A researcher uses an analysis of variance to test for mean differences among three

treatment conditions using a sample of n = 8 participants in each treatment. What degrees of
freedom (df) would the F-ratio from this analysis have?

a. df = 23
b. df = 2, 23
c. df = 3, 21
d. df = 2, 21

See your other post. That post will answer this question.

The degrees of freedom for the F-ratio in an analysis of variance are calculated based on the sample size and the number of treatment conditions.

In this case, the sample size for each treatment condition is n = 8, and there are 3 treatment conditions. Therefore, the total number of participants in the study is 3 * 8 = 24.

The degrees of freedom for the numerator (between-group variability) is equal to the number of treatment conditions minus 1, which is 3 - 1 = 2.

The degrees of freedom for the denominator (within-group variability) is equal to the total number of participants minus the number of treatment conditions, which is 24 - 3 = 21.

Therefore, the correct answer is option d: df = 2, 21.

To determine the degrees of freedom (df) for the F-ratio in an analysis of variance (ANOVA), we need to consider the number of groups or treatment conditions and the total sample size.

In this case, the researcher is comparing three treatment conditions. We have three groups, and since there are three groups, we subtract one from the number of groups to determine the numerator degrees of freedom. So, numerator df = 3 - 1 = 2.

The total sample size is given as n = 8 participants in each treatment condition. Since there are three treatment conditions, the total sample size is 3 * 8 = 24 participants. The total sample size minus the number of groups gives us the denominator degrees of freedom. Therefore, denominator df = (3 * 8) - 3 = 24 - 3 = 21.

So, the correct answer is option d. The F-ratio in this analysis of variance would have degrees of freedom of df = 2, 21.

df=23