![]() ![]() There was a significant association between class rank and living on campus ( Χ 2(1) = 138.9, p Since the p-value is less than our chosen significance level α = 0.05, we can reject the null hypothesis, and conclude that there is an association between class rank and whether or not students live on-campus.īased on the results, we can state the following: The corresponding p-value of the test statistic is so small that it is presented as p Because the crosstabulation is a 2x2 table, the degrees of freedom (df) for the test statistic is $$ df = (R - 1)*(C - 1) = (2 - 1)*(2 - 1) = 1 $$.The value of the test statistic is 138.926.We can confirm this computation with the results in the table labeled Statistics for Table of RankUpperUnder by LiveOnCampus: Computation of the expected cell counts and residuals (observed minus expected) for the crosstabulation of class rank by living on campus. For one-way frequency tables, PROC FREQ computes goodness. For n -way tables, PROC FREQ provides stratified analysis by computing statistics across, as well as within, strata. For two-way tables, PROC FREQ computes tests and measures of association. With the Expected Count values shown, we can confirm that all cells have an expected value greater than 5. The FREQ procedure produces one-way to n -way frequency and contingency (crosstabulation) tables. If you included the EXPECTED and DEVIATION options in your syntax, you should see the following: The first table in the output is the crosstabulation. TABLE RankUpperUnder*LiveOnCampus / CHISQ EXPECTED DEVIATION NOROW NOCOL NOPERCENT Suppose that we want to test the association between class rank and living on campus using a Chi-Square Test of Independence (using α = 0.05). The proportion of upperclassmen who live on campus is 5.6%, or 9/161.The proportion of upperclassmen who live off campus is 94.4%, or 152/161. ![]() The proportion of underclassmen who live on campus is 65.2%, or 148/227.The proportion of underclassmen who live off campus is 34.8%, or 79/227. ![]() Recall that the column percentages of the crosstab appeared to indicate that upperclassmen were less likely than underclassmen to live on campus: Let's continue the row and column percentage example from the Crosstabs tutorial, which described the relationship between the variables RankUpperUnder (upperclassman/underclassman) and LivesOnCampus (lives on campus/lives off-campus). ![]()
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