Discussion
In a chi-square test, what will be the degrees of freedom for a contingency table consisting of 3 rows (variable-1) and 2 columns (variable 2) ?
Answer: A
The degrees of freedom are 2.
For a chi-square test of independence on an r × c contingency table:
\[ \begin{aligned} df &= (r - 1)(c - 1) \\ &= (3 - 1)(2 - 1) = 2 \end{aligned} \]
Once the row and column totals are fixed, only two cell values can be chosen freely; the rest follow from the totals. 5 is the result of subtracting 1 from the total number of cells (6), the rule for a goodness-of-fit test, not a contingency table. 3 is the number of rows, and 6 is the number of cells.
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