intro to effect size

effect size

statistical estimate of a magnitude of an effect rather than a test

two families of effect size

D-family

• standardized differences (or ratios)

• Cohen’s d

• risks, odds, and risk and odds ratio

R-family

• standardized associations

• correlation

• R²

Cohen’s d

generally: d = raw difference/SD

transform raw difference into Z units

remember to use SD of the sample for one sample t, SD of the differences for paired sample and pooled SD for independent sample

looks like t statistic but the denominator is SD not SE

confidence interval for d

statistic ± critical value x SE

= d ± t_crit x √(1/n₁ + 1/n₂)

benchmarks

d = .2 small

d = .5 med

d = .8 large

risk

conditional probabiltiy of one outcome for a group

Risk(A|B) is the same calculation for P(A|B)

use total # in B group as the denominator

odds

ratio of one outcome to anohter outcome for a group

Odds(A|B) means 1) look at the outcome options given the B condition 2) find the ratio of the frequency of those outcome options given the B condition 3) the numerator is A

• ex. Odds(COVID|Vaccine) = everyone who got COVID with the vaccine compared to everyone who got COVID on the placebo

use # in the B group where A didn’t happen as the denominator

risk ratio (relative risk)

= Risk(A|B₁) / Risk(A|B₂)

… “the risk of A under condition B₁ is [ratio] higher than under B₂ condition

odds ratio

= Risk(A|B₁) / Risk(A|B₂)

… “the odds of A under condition B₁ is [ratio] higher than under B₂ condition