We’ll take a few shortcuts in calculating sums of squares for between-subjects, two-way ANOVA. Because SS_Total = SS_Between + SS_Within, if one calculates any two, one can figure out the missing sum of squares. And as SS_Between = SS_Rows + SS_Columns + SS_Interaction, once SS_Between is known, if we calculate SS_Rows and SS_Columns, we can figure out SS_Interaction by subtraction.

As shown in Table 12.21, the first step is to sum and square the data. These data are the raw data for the caffeine and sleep deprivation study. Of SS_Total, SS_Within, and SS_Between, the easiest to calculate are SS_Total and SS_Between. Following Equation 10.2, SS_Total is calculated as follows:

These data have been summed, squared, and arranged to expedite calculations of sums of squares for a between-subjects, two-way ANOVA.

Using Equation 10.3, SS_Between is

Then, SS_Within is calculated as

SS_Within = SS_Total – SS_Between

= 6,698.00 – 5,950.00

=748.00

474

The next step is to compute SS_Rows and SS_Columns:

The final sum of squares, SS_Interaction, is calculated by subtraction:

SS_Interaction = SS_Between – SS_Rows – SS_Columns

= 5,950.00 – 3,630.00 – 1,340.00

= 980.00