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How ANY-maze processes missing data and empty cells in two-way ANOVAs

Introduction

Ideally, when performing a two-way ANOVA, each cell will contain the same number of observations, i.e. the 'N' for each level of the independent variables will be the same. However, departures from this ideal are common (perhaps because you had to remove an animal from the experiment) and unequal cell sizes, or entirely empty cells can often occur - see figures 1 and 2.

Figure 1. Example of an experiment in which there are unequal cell sizes.

Figure 2. Example of an experiment in which there is an empty cell.

How ANY-maze manages unequal cell sizes

ANY-maze uses the general linear model approach to manage unequal cell sizes. This approach, which uses the marginal sums of squares (also called the Type III or adjusted sums of squares), is commonly used by almost all statistics software.

How ANY-maze manages empty cells

Entirely empty cells are a more complicated problem. In cases where there is just one empty cell, or where the non-empty cells are 'connected' it is theoretically possible to perform a two-way ANOVA, but you must assume that there is no interaction. As this seems rather a gross assumption, ANY-maze doesn't take this approach - instead it reports that it can't perform the analysis and suggests that you perform separate one-way ANOVAs for the two independent variables. Although this is a more conservative approach, it doesn't require you to make any assumptions about the nature of the data or experimental design.

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