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Calculators/Statistics/T-statistic (one or two sample)
Statistics

T-statistic (one or two sample) calculator

How many standard errors a sample mean, or the gap between two means, is from the reference value.

What this calculator does

T-statistic (one or two sample) works out how many standard errors a sample mean, or the gap between two means, is from the reference value. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.

The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.

The formula

FormulaOne-sample: t = (x̄−μ)/(s/√n); Two-sample (pooled, equal variance): t = (x̄₁−x̄₂)/(sp√(1/n₁+1/n₂))

The inputs explained

FieldWhat to enter
Test typeChoose from One sample vs a reference mean, Two independent samples.
Sample 1 meanA number. Starts at 52.
Sample 1 standard deviationA number. Starts at 8.
Sample 1 sizeA number. Starts at 25.
Reference mean (μ), one-sample onlyA number. Starts at 50.
Sample 2 mean, two-sample onlyA number. Starts at 47.
Sample 2 standard deviation, two-sample onlyA number. Starts at 9.
Sample 2 size, two-sample onlyA number. Starts at 22.

Worked examples

Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.

How the answer changes with sample 1 mean

Every other input is held at the calculator’s starting values while sample 1 mean varies. Select any row to load that scenario into the calculator.

How the answer changes with sample 1 mean
Sample 1 meant-statisticDegrees of freedomStandard error
26-15.000241.600
39-6.875241.600
521.250241.600
7817.500241.600
10433.750241.600
15666.250241.600