Statistics: Foundations and Practice
Statistics provides the principles and tools to learn from data. From experimental design to inference and prediction, it connects questions to defensible answers. This tutorial builds an end‑to‑end view for practitioners who want statistically sound analytics.
1) Asking Good Questions
Define estimands before looking at the data: means, differences, ratios, quantiles. Declare the target population and data‑generating process to avoid ‘garden of forking paths’ mistakes.
2) Experimental & Observational Studies
Randomised experiments protect against confounding but are not always feasible. Observational studies require careful design: matching, stratification, and sensitivity analyses.
3) Inference
Construct intervals and tests that reflect uncertainty. Prefer effect sizes and intervals to dichotomous ‘significant/non‑significant’ language. Use bootstrapping when formulas are fragile.
4) Prediction
Split data honestly, maintain a hold‑out set, and report multiple metrics. Use calibration to turn scores into probabilities and decision analysis to choose thresholds.
FAQ
What if my data are missing?
Start with simple diagnostics, apply multiple imputation where missingness is not random, and always report the mechanism and assumptions.
How many samples do I need?
Perform power analysis connected to your effect size of interest and practical constraints.