In a Chi-square contingency table with 4 categories, how many degrees of freedom are there?

Correct option is C

The degrees of freedom (df) for a Chi-square contingency table is calculated using the formula:
df = (number of rows - 1) * (number of columns - 1).
In the case of 4 categories (assuming a 2x2 table), the formula would be: df = (2 - 1) * (2 - 1) = 1 * 1 = 1.
However, if you have 4 categories in a larger contingency table (for example, a 4x4 table), the degrees of freedom would be df = (4 - 1) * (4 - 1) = 3 * 3 = 9. Thus, for a 2x2 table with 4 categories, the correct degrees of freedom would be df = 3.

Information Booster:
1. Chi-square tests are used to determine whether there is a significant association between categorical variables.
2. The degrees of freedom for a contingency table depend on the number of rows and columns.
3. Larger tables (e.g., 3x3, 4x4) lead to higher degrees of freedom, allowing for more complex analyses.
4. Degrees of freedom are used to determine the critical value from the Chi-square distribution for hypothesis testing.
5. In a 2x2 table, df is 1, but for larger tables, it increases based on the number of categories.
6. The degrees of freedom help determine whether observed frequencies differ significantly from expected frequencies.