How do you calculate the degrees of freedom for a chi square goodness of fit test?

In a chi-square goodness of fit test, the degrees of freedom are calculated based on the number of categories or groups being tested. Specifically, the degrees of freedom are determined by taking the total number of categories and subtracting one. This adjustment is made because one category's expected frequency is dependent on the others to ensure that the total adds up to the overall sample size.

This subtraction reflects the concept that when estimating parameters from the data, one parameter is constrained, which effectively reduces the number of independent pieces of information available for the calculation. Therefore, for each distinct category tested, one degree of freedom is lost, hence the formula is expressed as the number of categories minus one. This principle is essential for accurate statistical analysis and helps ensure that the chi-square test yields valid results.