Helpful tools for data work and reporting: Quick Table Generator, Math Formula Renderer, Word & Character Counter, Random Synonym Finder, Unit Converter, Citation formatting guide, Confidence Interval Calculator
What this calculator does
- Z tests: one sample mean with known sigma, two sample means with known sigmas, one sample and two sample proportions (pair with the Confidence Interval Calculator to add CIs to your report).
- T tests: one sample, two independent with Welch or pooled option, paired samples (see reporting tips in the reporting section).
- Chi square: goodness of fit and independence with Cramers V; build clean input tables with the Quick Table Generator.
- Explainers: shows formulas, steps and a small distribution chart with critical regions (export formulas as images via the Math Formula Renderer).
- Power hint: a quick power value helps you judge if n is in the right ballpark.
- Private: it runs locally so your data stays on your device.
Why hypothesis testing matters
Without a structured test you risk chasing noise. Hypothesis testing forces you to define H0 and H1, select a defensible alpha and quantify how extreme your data is under H0. When paired with effect size and a short power check, you balance statistical significance with practical significance. To present precision, include confidence intervals—see our Confidence Interval Guide.
How to choose the right test
- Type of outcome: numeric average or proportion leads to Z or T. Categorical counts lead to Chi square (prep data quickly in the CSV Viewer & Editor).
- Groups: one sample, two independent or paired.
- Variance knowledge: if sigma is known or n is very large with good conditions, Z is acceptable. Otherwise use T.
- Variance equality: for two independent means use Welch by default unless equal variances are justified.
- Tails: use two tailed when you care about any difference. Use one tailed only when a direction is justified in advance.
How to report results with effect sizes
Always include the test statistic, degrees of freedom if relevant, p value, effect size and a confidence interval if available. Clear reporting helps readers understand both statistical and practical meaning. You can compute and paste CIs directly from the Confidence Interval Calculator for means and proportions.
- Means: report Cohen d or Hedges g with a short interpretation like small, medium or large.
- Proportions: consider Cohen h or the raw difference with a confidence interval (see Wilson/Newcombe options in the CI guide).
- Tables: report Phi or Cramers V for Chi square results.
Worked examples
- One sample t: x̄ = 5.4, μ₀ = 5, s = 1.2, n = 40, two tailed, α = 0.05. The calculator gives t, p, critical t, Cohen d and Hedges g, with a visual marker on the curve. Add a 95% CI via the CI tool.
- Two proportions z: x₁ = 45 of 100 vs x₂ = 30 of 100, right tailed. You get z, p, pooled p, Cohen h and a quick power check. Present results in a clean table using the table generator.
- Chi square independence: paste a 3 by 2 table like 12,8 | 14,6 | 9,11. You get χ², df, p, critical χ² and Cramers V. Prepare the matrix in the CSV Viewer & Editor to avoid alignment errors.
Educational insights
- Alpha is a design choice: set it before seeing the data. 0.05 is common but not sacred.
- p values are not the probability H0 is true: they measure extremeness under H0, not belief.
- Effect sizes travel better than p values: they are unit free and easier to compare across studies.
- Power depends on meaningful effect: define the smallest effect worth detecting before collecting data.
- Assumptions matter: check independence and rough normality for means, and expected counts for Chi square. When summarizing assumptions or outputs, render formulas neatly with the Math Formula Renderer.
Try it now
Open the calculator, run a test, and copy the result block into your report: Go to Hypothesis Testing Calculator. Format your tables with the Quick Table Generator and render equations with the Math Formula Renderer. For confidence intervals to accompany your test, use the Confidence Interval Calculator.