Plain-language explanation.
Statistical inference is about drawing conclusions about a population from a sample. Instead of measuring everyone, we measure a subset and use mathematics to generalise. We test hypotheses (is this drug effective?), estimate quantities with uncertainty, and decide how confident we can be in our conclusions. Statistical reasoning is essential for understanding research and making evidence-based decisions.
Core concepts and standard treatment.
Statistical inference framework: descriptive statistics (mean, median, mode, variance, standard deviation, IQR, skewness, kurtosis); probability foundations (probability axioms, conditional probability, Bayes' theorem, probability distributions — normal, t, chi-squared, F, binomial, Poisson); sampling theory (simple random, stratified, cluster, systematic sampling; sampling distributions, Central Limit Theorem); and inferential tools (hypothesis testing, confidence intervals, p-values). Type I error (false positive — rejecting true null) and Type II error (false negative — failing to reject false null), power, and sample size calculation.
Deeper theory, debates and edge cases.
Frequentist vs. Bayesian inference: frequentist (Neyman-Pearson: long-run frequency of errors; p-value as probability of data given null hypothesis — widely misinterpreted); Bayesian (probability as degree of belief; prior distribution updated by data via Bayes' theorem to give posterior; Bayes factors as evidence; credible intervals vs. confidence intervals). Replication crisis: inflated Type I error rates due to p-hacking (multiple comparisons, optional stopping), HARKing (hypothesising after results known), and publication bias — leading to many published findings that do not replicate (Open Science Collaboration, 2015: only 36-39% of psychological experiments replicated).
How it is applied in practice.
Statistical inference in professional practice: clinical trials (randomised controlled trial design, pre-registration, FDA/EMA regulatory statistics, intention-to-treat analysis); A/B testing in tech companies (multiple comparison corrections, novelty effects, minimum detectable effect, sample ratio mismatch); econometrics (instrumental variables, regression discontinuity, difference-in-differences for causal inference from observational data); and quality control (statistical process control, Six Sigma — control charts, Cpk index). Practical significance vs. statistical significance: a statistically significant result may have trivial effect size (Cohen's d, odds ratio, risk ratio, NNT) — professional judgment requires assessing both.