Yes, Prism CAN do repeated measures three-way ANOVA!

The ability to perform repeated measures three-way ANOVA was introduced with Prism 8.0. Below, you'll find a quick walkthrough for how this can be done within Prism. But first, a couple of important things to keep in mind when performing this analysis:

• Three-way ANOVA can be challenging to interpret (and repeated measures three-way ANOVA even more so!). Be sure you understand what questions three-way ANOVA can answer (they might not actually be the questions you care about!).
• Currently, three-way ANOVA in Prism 8 is restricted to a 2 x 2 x K design. This means that two of your factors can only have to levels (for example, a factor could be "sex" and the levels of this factor could be "male" and "female"). The two factors that each have two levels will be defined by four columns. In the example below, these two factors are "Biofeedback" (with levels "Biofeedback" and "No biofeedback") and "Diet" (with levels "Diet Absent" and "Diet Present"
• Prism can analyze repeated measures three-way ANOVA with repeated measures in any 'direction'. Measurements for this analysis could be "repeated" across any factor or set of factors

Guided Walkthrough

We'll use the tutorial data available in Prism for this example. From the Welcome dialog, select the Grouped data table option on the left hand side, then select "Start with sample data to follow a tutorial", and finally choose "Three-way ANOVA 2 x 2 x K" and click Create.

You should now see a data table containing our experimental data. Each of the values in the data table represent a blood pressure measurement, while the rows and columns represent different experimental conditions. For this experiment, three different drugs (X, Y, and Z) were used to investigate their effect on blood pressure. Additionally, the effect of biofeedback (blood pressure monitoring) was investigated along with the effect of a controlled diet. The way the data are structures is important. There are four main columns (each with 6 subcolumns) and three rows of data. The four main columns represent all possible combinations of the levels of the Biofeedback and Diet factors:

• Biofeedback with Diet Absent
• Biofeedback with Diet Present
• No biofeedback with Diet Absent
• No biofeedback with Diet Present

Without knowing the details of the experimental setup or design, there are a number of ways that this data could be interpreted. For example, one of the simplest explanations is that every single value was obtained from a different person, and that this study involved 72 different individuals. If this were the case, we would not need repeated measures, and standard three-way ANOVA would be sufficient. However, there are a number of alternative explanations for how various data could have been collected from fewer individuals.

For this example, let's assume that individuals in this study belong to either a "Biofeedback" or "No biofeedback" group, but not both. And they belong to a "Diet Absent" or "Diet Present" group, but not both. However, each individual will be given all three drugs, and measurements will be taken after each drug administration (for the purposes of the study, we'll assume there's no carryover effect between drugs). In other words, in the data table above, each subcolumn contains three measurement values from a single individual, and there are now a total of 24 individuals in the study. Because we're taking measurements from the same individual across levels of our "Drug" factor, we will need to use a repeated measures style ANOVA.

To start our analysis, click the Analyze button in the toolbar, and on the Analyze Data dialog, under Grouped Analyses, select "Three-way ANOVA (or mixed model)" and click OK. On the first tab of the parameters dialog that appears, we can now specify the repeated measures design of our experiment. As described above, the values stacked in a subcolumn represent measurements from a single individual, and so we will want to select the third checkbox in these options:

Visually, we can see that this data arrangement matches our experimental design. Before we click OK, however, we can click on the "Factor Names" tab at the top of this parameters dialog and rename our factors based on our experimental design (these changes simply make interpreting the results a bit easier):

• Rename the default "(AB vs CD)" to "Biofeedback"
• Rename the default "(AC vs BD)" to "Diet"
• Rename the default "Row factor" to "Drug"
• The default "Subject" can be left as-is

Note that on this parameters dialog, you could also choose to have Prism perform multiple comparisons, change options for assuming sphericity, select graphs to be generated for model residuals, and more options. However, for the sake of this walkthrough, we'll simply leave these other options set to their defaults. Once you've got everything set, click "OK" which will take you to the analysis results. These results will provide information on some of the assumptions/options of the analysis, a table listing the different sources of variation along with their P values, an ANOVA table providing information required to calculate the F statistics, and a summary of the data in the original data table.