Question

In terms of systematic and unsystematic variability, and the conceptual equation for the F-ratio, explain what an F-ratio:

-Greater than 1 would tell you.

-Less than 1 would tell you.

Answer 1

F-ratio is defined as,

F-ratio = MSm / MSr

Where, MSm = SSm / (degree of freedom)

SSm is the systematic variance for model (m) i.e. sum of squares between groups.

& MSr = SSr / (degree of freedom)

SSr is the unsystematic variance for residuals (r) i.e. sum of squares within groups.

If F-ratio is greater than 1, implies systematic variance is greater than unsystematic variance i.e. variation among group means is more than variation within group means.

If F-ratio is less than 1, it implies systematic variance is less than unsystematic variance, which is not a good sign.