Paired t-Test Calculator
Test an entered mean paired difference with a two-sided Student t calculation and confidence interval from raw paired observations.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Analyze the mean and sample variance of within-pair first-minus-second differences using n−1 degrees of freedom.
t=(mean difference−null mean)/(sample SD of differences/√n)
Worked example
Differences 2, 2, 1, 2 and 3 have mean 2 and sample variance 0.5. With five independent pairs, t against null zero is about 6.324555.
Assumptions and input details
2–500 complete paired observations with the same measurement unit within each pair. Pairing is supplied by the user. Difference normality matters in small samples; independent pairs are assumed. Zero difference variance makes t inference undefined. Confidence limits describe the population mean difference under the model, not individual outcomes or practical importance.
References: SciPy: paired t statistic and degrees of freedom
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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