Can the F test statistic ever be a negative number? A. Yes, because s2/1 an take

Question

Can the F test statistic ever be a negative number?

A. Yes, because s2/1 an take on values from minus-1 to 1 inclusive.

B.Yes, because the numerator and denominator used to calculate the F test statistic can both take on negative and positive values.

C.NO bcause sample variances cannot be negative, and the result of dividing the squares of two nonnegative numbers is never negative.

D.No, because sample variances are always negative, and the result of dividing the squares of two negative numbers is never negative.

Explanation / Answer

it is not possible to get a negative FF-statistic of the type that occurs in statistics. Think about what an FF-statistic is. All FF-statistics are of the form:

F=MSeffect/MSresidual, the numerator and denominator are always +ive.

So, A , B are ruled out.

D is not possible as variances can never be 0

Answer is C.

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