Two-way Repeated Measures Anova Tool

Data Analysis Tool

Real Statistics Data Analysis Tool: The repeated measures ANOVA analysis required for two within-subjects factors can be performed using Real Statistics’ Two-way Repeated Measures Anova data analysis tool.

For Example 1 of Two-way Repeated Measures Anova, press Ctrl-m and click on the Anova tab (or choose the ANOVA option if using the original user interface). Next, choose the Two-way Repeated Measures Anova option. Fill in the dialog box that appears as shown in Figure 1. The data for this example is repeated in Figure 2.

Figure 1 – Two-way Repeated Measures Anova dialog box

Here, Factor A is the Time factor with the two values Pre and Post, as shown in Figure 2.

Figure 2 – Example Data

Tool Output

After clicking on the OK button on the dialog box, the output in Figures 3, 4, and 5 are displayed.

Figure 3 – Repeated Measures output (part 1)

Figure 4 – Repeated Measures output (part 2)

Results after applying a sphericity correction:

Figure 5 – Repeated Measures output (part 3)

Representative Formulas

Figure 6 displays representative formulas from Figure 3 regarding counts, factor means, and correction factors.

Figure 6 – Formulas from Figure 3

We also see that Figure 7 displays representative formulas from Figure 4 about degrees of freedom, while Figure 8 displays formulas about SS values.

Figure 7 – Df formulas from Figure 4

Figure 8 – SS formulas from Figure 4

The values in Figure 5 are the same as those in Figure 4 except that the Factor A df values are multiplied by the corresponding values in J23:J25, the Factor B df values are multiplied by the corresponding values in M23:M25, and the A × B df values are multiplied by the corresponding values in P23:P25.

Contrasts

Real Statistics Data Analysis Tool: The contrasts used in Examples 2 and 3 of Two-way Repeated Measures Anova (based on the data in Figure 2)  can also be produced using the Contrasts option of the Repeated Measures Anova data analysis tool found in the Real Statistics Resource Pack.

First, enter Ctrl-m and select One Factor Repeated Measures Anova from the Anova tab (or from the ANOVA option if using the original user interface). A dialog box will appear as in Figure 1 of Repeated Measures Anova Tool. Next, enter the appropriate range in the Input Range field, select the Contrasts option, choose the appropriate Alpha correction for contrasts option (see Figure 1 of Repeated Measures Anova Tool), and click on OK.

For Example 2 you should choose the range J5:K14 in the worksheet from Figure 2 as the input. For Example 3 you should choose the range M5:O14 as the input. In both cases, you will need to deselect the Column headings included with data option and add the headings manually.

Examples Workbook

Click here to download the Excel workbook with the examples described on this webpage.

References

Howell, D. C. (2010) Statistical methods for psychology (7^th ed.). Wadsworth, Cengage Learning.
https://labs.la.utexas.edu/gilden/files/2016/05/Statistics-Text.pdf

Maxwell, S. E., Delaney, H. D., Kelley, K. (2018) Designing experiments and analyzing data. Routledge.
https://www.routledge.com/Designing-Experiments-and-Analyzing-Data-A-Model-Comparison-Perspective/Maxwell-Delaney-Kelley/p/book/9781138892286