Statistics Guides

Plain-English tutorials that explain the "why" behind the calculators — no jargon, no PhD required.

How to Choose the Right Statistical TestA decision guide + flowchart linking every test to a free calculator. How to Interpret a P-ValueWhat it means, what it doesn't, and why 0.05 is the threshold. Confidence Intervals ExplainedWhy a range of plausible values beats a single p-value. Effect Size ExplainedCohen's d, r, and the difference between significant and important. T-Test vs Z-TestThe one question that decides which you should use. ANOVA vs T-TestWhy you can't just run a t-test on every pair of groups. Null vs Alternative HypothesisEvery test starts here — how to write H₀ and H₁ correctly. Type I & Type II ErrorsFalse positives vs false negatives, alpha, beta, and power. One-Tailed vs Two-TailedThe directional choice that halves your p-value. Mean, Median & ModeWhich "average" to use, and how outliers mislead. What Is Statistical Significance?What "significant" means — and why it isn't the same as important. SD vs Standard ErrorTwo things everyone mixes up, and when to use each. Correlation vs CausationWhy "they move together" doesn't mean "one causes the other." Degrees of FreedomWhat df means, why n−1, and the formula per test. Statistical Power ExplainedWhat 80% power means and how many participants you need. Parametric vs Nonparametric TestsWhich test replaces which, and how one outlier can change the answer. Confidence Level vs Significance LevelWhy 95% confidence and α = .05 are two sides of one coin. P-Hacking ExplainedHow 20 tests give a 64% chance of a false positive. Simpson’s ParadoxHow a treatment can win in every subgroup and still lose overall. Regression to the MeanWhy extreme results do not last, even when nothing has changed. How to Detect OutliersIQR, z-scores and Grubbs compared, and why z-scores can miss them. Skewness and Kurtosis ExplainedWhat the shape of your data tells you, with rules of thumb. Types of VariablesNominal, ordinal, interval and ratio, and which test fits each. Bayes’ Theorem ExplainedWhy a positive result from a 90% accurate test can mean only 15%. Welch vs Student’s T-TestWhy Student’s test can reach 29% false positives. Paired vs Independent SamplesThe same data can give p = .004 or p = .076. Critical Values ExplainedWhat they are and how to find them for t, z, chi-square and F. Margin of Error ExplainedWhat ±3% really means, and why a lead has double the margin. Coefficient of Variation ExplainedComparing variability across units, and when the CV gives nonsense. Percentile vs Percentile RankTwo opposite questions, and why neither is a percentage. Expected Value ExplainedDice, raffles and roulette, and why 3.5 is a fair answer. The Empirical Rule68–95–99.7, the exact numbers and when it fails. Two-Way ANOVA ExplainedMain effects, interactions and how to read the plot. The Friedman Test ExplainedRepeated measures without assuming normality. Sign Test vs WilcoxonWhy the same data gives p = .109 and p = .010. The Law of Large NumbersWhy averages settle down, and why a coin is never due.

Want the step-by-step calculation? The How-To section shows how to compute each statistic by hand and in Excel.

A suggested reading order

If you are learning hypothesis testing from scratch, these guides build on each other in this order:

  1. Types of variables, because the type decides which methods apply.
  2. Mean, median and mode and standard deviation vs standard error: describing data and the uncertainty in an average.
  3. Null and alternative hypotheses: what a test is actually testing.
  4. Statistical significance and how to interpret a p-value.
  5. Type I and Type II errors and one-tailed vs two-tailed tests.
  6. Confidence intervals and effect size: reporting how large an effect is, not only whether it exists.
  7. Choosing a statistical test, then the comparisons: t-test vs z-test and ANOVA vs t-test.
  8. Degrees of freedom and correlation vs causation.
  9. Statistical power, for planning a study.
  10. Then the traps: p-hacking, Simpson’s paradox and regression to the mean.

Each guide explains the idea in plain English first, then gives the formula and a worked example, and links to the calculator that does the computation.

Prefer to jump straight to a tool?

All 26 tools are free and need no sign-up. Start with descriptive statistics, the t-test, or browse the full list on the homepage.

Revising for an exam? The printable statistics formulas cheat sheet puts every key formula on one page.