A cognitive psychologist decided to investigate whether two beliefs about healthy living had any real impact on performance in college. She took 40, first-semester college  student volunteers and randomly assigned half to eat breakfast every day and the other half to skip breakfast every day. This was crossed with another variable. Half the students were randomly assigned to sleep at least 8 hours a night and half were randomly assigned to sleep less than 8 hours a night. At the end of the semester, she recorded each participant€™s GPA. The results are shown in this table: 

No nonrobust assumptions for a between subjects, two-way ANOVA were violated and the ANOVA was completed. Here is the summary table:

The eta squared values for rows, columns, and interaction are, respectively, 0.13%, 20.34%, and 0.91%. HSD_Cells is 0.50. Interpret the results.

Sleep Sleep 8 hours 3.20 Eat Breakfast Skip Breakfast Column Means 2.77 2.93 3.08 3.14 2.75 Degrees Source of Sum of of Mean Variability Squares Freedom Square ratio Between groups 1.64 Rows 0.01 0.01 0.06 Columns 1.56 1.56 9.18 Interaction 0.07 0.07 0.41 Within groups 6.03 36 0.17 Total 7.67 39