Question

When using a one-way within-groups ANOVA, the variability due to individual differences is reduced, resulting in a _____ F statistic and making it _____ to reject the null hypothesis.

a) larger; harder
b) smaller; easier
c) smaller; harder
d) larger; easier

Answer 1

In a one-way within-groups ANOVA, reduced variability due to individual differences leads to a larger F statistic, making it easier to reject the null hypothesis. The correct answer is option (d).

Step-by-step explanation:

When using a one-way within-groups ANOVA, the variability due to individual differences is reduced, resulting in a larger F statistic and making it easier to reject the null hypothesis. This is because one-way ANOVA compares the variation within each group to the variation of the mean of each group.

When individual differences are reduced, the within-group variability decreases, which leads to a larger F statistic since the F statistic is the ratio of variability between groups to variability within groups. A larger F statistic often corresponds to a smaller p-value, and in the context of hypothesis testing, it increases the likelihood of rejecting the null hypothesis, assuming the null hypothesis suggests no effect or no difference.

Therefore, the correct answer to the question is (d) larger; easier.