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:

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.