There are many statistical tests described. So how do we know which test to use? First of all we need to look at our data. If the data are not continuous, we will have to use a non parametric test. For nominal data, a frequency distribution such as the Chi Square test can be used. When data are ordinal (can be ranked), it is usually better to use a rank test, such as the Mann-Whitney U test. The Mann-Whitney U test can also be used for continuous data that are not Normally distributed.
When data are continuous, we might be able to use a parametric test. However, we need to demonstrate that the data are Normally distributed. This can be done with a test for Normality, such as the Shapiro-Wilk test, Kolomogorov-Smirnov test or a Quantile-Quantile plot.
If the data has a Normal distribution we can use parametric statistics. When the sample size is large (> 50), we can use the Normal distribution. For smaller sample sizes (< 50), a t-test is used. If possible, a parametric test is preferred as these tests are more powerful than non parametric tests.
If the data are not Normally distributed, we can not use a parametric test. In that case we could use, for example, the Mann-Whitney U test.
If in doubt about the distribution of data (Normal or not), a non parametric test can always be used. For example, it is ‘allowed’ to use the Mann-Whitney U test on Normally distributed data (although it is less powerful). However, it is incorrect to use a t-test on data that are not Normally distributed.
A summary is given in the table below:
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Obviously, there are many more tests described, but these are beyond the scope of this book.