Dependent Samples T Test Calculator

Calculator Inputs

First sample label

Second sample label

Hypothesized mean difference

Confidence level percent

Alternative hypothesis

Difference order

Decimal places

First sample values

Second sample values

Paired rows optional

When this box has data, separate sample boxes are ignored.

Example Data Table

Pair	Before	After	Before - After
1	72	76	-4
2	75	78	-3
3	71	75	-4
4	80	83	-3
5	77	82	-5

Formula Used

The calculator first converts each matched pair into a difference.

dᵢ = Xᵢ - Yᵢ, or the reverse order selected by the user.
mean difference = Σdᵢ / n
sᵈ = √[Σ(dᵢ - mean difference)² / (n - 1)]
SE = sᵈ / √n
t = (mean difference - hypothesized difference) / SE
df = n - 1
CI = mean difference ± t critical × SE
Cohen dz = mean difference / sᵈ

How to Use This Calculator

Enter labels for the two related measurements.
Paste each sample into its own box, one value per line.
You may also paste paired rows, such as 72,76.
Choose the difference order carefully.
Enter the hypothesized mean difference, usually zero.
Select the confidence level and alternative hypothesis.
Press calculate to view the result above the form.
Use the CSV or PDF button to save the output.

Understanding the Dependent Samples T Test

A dependent samples t test compares two related measurements. The same subject may be measured before and after treatment. A matched pair may also compare twins, stores, machines, or blocks. The test reduces each pair to one difference. It then checks whether the average difference is far from a chosen value.

Why Pairing Matters

Pairing controls many background differences. A person is compared with the same person. A machine is compared with its own baseline. This usually lowers random noise. It can reveal small changes that an independent test may miss. The method is powerful when pairs are truly linked. It is not suitable for unrelated groups.

What This Calculator Measures

This calculator finds the mean paired difference, standard deviation, standard error, t statistic, degrees of freedom, p value, and confidence interval. You can choose the order of subtraction. You can also set the hypothesized mean difference. The alternative hypothesis may be two sided, greater, or less. Effect size is added for practical reading.

Assumptions to Check

The paired t test assumes the differences are sampled independently. It also assumes the distribution of differences is roughly normal. Small samples need more care. Large samples are more tolerant. Extreme outliers can strongly change the mean and standard deviation. Review the difference column before trusting the final conclusion.

Interpreting the Output

A small p value suggests the observed mean difference would be unusual under the null hypothesis. The confidence interval shows a likely range for the true mean difference. If the interval excludes the hypothesized value, the result usually matches a significant two sided test. Effect size helps judge the size of change.

Good Reporting Practice

Report the test name, sample size, mean difference, t statistic, degrees of freedom, p value, confidence interval, and effect size. Also describe the two related measurements. Mention the chosen direction of subtraction. Clear reporting helps readers understand both the statistical result and the real meaning of the paired change.

When Not to Use It

Do not use this test for separate groups. Use another method when pairs are missing or mixed. For strongly skewed differences, consider a signed rank test. Always inspect data quality first, before making final study decisions.

FAQs

What is a dependent samples t test?

It is a test for two related measurements. It studies the difference inside each matched pair. It then checks whether the average difference is statistically different from a chosen value.

When should I use this calculator?

Use it for before and after scores, repeated measurements, matched subjects, paired devices, or linked observations. Do not use it for two unrelated groups.

What does the hypothesized mean difference mean?

It is the null value being tested. Most studies use zero. A nonzero value can test whether the average paired change differs from a required target.

Why is difference order important?

The order controls the sign of the mean difference and t statistic. The p value for a two sided test stays the same, but one sided results depend on direction.

What does the p value show?

The p value shows how unusual the observed result is under the null hypothesis. Smaller values provide stronger evidence against the null assumption.

What does Cohen dz mean?

Cohen dz is an effect size for paired data. It divides the mean paired difference by the standard deviation of paired differences.

Can I use unequal sample sizes?

No. Each value in the first sample must match one value in the second sample. Missing pairs should be removed or handled before testing.

Does this calculator check normality?

No. It calculates the paired t test. You should still inspect the difference values for strong skew, extreme outliers, or data entry problems.