Question

Several factors influence the size of the F-ratio. For each of the following, indicate whether it would influence the numerator or the denominator of the F-ratio, and indicate whether the size of the F-ratio would increase or decrease.

a) Increase the differences between the sample means.

b) Decrease error variance.

Answer 1

Solution:

F-ratio is given by formula:

$F = \frac{MSB}{MSE}$

MSB = Mean Square Between ( Between group variance)

MSE = Mean Square Error ( Error Variance)

Part a) Increase the differences between the sample means.

If we increase the differences between the sample means., then between group variance increases and MSB increases.

That is it influence the numerator of the F-ratio.

Thus if MSB increase F ratio is also increases.

Part b) Decrease error variance.

MSE = Mean Square Error is nothing but Error Variance

Thus if we decrease error variance, then it influence the denominator of the F-ratio.

Thus if denominator of F ratio decreases, then F ratio increases.