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Unformatted text preview: is is that there is no relationship between the two categorical variables. To test H0, we compare the observed counts in the table with the expected counts, the counts we would expect if H0 were true. If the observed counts are far from the expected counts, that is evidence against H0. Expected Counts The expected count in any cell of a two‐way table when H0 is true is row total × column total . expected count = table total Example (23.2) Observed Versus Expected Counts Let’s find the expected counts for our quality of life study. Here are the € counts with row totals: Quality of Life Canada United States Total Much Better 75 541 616 Somewhat Better 71 498 569 About the Same 96 779 875 Somewhat Worse 50 282 332 Much Worse 19 65 84 Total 311 2165 2476 As an example, the expected count for Canadians with much better quality of life a year after a heart attack is row 1 total × column 1 total (616)( 311) = = 77.37 table total 2476 Here is the table of expected counts: € 4 M316 Chapter 23 Dr. Berg Quality of Life Canada United States Total Much Better 77.37 538.63 616 Somewhat Better 71.47 497.53 569 About the Same 109.91 765.09 875 Somewhat Worse 41.70 290.30 332 Much Worse 10.55 73.45 84 Total 311 2165 2476 To see how the data diverge from the null hypothesis, compare the observed counts with these expected counts. You see, for example, that 19 Canadians reported much worse quality of life, whereas we would expect 10.55 if the null hypothesis were true. The formula is based on the expected value or mean o...
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- Spring '08