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Paired samples t-test calculator

Compares two related measurements — before/after, condition A/condition B on the same cases — via a t-test on the paired differences.

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Your data

Two columns of equal length — values are paired by position (row 1 with row 1, row 2 with row 2, …). Keep each participant on the same line in both boxes.

n = 0
n = 0
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When to use this

Use a paired-samples (dependent) t-test when the same cases are measured twice — before vs. after an intervention, with vs. without a treatment, morning vs. evening — or when cases are matched one-to-one across conditions. Because each case serves as its own control, the test works on the within-pair differences, which removes stable between-person variation and usually gives much more statistical power than comparing two independent groups of the same size.

Key assumptions

  • Each pair of values belongs to the same case (or to deliberately matched cases).
  • The differences (not the raw scores) are approximately normally distributed, or n is reasonably large.
  • Pairs are independent of one another.
  • The outcome is interval or ratio scaled.

Common mistakes

  • Pasting the two columns in a different case order — values are paired by row, so a shuffled column silently produces nonsense.
  • Using the independent t-test on paired data, throwing away the design’s power.
  • Reporting Cohen’s d for independent groups instead of dₖ (the mean difference divided by the SD of the differences).

Frequently asked questions

What is Cohen’s d_z and how does it differ from Cohen’s d?
d_z divides the mean difference by the standard deviation of the differences — the natural effect size for paired designs. It is usually larger than the between-groups d for the same data because pairing removes between-person variance. Say which one you report.
My two columns have different lengths — why is that an error?
The test pairs values by position, so every case needs a value in both columns. If a case is missing one measurement, remove that case from both columns (listwise deletion) before pasting.
What is the nonparametric alternative?
The Wilcoxon signed-rank test (or the sign test for a minimal-assumptions check). Use it when the differences are clearly non-normal and the sample is small.

Related free tools

Sample size calculatorSample size for two groupsEffect size (Cohen's d)Descriptive statisticsOne-sample t-testIndependent t-testOne-way ANOVAz-table (standard normal)t-table (critical values)Chi-square table

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