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Paired T-Test Calculator

Paste two matched lists and get the paired t statistic, p-value and working.

Test
Data entry
10 values read. Separate with commas, spaces or new lines.
10 values read. Separate with commas, spaces or new lines.

Paired lists need the same length. The test uses the differences (first minus second).

Alternative hypothesis
Significance level (α)

Paired t-test

t = -4.0621, p = 0.003
Degrees of freedom
9
Critical values
-2.262 and 2.262
Mean difference
-1.58
Standard error
0.38896
95% interval
-2.46 to -0.7001
Cohen's d
-1.28 (large)

p = 0.003 < α = 0.05, so reject H0: μ = 0. There is evidence that the population mean is different from 0. In plain terms, the mean paired difference differs from 0. The mean difference is -1.58, with an interval of -2.46 to -0.7001. Cohen's d = -1.28, a large effect.

Rejection region and t statistic

Rejection region and t statisticRejection region and t statistic. The two tails is shaded. The t is -4.062.-4-3-2-101234t (df = 9)t = -4.062

The shaded area is the rejection region (total area 0.05): values below -2.262 or above 2.262. The dashed line is your statistic.

Step-by-step working

  1. 1Hypotheses
    H0: μd=0H_0:\ \mu_d = 0H0​: μd​=0
    ↓
    H1: μd≠0H_1:\ \mu_d \neq 0H1​: μd​=0

    two-tailed test at α = 0.05; d is the difference within each pair

  2. 2Summary
    dˉ, s, n\bar d,\ s,\ ndˉ, s, n
    ↓
    −1.58, 1.23, 10-1.58,\ 1.23,\ 10−1.58, 1.23, 10
  3. 3Standard error
    SE=snSE = \dfrac{s}{\sqrt{n}}SE=n​s​
    ↓
    SE=1.2310=0.38896SE = \dfrac{1.23}{\sqrt{10}} = 0.38896SE=10​1.23​=0.38896
  4. 4t statistic
    t=dˉ−0SEt = \dfrac{\bar d - 0}{SE}t=SEdˉ−0​
    ↓
    t=−1.58−00.38896=−4.0621t = \dfrac{-1.58 - 0}{0.38896} = -4.0621t=0.38896−1.58−0​=−4.0621
  5. 5p-value and critical value
    df=n−1=9df = n - 1 = 9df=n−1=9
    ↓
    p=0.002833, tc=−2.262 and 2.262p = 0.002833,\ t_c = -2.262\ \text{and}\ 2.262p=0.002833, tc​=−2.262 and 2.262
  6. 6Confidence interval
    dˉ±tα/2 SE\bar d \pm t_{\alpha/2}\,SEdˉ±tα/2​SE
    ↓
    −1.58±2.262×0.38896=[−2.46, −0.7001]-1.58 \pm 2.262\times 0.38896 = [-2.46,\ -0.7001]−1.58±2.262×0.38896=[−2.46, −0.7001]
  7. 7Cohen's d
    d=dˉ−0sd = \dfrac{\bar d - 0}{s}d=sdˉ−0​
    ↓
    d=−1.285d = -1.285d=−1.285

    large effect

  8. 8Decision
    p<αp < \alphap<α
    ↓
    reject H0\text{reject } H_0reject H0​
  1. Tools
  2. Statistics
  3. T-Test Calculator
  4. Paired T-Test Calculator

About Paired T-Test Calculator

This paired t-test calculator compares two measurements taken on the same subjects, such as before and after a treatment, by testing whether the mean difference is zero. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.

Paste the first measurement in one box and the second in the other, in the same order. The calculator subtracts them pair by pair and runs a one-sample t-test on the differences. If you only have the mean, standard deviation and count of the differences, switch to summary statistics.

Pairing matters because each subject acts as its own control. The same sleep data analysed as two independent groups is not significant at 0.05, but analysed as pairs it is clearly significant.

How to use Paired T-Test Calculator

  1. 1Choose the test: one-sample, paired or two-sample.
  2. 2Choose raw data or summary statistics. For raw data, paste each list; for paired data, keep the two lists in the same order and the same length.
  3. 3For a one-sample test type the hypothesised mean. For two samples pick Welch or Student.
  4. 4Pick the alternative hypothesis (two-tailed, right or left) and the significance level.
  5. 5Read the t statistic, p-value, interval and Cohen's d, then open the working to see every formula.

Features

  • One-sample, paired and independent two-sample t-tests.
  • Welch (unequal variances) and Student (pooled) two-sample tests, compared side by side with a recommendation.
  • Raw data or summary statistics (mean, standard deviation, n).
  • Cohen's d with a size label, plus the standard error and a confidence interval.
  • Left, right or two-tailed tests, with the critical value for your significance level.
  • A bell curve with the rejection region shaded and the t statistic marked.
  • Step-by-step KaTeX working and a plain-English conclusion.

Paired t-test

Take the difference of each pair, then test the mean difference against zero.

d_i = a_i − b_i
t = d̄ / (s_d / √n),   df = n − 1

Worked examples

  • Sleep data, drug 1 minus drug 2, 10 patients, two-tailed → gives t = -4.062, df = 9, p = 0.003

    R: t.test(extra ~ group, data = sleep, paired = TRUE) gives t = -4.0621, df = 9, p = 0.002833.

  • Drug 2 minus drug 1, right-tailed (is drug 2 better?) → gives t = 4.062, p = 0.001

Privacy: how it works

  • The test is calculated by code in your own browser tab. Your data is not sent to Ulkaa or to any other server.
  • There is no account and nothing is stored. Closing the tab clears what you entered.

Tips

  • Use the paired test when the same people or items are measured twice. Using the two-sample test on paired data throws away the pairing and usually loses power.
  • Decide one-tailed or two-tailed before you see the data. A two-tailed test is the safe default.
  • Report the effect size and the interval with the p-value. A tiny p-value with a negligible Cohen's d is statistically significant but may not matter in practice.
  • If your lists have different lengths, that is fine for the two-sample test, but the paired test needs equal lengths.

Frequently asked questions

Is it really free?

Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.

Do I need an account?

No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.

Does it run in my browser?

Yes. Your data are processed by code running in your browser tab, on your own device.

Is my data uploaded?

No. Your data are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.

Do the two lists need the same length?

Yes. Each value in the first list is matched with the value at the same position in the second. The calculator tells you if the lengths differ.

What is the difference between a paired and an independent t-test?

A paired test uses the differences within matched pairs and removes between-subject variation. An independent test treats the groups as unrelated. Use the paired test only when each value really has a partner.

More T-Test Calculator pages

  • T-Test CalculatorRun a one-sample, paired or two-sample t-test from raw data or summary statistics, with Cohen's d, the p-value and the working.
  • One-Sample T-Test CalculatorCompare the mean of one sample with a value you expect and see the t statistic, p-value and working.
  • Two-Sample T-Test CalculatorCompare the means of two independent groups with the classic pooled Student t-test.
  • Welch's T-Test CalculatorCompare two means without assuming equal variances, with Welch-Satterthwaite degrees of freedom.
  • Cohen's d CalculatorGet Cohen's d for two groups from summary statistics, with the matching t-test and a size label.

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