- Give back homework

- Scientific contex
- Suppose we compare two groups
- one typically called X other typically called Y.
- Or scientifically: control and treatment group
- EG: Do people with ACL replacements do "better" than those without ACL replacement?
- interested in deciding which group is better/larger/higher mean.

- How can we compare two group?
- Traditional answer: two sample t-test (keyword = pooled)
- Also called simple regression
- Let indicator represent each group
- Run regression of outcome on indicator variable

- What if the two groups have different variances?
- Traditional answer: Welchs approximation (also large sample)
- Also called simple regression using the sandwich estimator
- Done automatically by all statistical packages

- What if we take two measurement on each person?
- Traditional answer: paired t-test
- Also called multiple regression
- First indicator called treatment (1=treatment, 0=control)
- Add one indicator for each person (called "row effect")
- Don't look at row effects, only at column effect
- Easy to represent in a table

- Scientific context
- Suppose we compare more than two groups
- EG: Which surgery is best, ACL reconstruction, cadavorious replacement, none, Teflon replacment
- interested in deciding which group is best.

- How can we compare many groups?
- Traditional answer: one-way ANOVA
- Also called multiple regression
- have one indicator for each group (no constant)
- Multiple comparisons come up

- What if the two groups have different variances?
- Traditional answer: Oops, don't like doing that
- Easy with sandwich estimator

- What if we take several measurements on each person?
- Traditional answer: two way ANOVA (keyword randomized block design)
- Also done as multiple regression

- Compare to grand mean (Bonferroni = sqrt(2 log p))
- Compare all pairs (balanced design Bonferroni = 2 sqrt(2 log p), work out both ways of thinking about this)
- Improvement: Tukey-Cramer, uses dependencies in situation and hence get a slight improvement over Bonferroni
- Easier problem: HSU, uses the fact that we don't care which is best, only if each category COULD be best or not.

Last modified: Tue Feb 27 08:48:49 2001

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