The degrees of freedom (df) for a chi-square test of independence can be calculated using a simple formula based on the dimensions of the contingency table used in the test. Here’s how to find it:
- Identify the Variables: In a chi-square test of independence, you start with two categorical variables. For instance, you might be interested in studying the relationship between ‘Gender’ (Male, Female) and ‘Preference’ (Coffee, Tea).
- Determine the Number of Categories: Count the number of categories for each variable. In our example, ‘Gender’ has 2 categories, and ‘Preference’ also has 2 categories.
- Use the Degrees of Freedom Formula: The formula to calculate the degrees of freedom for a chi-square test of independence is:
- Apply the Formula: Substitute the counts from your contingency table into the formula.
df = (number of rows - 1) * (number of columns - 1)
Continuing with the example:
- Number of rows (categories for ‘Gender’) = 2
- Number of columns (categories for ‘Preference’) = 2
So the calculation would be:
df = (2 - 1) * (2 - 1) = 1 * 1 = 1
Thus, the degrees of freedom for this chi-square test of independence is 1.
In summary, to find the degrees of freedom for a chi-square test of independence, simply subtract one from the number of categories in each variable and multiply the results together. This gives you the information you need to perform further statistical analysis or to interpret the results of your test effectively.