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 Wilcoxon / Mann-Whitney U test. The Wilcoxon 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 (less patients required) than non parametric tests.
If the data do not conform a Normal distribution, we can’t use a parametric test. In that case we should use a non parametric test; for example, the Wilcoxon 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 Wilcoxon test on Normally distributed data. However, it is incorrect to use a t-test on data that do not conform a Normal distribution.
A summary is given in the table below:
| Data | Sample Size | Test |
|---|---|---|
| Continuous | > 50 | Normal |
| < 50 Normal | t-Test | |
| Not Normal | Wilcoxon | |
| Ordinal | Wilcoxon | |
| Nominal | Chi Squared |
Obviously, there are many more tests described, but these are beyond the scope of this book.