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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
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2 Answers

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.
answer: A
Answer (A).  Provided all the underlying assumptions for applying ANOVA are satisfied.
ANOVA provides a simultaneous test of of the null hypothesis that the group population means are equals for three or more groups.  The alternative hypothesis is that at least one group mean (population) is different from the rest.  The rejection region (in favor of the alternative hypothesis) is that the calculated F ratio is "too high"  (higher than the critical value of F at a prescribed level of significance).