Behavioral Research: Statistical Methods

Walk through the base-rate fallacy with the mammogram example. Compute P(cancer | positive) given P(cancer)=0.01, P(+|cancer)=0.9, P(+|¬cancer)=0.07. Comment on the practical implication for clinical screening.

Distinguish reliability and validity. Can a measurement be valid without being reliable? Concrete example.

Define the four scales of measurement (NOIR). For each, give one example and one statistic that becomes meaningful at that level.

State the Central Limit Theorem and explain why it matters for inference.

Distinguish Law of Large Numbers from CLT.

Define statistical power. List five factors that affect it. A study finds p = 0.18 with n = 30 per group and claims 'no effect of the treatment'. Critically evaluate.

Differentiate Type I and Type II errors. Explain the trade-off.

Differentiate FWER and FDR. When use each? Which is more conservative?

Match nonparametric tests to their parametric counterparts.

Multiple regression Income ~ Education + Experience + Age, n = 200. R² = 0.42; β_Education = 4500 (p < .001); β_Experience = 1200 (p < .01); β_Age = 50 (p = .74). VIFs 9.8, 11.3, 12.1. Interpret R², interpret each β, explain why Age is non-significant, what the VIFs reveal, and what to do.

Why not multiple t-tests across 3+ groups? How does ANOVA fix it?

What is sphericity in RM-ANOVA? How is it tested? What if violated?

R² vs adjusted R². Which to report and why?

Walk through Bayesian inference: prior, likelihood, posterior. Apply to a coin flipped 10 times with 8 heads under Beta(1,1) prior. Compute posterior, credible interval, and BF₁₀ informally.

Why can't OLS regression model a 0/1 outcome? What does logistic regression do instead?

List the three components of a GLM with an example for each.

PCA vs Factor Analysis — conceptual differences and when to use each.

Discuss the replication crisis. What is it, three statistical contributors, five reforms, and how Bayesian methods help.