Chapter 13, Problem 1P

What is the relationship between the F-ratio for a repeated-measures ANOVA and the F-ratio for an independent-measures ANOVA? Specifically, describe the role of individual difference in each.

To determine

Relationship between the F-ratio for a repeated-measure ANOVA and the F-ratio for an independent-measure ANOVA.

Answer to Problem 1P

Repeated-measures ANOVA use fewer participants than independent-measures and ANOVA. There exist individual differences in both numerator and denominator of F-ratio of independent measure ANOVA while in case of repeated-measures design individual differences get automatically eliminated from the numerator of F-ratio but individual differences need to be computed and eliminated from the denominator of F-ratio.

Explanation of Solution

Both the F-ratio for repeated-measures ANOVA and independent-measures ANOVA are used compare the mean differences for more than two treatments but in case of repeated-measures study, same participants are used for all treatments while in case of independent-measures ANOVA, participants in each treatment are different. So, repeated-measures ANOVA uses fewer participants than independent-measures ANOVA.

Also, in F-ratio of independent measure ANOVA, there exist individual differences between treatments and within treatments because participants in each treatment are not same while in case of repeated-measures design individual differences get automatically eliminated from the numerator of F-ratio but individual differences need to be computed and eliminated from the denominator of F-ratio.

Conclusion:

Repeated-measures ANOVA use fewer participants than independent-measures and ANOVA. There exist individual differences in both numerator and denominator of F-ratio of independent measure ANOVA while in case of repeated-measures design individual differences get automatically eliminated from the numerator of F-ratio but individual differences need to be computed and eliminated from the denominator of F-ratio.