Behavioral Research: Statistical Methods

Why human intuition is unreliable for probabilistic reasoning, the biases statistics protects against (belief bias, confirmation bias, Simpson's paradox, base-rate fallacy), and Bayes' rule as the formal corrective.

Operational definitions, the four scales of measurement (NOIR), reliability (test-retest, inter-rater, parallel forms, internal consistency), and validity (internal, external, construct, face, ecological).

Frequentist vs Bayesian probability, PDFs and CDFs, the core distributions (Bernoulli, Binomial, Normal, t, χ², F), the Central Limit Theorem, sampling distributions, and the Law of Large Numbers.

Why visualise before you analyse (Anscombe's quartet), matching plots to data types, and the catalogue of plots: histogram, boxplot, scatter, bar/pie, mosaic, violin/raindrop, heatmap — plus pitfalls (rainbow palettes, truncated axes, dual-y).

Central tendency (mean, median, mode — robustness to outliers), dispersion (range, IQR, variance, SD, MAD), standardisation (z-scores), and Bessel's correction.

Pearson r (continuous-continuous), Spearman ρ (rank-based, nonlinear monotone), Kendall τ, partial vs semi-partial correlations. Cohen's κ, Cronbach's α for reliability.

Steps of NHST, Type I (α) and Type II (β) errors, statistical power (1 − β), Cohen's d, sample-size planning, one- vs two-tailed tests, t-tests (one-sample, independent, paired, Welch).

Family-wise type-I inflation, Bonferroni and Holm corrections (FWER), Benjamini-Hochberg (FDR), permutation tests, and how multiple comparisons drive the replication crisis.

Chi-square (goodness-of-fit and independence), Mann-Whitney U, Wilcoxon signed-rank, Kruskal-Wallis, Friedman, Spearman ρ, McNemar's test. When parametric assumptions fail.

VIF and what multicollinearity does to regression coefficients; PCA for dimensionality reduction; EFA vs CFA for psychometric scale validation; scree plots and parallel analysis.

Why ANOVA over multiple t-tests; SS_total = SS_between + SS_within; F = MS_between/MS_within; one-way, repeated-measures (sphericity, Mauchly, Greenhouse-Geisser), two-way (main effects + interaction), post-hoc (Tukey HSD).

Simple regression Y = β₀ + β₁X + ε; OLS minimises sum of squared residuals; R² vs adjusted R²; LINeM assumptions (linearity, independence, normality, equal variance, no multicollinearity); residual diagnostics; categorical predictors via dummy coding.

Bayes' theorem with prior, likelihood, posterior; Bayes Factor and its interpretation (3–10 moderate · 10–30 strong · >30 very strong); BayesFactor R package; Bayesian advantages (evidence for null, optional stopping, priors).

Why OLS fails for binary outcomes; the logit link; GLM components (random, systematic, link); odds ratios; maximum likelihood estimation; interpreting coefficients on the log-odds scale.

Maya's final walk-through: the 'Which test do I use?' decision tree, common confusions to memorise (PCA vs FA, FWER vs FDR, reliability vs validity), the report checklist (test statistic, df, p, effect size, CI), and exam-day rules of thumb.