# What are the “degrees of freedom” in this Chi Squared test?

I have learnt that the degrees of freedom are the (number of rows - 1) multiplied by (the number of columns - 1). However, I am stuck as to what the degrees of freedom are in the following set-up for a Chi-squared test.

In a genetic experiment, two different varieties of a certain species are crossed and a specific characteristic of the offspring can occur at only three levels A, B, andC. According to a proposed model, the probabilities for A, B and C are $$\frac{1}{12}$$, $$\frac{3}{12}$$ and $$\frac{8}{12}$$ respectively. Out of 60 offspring, 6, 18, and 36 fall into levels A, B, and C, respectively.

Surely this would give us one column and three rows and therefore the degrees of freedom are $$2\cdot0=0$$, which doesn't seem correct.

• There are 2 degrees of freedom: $2\cdot 1 = 2$. – Wuestenfux May 10 '19 at 8:19
• @Wuestenfux why is it $1$ and not $0$? – user499701 May 10 '19 at 8:24

## 1 Answer

The term degrees of freedom means the number of values which can be chosen arbitrarily under the given restriction.
Here the restriction is 60 offsprings, now given any 2 values you can determine the third value which is 60 - (sum of other 2 values) so your degree of freedom is the number of samples - 1
So where row or column number is zero your degree of freedom becomes n - 1, in your case it's 2.
Comment if something can be improved.