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# The larger the value of the calculated F-ratio?

Choose one of the following:

A) the less likely an observed difference is due to chance
B) the more likely an observed difference is due to chance
C) the larger the sum of squares - within compared to the sum of squares - between
D) the larger the mean square - within compared to the mean square - between

### 2 Answers by Expert Tutors

Garnet H. | Calculus, Physics, Stat, Linear Algebra, GRE, GMAT, SAT... TutoringCalculus, Physics, Stat, Linear Algebra,...
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The F-ratio is a ratio of the variation between your treatments to the variation within your treatments.
Or, put algebraically, F = (variation between treatments) / (variation within treatments).

The within-treatment variation is the variation due to chance. So, obviously, the bigger the numerator, the bigger F. Also, the smaller the denominator the bigger F.

A larger F would therefore mean a larger variation (observed differences) between treatments compared to the variation due to chance, implying that it's less likely that a difference is due to chance.