a statistical procedure used to determine whether the mean difference between two sets of observations is zero.

The dependent variable must be continuous (interval/ratio) in paired t test.

Wilcoxon signed rank test:

The Wilcoxon signed-rank test is a non-parametric equivalent of the paired t-test.

It is most commonly used to test for a difference in the mean (or median) of paired observations - whether measurements on pairs of units or before and after measurements on the same unit. It can also be used as a one-sample test to test whether a particular sample came from a population with a specified median.

The measurement scale is such that the paired differences can be ranked.

It might therefore appear that measurement needs to be on the interval scale of measurement. However, strictly speaking one only needs to know that a difference between a score of 10 and 50 is greater than the difference between a score of 10 and 20 - not that the difference is four times greater (40 rather than 10). Such a scale is intermediate between an ordinal scale and an interval scale and is known as an ordered metric scale.