An analysis of variance comparing three treatment conditions produces df_within = 21.If the samples are all the same size,how many individuals are in each sample? A)7 B)8 C)21 D)22

Question

Quizplus · Accepted Answer

The formula for calculating the degrees of freedom for the within-group variance in a one-way ANOVA with k treatment groups and n observations per group is:

df_within = (k-1) * (n-1)

In this case, we are given that df_within = 21 and are asked to find n. We can rearrange the formula and solve for n:

n = df_within / (k-1) + 1

Since we are not given the value of k (the number of treatment conditions), we cannot determine n exactly. However, we do know that n must be a positive integer, so we can test the answer choices and see which one gives a whole number when substituted into the formula.

Trying answer choice B, we get:

n = 21 / (3-1) + 1 = 11

Since 11 is an integer, we conclude that the answer is:

Answer: B
 If the samples are all the same size, each sample contains 8 individuals.

An Analysis of Variance Comparing Three Treatment Conditions Produces Dfwithin

An Analysis of Variance Comparing Three Treatment Conditions Produces Df_within