MasterTool

Hypothesis Test Calculator

Calculate hypothesis test using your data.

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What this tool does

Calculate hypothesis test using your data. Summary-statistic tests: enter means, SDs and sizes rather than raw data. The z-test treats the entered SD as the known population SD; use the t-test when it is a sample SD.

How to use the Hypothesis Test Calculator

  1. Enter or select test type.
  2. Enter or select sample mean 1.
  3. Enter or select hypothesized mean (μ₀).
  4. Enter or select standard deviation 1.
  5. Enter or select sample size 1.
  6. Enter or select sample mean 2 (two-sample only).
  7. Enter or select standard deviation 2 (two-sample only).
  8. Enter or select sample size 2 (two-sample only).
  9. Enter or select significance level (α).
  10. Read the calculated result; change any measurement to compare alternatives.

Formula

z = (x̄−μ₀)/(σ/√n); one-sample t uses s/√n with df = n−1; Welch two-sample t uses both samples' variances with the Welch–Satterthwaite df; p-values are two-sided
mode
Test type
m1
Sample mean 1
mu0
Hypothesized mean (μ₀)
s1
Standard deviation 1
n1
Sample size 1
m2
Sample mean 2 (two-sample only)
s2
Standard deviation 2 (two-sample only)
n2
Sample size 2 (two-sample only)
alpha
Significance level (α)

Summary-statistic tests: enter means, SDs and sizes rather than raw data. The z-test treats the entered SD as the known population SD; use the t-test when it is a sample SD.

Worked example

For hypothesis test calculator, the following measurements illustrate the exact method: Test type: one-z; Sample mean 1: 105; Hypothesized mean (μ₀): 100; Standard deviation 1: 15; Sample size 1: 36; Sample mean 2 (two-sample only): 98; Standard deviation 2 (two-sample only): 14; Sample size 2 (two-sample only): 36; Significance level (α): 0.05.

Inputs

  • Test typeOne-sample z-test
  • Sample mean 1105
  • Hypothesized mean (μ₀)100
  • Standard deviation 115
  • Sample size 136
  • Sample mean 2 (two-sample only)98
  • Standard deviation 2 (two-sample only)14
  • Sample size 2 (two-sample only)36
  • Significance level (α)5%

Result

  • Test statistic2
  • Two-sided p-value0.05
  • Reject H₀ at α = 0.05?Yes

Results explained

Test statistic
Test statistic from the formula above. Summary-statistic tests: enter means, SDs and sizes rather than raw data. The z-test treats the entered SD as the known population SD; use the t-test when it is a sample SD.
Two-sided p-value
Two-sided p-value from the formula above. Summary-statistic tests: enter means, SDs and sizes rather than raw data. The z-test treats the entered SD as the known population SD; use the t-test when it is a sample SD.
Reject H₀ at α = 0.05?
Reject H₀ at α = 0.05? from the formula above. Summary-statistic tests: enter means, SDs and sizes rather than raw data. The z-test treats the entered SD as the known population SD; use the t-test when it is a sample SD.

Frequently asked questions

z = (x̄−μ₀)/(σ/√n); one-sample t uses s/√n with df = n−1; Welch two-sample t uses both samples' variances with the Welch–Satterthwaite df; p-values are two-sided

Summary-statistic tests: enter means, SDs and sizes rather than raw data. The z-test treats the entered SD as the known population SD; use the t-test when it is a sample SD.

Enter numbers only, in the units and format each label describes. Remove missing values rather than substituting zero, unless zero is a real observation.

No. Results describe the numbers you entered. Statistical inference also depends on sampling design, independence, model fit and interpretation; a p-value is not the probability that a hypothesis is true.

No. Every calculation, including the distribution algorithms, runs entirely in your browser.