Which of the following is NOT an assumption of the F test?

Which of the following is NOT an assumption of the F test?

• A. F=t^2
• B. Independence of Observations
• C. The scores in each population are normally distributed
• D. The scores in each group have homogeneity of variance

Answer: (A)

The key idea is understanding what the F test assumes about the data. An F test rests on three main conditions: the observations are independent, the scores in each population are normally distributed, and the variances across the groups are equal (homogeneity of variance). The statement F equals t squared is not an assumption about the populations or the data; it’s a mathematical relationship that holds in the two-group case when comparing means using the t statistic with equal variances. In that scenario, the F statistic with one degree of freedom in the numerator is simply the square of the corresponding t statistic, but this is a derived connection, not a premise about the data. Therefore, F = t^2 is not an assumption of the F test, while the other statements describe actual assumptions that underlie the test’s validity.

The key idea is understanding what the F test assumes about the data. An F test rests on three main conditions: the observations are independent, the scores in each population are normally distributed, and the variances across the groups are equal (homogeneity of variance). The statement F equals t squared is not an assumption about the populations or the data; it’s a mathematical relationship that holds in the two-group case when comparing means using the t statistic with equal variances. In that scenario, the F statistic with one degree of freedom in the numerator is simply the square of the corresponding t statistic, but this is a derived connection, not a premise about the data. Therefore, F = t^2 is not an assumption of the F test, while the other statements describe actual assumptions that underlie the test’s validity.