1. Confidence Intervals and Hypothesis Tests
Day 3
Confidence Intervals and Hypothesis Tests

2. 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?

3. 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

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

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

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

7. 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?

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

9. 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)

10. 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)

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