Question

A researcher uses an ANOVA to compare nine treatment conditions with a sample size of n = 13 in each treatment. For this analysis find the degrees of freedom.

What is df(treatment)?
This is sometimes referred to as the “numerator degrees of freedom.”

What is df(error)?
This is sometimes referred to as the “denominator degrees of freedom.”

If the scenario was changed so that there were still nine treatments, but there were different sample sizes for each treatment (a.k.a. an unbalanaced design), which of the following degrees of freedom would NOT change?

• df(treatment)
• df(error)
• both change
• neither change

Answer 1

We are given the number of treatments = 9

Total sample size = 13

So, in an ANOVA table

the total degrees of freedom = one less than the sample size = 13 - 1 = 12

There are 9 treatments.

So, degrees of freedom for treatment = one less than the number of treatments = 9 - 1 = 8

and finally, the degrees of freedom for error is obtained by subtracting the degrees of freedom for treatments from total degrees of freedom =  12 - 8 = 4

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If the scenario was changed so that there were still nine treatments, but there were different sample sizes for each treatment

On changing the sample sizes for each treamtment the total sample size would be change that means total degrees of freedom would be change.

But there are still 9 treatments are available so, the degrees of freedom for treatment would be the same which is just one less than the number of treatments(which is still the same).

But degrees of freedom for error would be changed since it is the subtraction of treatment degrees of freedom from total degrees of freedom(which has been changed).

So, the correct answer would be degrees of freedom for treatments.

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