2. Inference using t-distributions

The Statistical Sleuth, chapter 2

• useful in regression and analysis of variance structures
• derived under random sampling models when populations are normally distributed
• can function as approximation to randomization tests
• often work quite well even when populations are not quite normal

Evolution - house sparrows survival and death through harsh winter. Is humerus length different for the two populations?

Two-sided p-value: .08 from two-sample t-test. Mean length 0.010 in greater, 95% confidence interval from -0.001 to +0.021.

Observational - no causal inference. Non-random population. (Very weak difference).

Post-mortem difference in size of brains, after controlling for confounding factors by choosing monozygotic twins.

Two-sided p-value: .006, from paired t-test). Mean volume 0.20 cm3 smaller, (11%), 95% confidence interval from 0.07 to 0.33 cm3.

Not randomly selected, and no causal inference - whether brain size preceded schizophrenia or not.