11.83 Standardized residuals for 2 : 2 tables The table that follows shows the standardized residuals in parentheses for GSS data about the statement, “Women should take care of running their homes and leave running the country up to men.” The absolute value of the standardized residual is 13.2 in every cell. For chi-squared tests with 2 * 2 tables, since df = 1, only one nonredundant piece of information exists about whether an association exists. If observed count 7 expected count in one cell, observed count 6 expected count in the other cell in that row or column. Explain why this is true, using the fact that observed and expected counts have the same row and column totals. (In fact, in 2 * 2 tables, all four standardized residuals have absolute value equal to the square root of the X 2 test statistic.)

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Year 1974 1998 Agree Disagree 509 (13.2) 280 (-13.2) 924 (-13.2) 1534 (13.2)