| Statistics Toolbox | |
N-Way Analysis of Variance
You can use N-way ANOVA to determine if the means in a set of data differ when grouped by multiple factors. If they do differ, you can determine which factors or combinations of factors are associated with the difference.
N-way ANOVA is a generalization of two-way ANOVA. For three factors, the model can be written
In this notation parameters with two subscripts, such as (
)ij., represent the interaction effect of two factors. The parameter (
)ijk represents the three-way interaction. An ANOVA model can have the full set of parameters or any subset, but conventionally it does not include complex interaction terms unless it also includes all simpler terms for those factors. For example, one would generally not include the three-way interaction without also including all two-way interactions.
The anovan function performs N-way ANOVA. Unlike the anova1 and anova2 functions, anovan does not expect data in a tabular form. Instead, it expects a vector of response measurements and a separate vector (or text array) containing the values corresponding to each factor. This input data format is more convenient than matrices when there are more than two factors or when the number of measurements per factor combination is not constant.
The following examples explore anovan in greater detail:
| | Example: Two-Way ANOVA | Example: N-Way ANOVA with Small Data Set | |