Hypothesis Testing Calculator
Test means and proportions with one-sample and two-sample options. Get test statistic (z or t), degrees of freedom, p-values, critical values, and decisions at your chosen α and tail.
Enter your values
Results
Test statistic (z or t)
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Degrees of freedom (df)
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Critical value
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Tail
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p (two-tailed)
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p (left)
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p (right)
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Decision at α
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Two-tailed comparison unless you chose left/right tail.
Hypothesis Testing: Quick, Friendly Guide
Hypothesis testing helps you decide whether an observed effect (difference, change, or association) is likely real or due to random variation. You set a null hypothesis H₀, choose a significance level α, pick one- or two-tailed, compute a test statistic, and compare p-values or critical values to decide.
Common tests in this tool
- Means: one-sample (z or t), two-sample (z with known σ, or t as Welch/pooled when σ unknown)
- Proportions: one-sample and two-sample (normal approximation)
Two ways to conclude
- p-value: if p ≤ α, reject H₀; otherwise fail to reject
- Critical value: if test statistic crosses the critical threshold, reject H₀
Choosing tails
Use two-tailed when you care about any difference. Use left/right-tailed if your alternative hypothesis specifies a direction.
Tips
- Check assumptions (independence, approximate normality for small n, equal variances for pooled t).
- Avoid over-reliance on p-values—consider effect sizes and confidence intervals too.
- For proportions, ensure sample sizes are large enough for the normal approximation.