# Multiple comparison procedures for the effect means in a linear model

Methods of controlling the Type I error and dependencies between point estimates when making multiple comparisons between effect means in a linear model.

Procedure | Purpose / Assumptions |
---|---|

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. Controls the Type I error rate individually 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. |

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. |

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. |

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**

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- What is Analyse-it?
- Administrator's Guide
- User's Guide
- Statistical Reference Guide
- Distribution
- Compare groups
- Compare pairs
- Contingency tables
- Correlation and association
- Principal component analysis (PCA)
- Factor analysis (FA)
- Item reliability
- Fit model
- Linear fit
- Simple regression models
- Fitting a simple linear regression
- Advanced models
- Fitting a multiple linear regression
- Performing ANOVA
- Performing 2-way or higher factorial ANOVA
- Performing ANCOVA
- Fitting an advanced linear model
- Scatter plot
- Summary of fit
- Parameter estimates
- Effect of model hypothesis test
- ANOVA table
- Predicted against actual Y plot
- Lack of Fit
- Effect of terms hypothesis test
- Effect leverage plot
- Effect means
- Plotting main effects and interactions
- Multiple comparisons
- Multiple comparison procedures
- Comparing effect means
- Residual plot
- Residuals - normality
- Residuals - independence
- Plotting residuals
- Outlier and influence plot
- Identifying outliers and other influential points
- Prediction
- Making predictions
- Saving variables
- Logistic fit
- Study design
- Method comparison
- Measurement systems analysis (MSA)
- Reference interval
- Diagnostic performance
- Control charts
- Process capability
- Pareto analysis
- Study Designs
- Bibliography

Version 5.40

Published 29-Jul-2019