If the mean and variance are computed for each sample in an independent-measures two-factor experiment,then which types of sample data will tend to produce large F-ratios for the two-factor ANOVA?
A)large differences between sample means and small sample variances
B)large differences between sample means and large sample variances
C)small differences between sample means and small sample variances
D)small differences between sample means and large sample variances

Question

If the mean and variance are computed for each sample in an independent-measures two-factor experiment,then which types of sample data will tend to produce large F-ratios for the two-factor ANOVA?​
A)​large differences between sample means and small sample variances
B)​large differences between sample means and large sample variances
C)​small differences between sample means and small sample variances
D)​small differences between sample means and large sample variances

Quizplus · Accepted Answer

Large differences between sample means and small sample variances tend to produce large F-ratios in a two-factor ANOVA because the F-ratio is designed to measure the ratio of between-group variance to within-group variance. Large differences among sample means increase the numerator (indicating more variance between groups due to the treatment effect), and small variances within each sample decrease the denominator (indicating less random or error variance), both of which contribute to a larger F-ratio.

If the Mean and Variance Are Computed for Each Sample