Behavioral Research: Statistical Methods
CG3.402Vinoo Alluri•Monsoon 2025-26•4 credits
Last-Week Revision Pack
The final condensed layer. Open this on exam morning.
CheatsheetWhich test do I use? Categorical DV → χ². 2 indep continuous → independent t (Welch if unequal var) / Mann-Whitney. 2 paired → paired t / Wilcoxon. 3+ indep → one-way ANOVA / Kruskal-Wallis. 3+ paired → RM-ANOVA / Friedman. Continuous × continuous → Pearson r / Spearman / regression.
FormulaBayes: . Mammogram → P(cancer | +) ≈ 9%.
FormulaCohen's d = (M₁ − M₂) / SD_pooled. 0.2 / 0.5 / 0.8.
FormulaANOVA: F = MS_between / MS_within. η² = SS_between / SS_total.
Formulaχ² = Σ (O − E)² / E. df = (r−1)(c−1) for independence.
FormulaVIF_j = 1 / (1 − R²_j). > 5–10 is severe multicollinearity.
FormulaLogit: log(p/(1−p)) = β₀ + β·X. OR = exp(β).
Memory TriggerBonferroni: per-test α = α_FW / m. Holm: stepwise FWER. BH: stepwise FDR.
Memory TriggerReliability = consistency; Validity = accuracy. Cannot be valid without being reliable.
Memory TriggerFrequentist non-significance is NOT evidence for null. Use Bayes Factor.
High YieldPower = 1 − β. Factors: n, effect size, α, variance, design (within > between).
High YieldSphericity violated in RM-ANOVA → Greenhouse-Geisser (or Huynh-Feldt) corrects df.
High YieldPCA = variance reduction (no latent model). FA = latent-variable model with unique error.
High Yieldp-value is P(data | H₀). NOT P(H₀ | data).
Common MistakeDon't 'accept' H₀ — only 'fail to reject'.
Common MistakeDon't switch one-tailed post-hoc — p-hacking.
Common MistakeDon't compare raw R² across models with different k — use adjusted R².
Common MistakeDon't run pairwise t-tests across 3+ groups — use ANOVA + post-hoc.
Common MistakeDon't apply OLS assumptions (normality, homoscedasticity) to logistic regression.
Weak AreaBayes update — practice the 3-step pattern (prior, likelihood, evidence).
Weak AreaANOVA SS partition by hand on a 3-group, 3-numbers dataset.
Weak Areaχ² 2×3 expected counts: E = row_total × col_total / grand_total.
Weak AreaLogistic regression OR computation: β = 0.7 → OR = e^0.7 ≈ 2.01.
DerivationBessel's correction: sample variance ÷ (n − 1) is unbiased; one DoF spent on x̄.
DerivationWhy F = MS_between/MS_within tests means: under H₀ both estimate σ²; under H₁, MS_between estimates σ² + n·Var(μ).