Overview of Statistical Tests

The table below shows which statistical methods can be used given the research set-up. The research set-up is based on 1) the type of *independent* variable(s) and 2) the type of *dependent* variable(s), which are listed in the rows and columns of the table respectively. Please click on a test to retrieve more information.

The most straightforward methods are shown per research set-up. However, in some cases, other methods can be used as well, and will often give the same or similar results. In order to keep the table relatively simple, these methods are omitted from some of the cells. If you want to add these methods to the cells, press the button below. These methods will have a dotted border in the table.

Independent variable(s) or "Variable 1" | One categorical with 2 independent groups | One categorical with $J$ independent groups ($J \geqslant 2$) | One of ordinal level | One quantitative of interval or ratio level | Two or more quantitative of interval or ratio level |
---|---|---|---|---|---|

None | Goodness of fit test $z$ test for a single proportion Binomial test for a single proportion | Goodness of fit test | One sample Wilcoxon signed-rank test | One sample $z$ test for the mean One sample $t$ test for the mean | |

2 paired groups | McNemar's test | Marginal Homogeneity test / Stuart-Maxwell test | Sign test | Paired sample $t$ test Wilcoxon signed-rank test One sample $t$ test for the mean Repeated measures ANOVA | |

One categorical with 2 independent groups | Chi-squared test for the relationship between two categorical variables $z$ test for the difference between two proportions Logistic regression | Chi-squared test for the relationship between two categorical variables Multinomial logistic regression | Mann-Whitney-Wilcoxon test Ordinal logistic regression | Two sample $z$ test Two sample $t$ test - equal variances not assumed Two sample $t$ test - equal variances assumed One way ANOVA Regression (OLS) | One way MANOVA Multivariate regression |

One categorical with $I$ independent groups ($I \geqslant 2$) | Chi-squared test for the relationship between two categorical variables Logistic regression | Chi-squared test for the relationship between two categorical variables Multinomial logistic regression | Kruskal-Wallis test Ordinal logistic regression | One way ANOVA Regression (OLS) | One way MANOVA Multivariate regression |

Two categorical, the first with $I$ independent groups and the second with $J$ independent groups ($I \geqslant 2$, $J \geqslant 2$) | Logistic regression | Multinomial logistic regression | Ordinal logistic regression | Two way ANOVA Regression (OLS) | Two way MANOVA Multivariate regression |

Three or more categorical with independent groups | Logistic regression | Multinomial logistic regression | Ordinal logistic regression | Three or more way ANOVA Regression (OLS) | Three or more way MANOVA Multivariate regression |

One or more categorical with independent groups, and one or more quantitative control variables of interval or ratio level (covariates) | Logistic regression | Multinomial logistic regression | Ordinal logistic regression | ANCOVA Regression (OLS) | MANCOVA Multivariate regression |

One quantitative of interval or ratio level | Logistic regression | Multinomial logistic regression | Ordinal logistic regression | Pearson correlation Regression (OLS) | Multivariate regression |

One or more quantitative of interval or ratio level and/or one or more categorical with independent groups, transformed into code variables | Logistic regression | Multinomial logistic regression | Ordinal logistic regression | Regression (OLS) | Multivariate regression |

One or more quantitative of interval or ratio level and/or one or more categorical with independent groups, transformed into code variables, plus at least one random factor | Multilevel logistic regression | Multilevel multinomial logistic regression | Multilevel ordinal logistic regression | Multilevel analysis | Multivariate multilevel analysis |

One of ordinal level | Spearman's rho | ||||

One within subject factor ($\geq 2$ related groups) | Cochran's Q test | Madansky test of interchangeability | Friedman test | Repeated measures ANOVA Multilevel analysis | |

One or more within subjects factors (related groups) and possibly one or more between subjects factors (independent groups) | Repeated measures ANOVA Multilevel analysis | ||||

One or more within subjects factors (related groups), one or more quantitative control variables of interval or ratio level (covariates), and possibly one or more between subjects factors (independent groups) | Repeated measures ANCOVA Multilevel analysis |