Ten practical guides
Statistics for Clear Quantitative Reasoning
Use these pages to build a reliable mental model for data reasoning. Each topic explains the core idea, shows a worked example, and highlights interpretation errors to avoid.
Statistics skills are widely used in operations, research, product analysis, quality work, and decision support where evidence quality matters.
Descriptive stats
Learn to summarize data with mean, median, spread, and shape, then choose summaries that stay informative when skew, outliers, or uneven scales are present.
Probability rules
Apply complement, addition, and multiplication rules to compute event chances correctly, account for overlap, and avoid mistakes about independence.
Conditional and Bayes
Use conditional probability and Bayes rule to update beliefs from new evidence, while handling base rates carefully so test results are interpreted correctly.
Sampling and bias
Compare random, stratified, and cluster sampling methods, then identify selection, nonresponse, and measurement bias before drawing conclusions from results.
Random variables
Model uncertain outcomes with discrete or continuous random variables, read probability distributions, and compute expected value and variance for interpretation.
CLT
Understand why sample means become approximately normal under repeated sampling, when that approximation is reliable, and how standard error changes with n.
Confidence intervals
Construct and interpret confidence intervals for means and proportions, linking margin of error to variability, sample size, and method assumptions.
Hypothesis tests
Run hypothesis tests by stating null and alternative claims, calculating a test statistic and p value, and separating statistical significance from practical impact.
Correlation vs causation
Distinguish association from causation by checking confounding, reverse direction, and study design limits before making causal claims from correlated data.
Linear regression
Fit and interpret simple linear regression models, read slope and intercept in context, and validate assumptions with residual checks before using predictions.