# For testing independence in a contingency table of size r Ã c, the degrees of freedom (df) for the chi-squared distribution equal df = (r - 1) Ã (c - 1). They have the following interpretation: Given the row and column marginal totals in an r Ã c contingency table, the cell counts in a rectangular block of size (r

a. Given the cell counts and the row and column totals, fill in the counts that must appear in the blank cells.

b. Now, suppose instead of the preceding table, you are shown the following table, this time only revealing a

2 Ã— 1 block in the lower-right part. Find the counts in the remaining cells.

This example serves to show that once the marginal totals are fixed in a contingency table, a block of only (r - 1) Ã— (c - 1) cell counts is free to vary. Once these are given (as in part a or b), the remaining cell counts follow automatically. The value for the degrees of freedom is exactly the number of cells in this block, or df = (r - 1) Ã— (c - 1).

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## Statistics The Art And Science Of Learning From Data

4th Edition

**Authors:** Alan Agresti, Christine A. Franklin, Bernhard Klingenberg

**ISBN:** 9780321997838