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Unformatted text preview: violation of H0 tends to produce a large value of Χ2. Small values of Χ2 are not evidence against H0. Using Technology Computing the expected counts and then the chi‐square statistic by hand is tedious. Software saves time and always gets the arithmetic right. Here are the outputs for the chi‐square test for the quality of life data from a graphing calculator, two statistical programs and a spreadsheet. 6 M316 Chapter 23 Dr. Berg 7 M316 Chapter 23 Dr. Berg Example (23.3) Chi‐Square From Software The outputs differ in the information they give. All except the Excel spreadsheet tell us that the chi‐square statistic is Χ 2 = 11.725 , with P‐value 0.020. There is quite good evidence that the distributions of outcomes are different in Canada and the United States. The two statistical programs repeat the two‐way table of observed counts € and add the row and column totals. Both programs offer additional information on request. We asked CrunchIt! to add the column percents that enable us to compare the Canadian and American distributions. The chi‐square statistic is a sum 10 terms, one for each cell in the table. We asked Minitab to give the expected count and the contribution to chi‐square for each cell. More than half the value of Χ2 comes from just one cell. This points to the most important difference between the two countries: a higher proportion of Canadians report a much worse quality of life. Excel, as usual, is more awkward than software designed for statistics. It lacks a menu selection for the chi‐square test. You must program the spreadsheet to calcul...
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