Confidence Intervals and Hypothesis Tests Day 3 Confidence Intervals and Hypothesis Tests

Motivating Question(s) On average, how much does this procedure (i.e. abdominal aortic surgery) cost? Is it the same for those with and without complications? males versus females? those in hospitals with high versus low volumes? What about length of stay?

What can we say about the average cost? We want not only the average cost, but a confidence interval for the average cost Confidence interval command: ci totchg

Gender Difference? Is average cost the same for males versus females? sort sex ci totchg, by(sex)

What about reintubation? sort reintuba ci totchg, by(reintuba) ci totchg, by(reintuba) level(99)

Hospital Volume? sort hospvol ci totchg, by(hospvol)

Are the differences in means signficant? We can perform 2 sample t-tests to compare means. Example: group 1 is males group 2 is females Is the mean total charge for men the same as for women?

ttests Gender differences? ttest totchg, by(sex) Reintubate? ttest totchg, by(reintuba) Hospital Volume? ttest totchg, by(hospvol)

But what about skewness? Because sample is “large”, we can rely on the central limit theorem and skewness of total charges is okay when comparing the means. Problems arise when comparing means and one group is relatively rare (i.e. sample size <40)

Does septicemia affect total charges? If we tabulate the septicemia data, we see that only 13 patients had septicemia. We can’t rely on the Central Limit Theorem and so we need to use a non-parametric test Wilcoxon Rank Sum ranksum totchg, by(septicem)

Why not always use non-parametric tests? They throw away information They only consider ranks and not the actual numeric values