STAT 541: Two-Sample

# Statistics 541: Two-Sample

## Admistrivia

• Give back homework

## Two sample t-test

• 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

## ANOVA

• 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

## The interesting new issue is multiple comparisons

• 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