# Multiple comparison procedures for the means/medians of independent samples

Methods of controlling the Type I error and dependencies between parameters when making multiple comparisons between many means/medians of independent samples.

Procedure | Purpose |
---|---|

Student's t (Fisher's LSD) | Compare the means of each pair of groups using the Student's t method. When making all pairwise comparisons this procedure is also known as unprotected Fisher's LSD, or when only performed following significant ANOVA F -test known as protected Fisher's LSD. Control the type I error rate is for each contrast. |

Wilcoxon-Mann-Whitney | Compare the median/means each pair of groups using the Wilcoxon nonparametric method. Control the type I error rate for each contrast. |

Tukey-Kramer | Compare the means of all pairs of groups using the Tukey-Kramer method. Controls the error rate simultaneously for all k(k+1)/2 contrasts. |

Steel-Dwass-Critchlow-Fligner | Compare the median/means of all pairs of groups using the
Steel-Dwass-Critchlow-Fligner pairwise ranking nonparametric method. Controls the error rate simultaneously for all k(k+1)/2 contrasts. |

Hsu | Compare the means of all groups against the best of the other groups using the Hsu
method. Controls the error rate simultaneously for all k contrasts. |

Dunnett | Compare the means of all groups against a control using the Dunnett
method. Controls the error rate simultaneously for all k-1 contrasts. |

Steel | Compare the medians/means of all groups against a control using the Steel
pairwise ranking nonparametric method. Controls the error rate simultaneously for all k-1 comparisons. |

Scheffé | Compare the means of all groups against all other groups using the Scheffé F
method. Controls the error rate simultaneously for all possible contrasts. |

Student-Newman-Keuls (SNK) | Not implemented. As discussed in Hsu (1996) it is not a confident inequalities method and cannot be recommended. |

Duncan | Not implemented. As discussed in Hsu (1996) it is not a confident inequalities method and cannot be recommended. |

Dunn | Not implemented in Analyse-it version 3 onwards. Implemented in version 1. A joint-ranking nonparametric method but as discussed in Hsu (1996) it is not a confident inequalities method and cannot be recommended. Use the Dwass-Steel-Critchlow-Fligner or Steel test instead. |

Conover-Iman | Not implemented in Analyse-it version 3 onwards. Implemented in version 2. As discussed in Hsu (1996) applying parametric methods to the rank-transformed data may not produce a confident inequalities method even if the parametric equivalent it mimics is. Use the Dwass-Steel-Critchlow-Fligner or Steel test instead. |

Bonferroni | Not a multiple comparisons method. It is an inequality useful in producing easy to compute multiple comparisons. In most scenarios, there are more powerful procedures such as Tukey, Dunnett, Hsu. A useful application of Bonferroni inequality is when there are a small number of pre-planned comparisons. In this case, use the Student's t (LSD) method with the significance level (alpha) set to the Bonferroni inequality (alpha divided by the number of comparisons). In this scenario, it is usually less conservative than using Scheffé all contrast comparisons. |

**Available in Analyse-it Editions**

Standard edition

Method Validation edition

Quality Control & Improvement edition

Ultimate edition

- What is Analyse-it?
- What's new?
- Administrator's Guide
- User's Guide
- Statistical Reference Guide
- Distribution
- Compare groups
- Calculating univariate descriptive statistics, by group
- Side-by-side univariate plots
- Creating side-by-side univariate plots
- Equality of means/medians hypothesis test
- Equivalence of means hypothesis test
- Tests for means/medians
- Testing equality of means/medians
- Testing equivalence of means
- Difference between means/medians effect size
- Estimators for the difference in means/medians
- Estimating the difference between means/medians
- Multiple comparisons
- Mean-Mean scatter plot
- Multiple comparison procedures
- Comparing multiple means/medians
- Homogeneity of variance hypothesis test
- Tests for homogeneity of variance
- Testing homogeneity of variance
- Study design
- Compare pairs
- Contingency tables
- Correlation and association
- Principal component analysis (PCA)
- Factor analysis (FA)
- Item reliability
- Fit model
- Method comparison / Agreement
- Measurement systems analysis (MSA)
- Reference interval
- Diagnostic performance
- Survival/Reliability
- Control charts
- Process capability
- Pareto analysis
- Study Designs
- Bibliography

Version 6.15

Published 18-Apr-2023