Author Question: What is the rationale for df = (r - 1)(k - 1) in conducting a chi-square test of independence for a ... (Read 80 times)

Garrulous · **on:** Jun 24, 2018

What is the rationale for df = (r - 1)(k - 1) in conducting a chi-square test of independence for a contingency table with r rows and k columns?

Question 2

In carrying out a chi-square goodness-of-fit test, what are the k and m terms in the df = k - 1 - m expression and why is each term present?

tuwy · **Reply #1 on:** Jun 24, 2018

Answer to Question 1

The rationale for df = (r-1) (k-1) is that this quantity represents the number of cell frequencies that are free to vary. Given that we know the sample size (the total number of observations in the table), we need only know the contents of (r-1) rows and (k-1) columns in order to completely fill in the cells within the r x k table.

Answer to Question 2

Given k is the number of categories or groups in the, and m is the number of population parameters that must be estimated from sample data in order to carry out the test. k-1 cells to determine the count in the kth cell. In addition, each population parameter that must be estimated also reduces our degrees of freedom.