t-test (parametric) in SPSS and R & Wilcoxon Signed-Rank (nonparametric) test

Example
Suppose we would like to know does the use of a mobile phone while driving change reaction time. We have 6 individuals and tested their reaction time with and without mobile as below:


1. In the SPSS, choose [Analyze]->[Compare Means]->[Paired-Samples T Test]


2. Add variables

3. Click OK and the SPSS will do all the jobs for you..

4. two-tailed to one-tailed
 If you wanted the one-tailed significance value, just divide the two-tailed value in half.


Robust t-test in R


The Wilcoxon Signed-Rank (nonparametric) test


Parametric tests such as t-test are based on assumptions about the distribution of the underlying population from which the sample was taken. The most common parametric assumption is that data are approximately normally distributed.

The Wilcoxon Signed-Rank (nonparametric) test is a non-parametric counterpart to the paired-samples t-test, which can be used in the case of the data is not normally distributed. The pros and cons can be found at https://www.mayo.edu/mayo-edu-docs/center-for-translational-science-activities-documents/berd-5-6.pdf


Welch's t-test

In statistics, Welch's t-test, or unequal variances t-test, is a two-sample location test which is used to test the hypothesis that two populations have equal means. It is an adaptation of Student's t-test, and is more reliable when the two samples have unequal variances and/or unequal sample sizes.