Stat 418 – Day 14Last Time – Testing significance of conditional associationSummaryHypothesesFrom the SAS documentationTo DoStat 418 – Day 14Intro to General Linear Models (Ch. 3)Last Time – Testing significance of conditional associationCan create partial tables at difference values of Z and examine the X,Y relationship in each table.If the X,Y relationship is homogenous across the levels of Z (common odds ratio), can test whether this common odds ratio is significantly different from one using the CMH test.SummaryThe marginal table relating smoking to survival in Whickham does not provide a meaningful summary of the relationship.CHM = 5.84, p-value = .016  reject conditional independence of smoking and survival given ageEstimated common OR = .655  given age, being a smoker is associated with a 35% lower odds of being alive 20 years later than being a nonsmoker; 95% CI = (.463, .925)(SAS) The Breslow-Day statistic p-value .80  homogenous association is reasonable for all age groups (ignoring last uninformative age group)HypothesesCMH:H0: XY(1) = XY(2) = … = XY(K) = 1Breslow-Day:H0: XY(1) = XY(2) = … = XY(K) Both should have large sample sizes to use the chi-square distributionCMH works better than BD with small sample sizesFrom the SAS documentation“CAUTION: The CMH statistics have low power for detecting an association in which the patterns of association for some of the strata are in the opposite direction of the patterns displayed by other strata. Thus, a nonsignificant CMH statistic suggests either that there is no association or that no pattern of association has enough strength or consistency to dominate any other pattern.”To DoFinish Investigation 3Be reading Ch. 3, 4Practice problem in