Analysis of Variance Package
This package provides functions for performing a univariate Analysis of Variance (ANOVA) to examine the differences between groups of means. The function ANOVA can handle models with any number of fixed factors in a crossed design. It can handle both balanced and unbalanced data with or without missing elements. All results are given as type I sums of squares. ANOVA also provides a number of post‐hoc tests for comparisons.
The ANOVA function.
The data must be of the form {{α1,β1,…,y1},{α2,β2,…,y2},…} where αi, βi, and so on are the values of the categorical variables vars associated with the ith response, yi.
The vars argument is a list of symbols representing the categorical variables in the model.
The model argument is a list of main effects and interactions that together specify the model. The interaction terms are given as the product of variables. For example, the full factorial model for a three‐way analysis of variance can be written as {α,β,γ,α β,α γ,β γ,α β γ}, where α, β, γ are the main effects, α β, α γ, β γ are the two‐way interactions, and α β γ is the three‐way interaction. Models can also be written using All to represent all main effects and interactions between the specified categorical variables. The full factorial model for a three‐way analysis of variance can therefore also be written as {α,β,γ,All}.
This loads the package. This defines data of one categorical variable. This performs a one‐way ANOVA on the data. This defines data of a categorical variable with two levels and a categorical variable with three levels. This performs a full factorial two‐way ANOVA. Dropping the point {2,2,28.7} gives an unbalanced two‐way ANOVA with an empty cell. Here is a balanced three‐way dataset. Here is a three‐way ANOVA with main effects and two‐way interactions.Options for ANOVA.
Available tests for the PostTests option.
Tukey's test finds groups 1 and 4 significantly different from group 3 at the 5% level. Bonferroni and Tukey's tests find groups 3 and 4 significantly different at the 1% level.