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Hypothesis testing calculator

Walk through a hypothesis test one step at a time with your own numbers: one-sample t, z, or a test of a single proportion.

Test
Alternative H₁
  1. Hypotheses. H₀: μ = 100   H₁: μ ≠ 100
  2. Significance level. α = 0.05; two-tailed, so the critical value is ±2.03 (df = 35).
  3. Test statistic. t = (104.2 − 100) / 2 = 2.1
  4. p-value. p = .043: the chance of a t this extreme if H₀ were true.
  5. Decision. Reject H₀ The data provide evidence that μ ≠ 100.
your statistic

Which test fits my research question?

Describe your hypothesis and data, and get a recommended test with the reasoning, assumptions to check and the calculator to use.

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The logic in one paragraph

Assume nothing is going on (H₀). Work out how surprising your data would be under that assumption. If they would be very surprising (p ≤ α), conclude the assumption is probably wrong. The shaded tails in the plot are the rejection region: they hold exactly α of the probability under H₀, so landing there by chance happens only α of the time. Step through the calculator above to watch the statistic arrive.

Choosing the right test

  • One mean vs a reference value, σ estimated from the sample: one-sample t.
  • One proportion vs a reference: one-proportion z (needs np₀ and n(1 − p₀) ≥ 10).
  • Two groups: t-test for means, two-proportion test for rates.
  • Categorical association: chi-square. Relationship between two measures: correlation.

Frequently asked questions

What are the steps of hypothesis testing?

1) State H₀ and H₁. 2) Choose α. 3) Compute the test statistic from your data. 4) Find the p-value (or compare with the critical value). 5) Decide and interpret in context: reject H₀ if p ≤ α, otherwise fail to reject it.

What is the difference between a null and alternative hypothesis?

H₀ is the “no effect” statement you try to find evidence against, such as μ = 100. H₁ is what you conclude if the evidence is strong enough: μ ≠ 100 (two-tailed), μ > 100 or μ < 100 (one-tailed).

Why “fail to reject” rather than “accept” H₀?

A non-significant result means the data are compatible with H₀, not that H₀ is proven. The study may simply have lacked power. To show an effect is negligible, use an equivalence test.

When is a one-tailed test appropriate?

Only when the direction was specified before seeing the data and an effect in the other direction would be treated the same as no effect. Otherwise use two-tailed.