Question

For an ANOVA tell me whether the F-ratio and P value will in-crease or decrease under the following circumstances.

(a)The group sum of squares increases.

(b)The among group mean square increases.

(c)The within group sum or squares decreases.

(d)The within group mean square decreases.

I'm having trouble understanding conceptually how this works.

Answer 1

For ANOVA test,

F = among group mean square / within group mean square = (group sum of squares / Numerator df) / (within group sum or squares / Denominator df)

Also, if F-ratio increases, P-values will decrease and approaches to zero.  

P-value = P(F > F-ratio, Numerator df, Denominator df)

(a)The group sum of squares increases.

F = (group sum of squares / Numerator df) / (within group sum or squares / Denominator df)

Thus, F-ratio will increase as group sum of squares increases.

As, F-ratio increases, P-values will decrease.

(b)The among group mean square increases.

F = among group mean square / within group mean square

Thus, F-ratio will increase as among group mean squares increases.

As, F-ratio increases, P-values will decrease.

(c)The within group sum or squares decreases.

F = (group sum of squares / Numerator df) / (within group sum or squares / Denominator df)

Thus, F-ratio will increase as within group sum or squares decreases.

As, F-ratio increases, P-values will decrease.

(d)The within group mean square decreases.

F = among group mean square / within group mean square

Thus, F-ratio will increase as within group mean squares increases.

As, F-ratio increases, P-values will decrease.