In a chi-square test, how are the degrees of freedom calculated?

In a chi-square test, how are the degrees of freedom calculated?

• A. n minus 1 (n is the number of categories)
• B. n
• C. 2n minus 1
• D. n plus 1

Answer: (A)

Degrees of freedom reflect how many values can vary independently when you’re comparing observed counts to what a model predicts. In a goodness-of-fit chi-square test, you have observed counts across a certain number of categories. The total count fixes the sum of all category counts, so once you know the counts for all but one category, the last category’s count is determined by subtracting from the total. That means you only have as many independent counts as there are categories minus one. Therefore, the degrees of freedom equal the number of categories minus one. For example, with four categories, you can freely determine counts for three categories; the fourth is fixed by the total, giving three degrees of freedom.

Degrees of freedom reflect how many values can vary independently when you’re comparing observed counts to what a model predicts. In a goodness-of-fit chi-square test, you have observed counts across a certain number of categories. The total count fixes the sum of all category counts, so once you know the counts for all but one category, the last category’s count is determined by subtracting from the total. That means you only have as many independent counts as there are categories minus one. Therefore, the degrees of freedom equal the number of categories minus one. For example, with four categories, you can freely determine counts for three categories; the fourth is fixed by the total, giving three degrees of freedom.