There are several tests and which one to use depends on the properties of your data and the setup of your study:

**Independent or paired samples:**

This depends on the setup of your study. Consider an example where you want to know if a Volvo is as comfortable as an Audi. You have 40 participants in your study. The independent approach is if you let 20 participants test the Volvo and fill in a questionnaire, and the other 20 participants test the Audi and fill in a questionnaire. The paired (dependent) approach is if all 40 participants first test the Volvo and fill in a questionnaire, then test the Audi and fill in a questionnaire. Another example of a dependent approach is if you measure the same variable several times (repeated measurements), for example the effect of a treatment is measured every month for a year.**Equal or unequal variances:**

If the variances of the samples differ significantly, you shall use a test for unequal variances. You can check if two samples have equal variances or not using the F-test for equal variances. If you have three or more samples, use the Bartlett's test for equal variances instead.**Normally or not normally distributed samples:**

Generally, parametric tests require that your samples are normally distributed. If one or more sample is not normally distributed, consider using a non-parametric test instead. Note that many parametric tests are fairly robust to not normally distributed samples, so unless the samples are severely non-normal you can still use the parametric tests. You can check if a sample is normally distributed using the Shapiro-Wilk Expanded test.

Parametric tests Requires that the samples are normally distributed |
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Number of samples | Variance? | Dependency? | Use the following test |

1 (and a specified mean) | - | - | T-test (single sample) |

2 | Equal | Independent | T-test (independent, equal variances) |

2 | Unequal | Independent | T-test (independent, unequal variances) |

2 | - | Dependent | T-test (paired) |

3 or more | Equal | Independent | One-way ANOVA |

3 or more | Dependent | Repeated Measures ANOVA |

Non-parametric tests Does not require that the samples are normally distributed |
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---|---|---|---|

Number of samples | Variance? | Dependency? | Use the following test |

1 (and a specified mean) | - | - | Wilcoxon Signed-Ranks (single sample) |

2 | - | Independent | Wilcoxon Rank-Sum test |

2 | - | Dependent | Wilcoxon Signed-Ranks test |

3 or more | - | Independent | Kruskal-Wallis test |

3 or more | Dependent | Friedman test |

- Calculate the relationship (correlation) between two samples.
- Calculate line of best fit (basic linear regression) between two samples.

- Find outliers using the Generalized Extreme Studentized (ESD) test.

- Calculate confidence intervals for a sample.

- t-distribution
- F-distribution
- Chi-Square distribution
- Normal distribution
- Demonstration of the Central Limit Theorem