Dependent Means T Test Calculator

Calculator

Input mode

Hypothesized difference

Alpha

Alternative hypothesis

Summary n

Summary mean difference

Summary SD of differences

Correlation mode n

Mean first condition

Mean second condition

SD first condition

SD second condition

Paired correlation r

Raw paired scores

Enter one pair per line. Use comma, tab, semicolon, or spaces. Difference equals second score minus first score.

Example Data Table

Subject	Before	After	Difference
1	82	88	6
2	91	95	4
3	76	81	5
4	84	90	6
5	89	92	3

Formula Used

Difference score: d = X2 - X1

Mean difference: mean d = sum(d) / n

Standard error: SE = sd(d) / sqrt(n)

Test statistic: t = (mean d - hypothesized difference) / SE

Degrees of freedom: df = n - 1

Confidence interval: mean d +/- t critical * SE

Effect size: dz = (mean d - hypothesized difference) / sd(d)

How to Use This Calculator

Select the input mode that matches your data.
Use raw paired scores when each subject has two results.
Use summary mode when you know the mean difference and its standard deviation.
Use correlation mode when you know both means, both standard deviations, and paired r.
Enter alpha, usually 0.05, and choose the alternative hypothesis.
Press Calculate to display the result above the form.
Use CSV or PDF buttons to save a report.

Dependent Means T Test Guide

What It Compares

A dependent means t test compares two related measurements. It is often called a paired t test. The same subjects are measured twice. The scores may be before and after treatment. They may also be matched pairs from a controlled design.

Input Choices

This calculator handles raw pairs and summary data. Raw data is best when you have every observation. Summary mode is useful when a report gives the mean difference and standard deviation. Correlation mode is helpful when two means, two standard deviations, and the paired correlation are known.

The key value is the difference score. Each second score is subtracted from its matching first score. The test then checks whether the average difference is far from a hypothesized value. Most studies use zero as the hypothesized difference. A nonzero value can test a planned minimum change.

Reading the Results

The standard error shows how much the mean difference may vary. A small standard error makes the t value larger. A large standard deviation of differences makes the t value smaller. The degrees of freedom equal the number of pairs minus one.

Use the alternative hypothesis with care. A two tailed test checks for any change. A greater test checks whether the mean difference is above the hypothesized value. A less test checks whether it is below that value. Choose the direction before reviewing the result.

The confidence interval gives a practical range for the average paired change. If a two tailed interval excludes zero, the paired change is significant at the matching alpha level. The effect size dz explains the change in standard deviation units. It helps compare results across studies.

Best Practice

Good analysis starts with clean pairs. Remove unmatched rows. Check obvious entry mistakes. Keep units consistent. Large outliers can strongly influence the result. For very small samples, inspect the differences carefully. The dependent means t test assumes difference scores are approximately normal, not that both original columns are normal.

The result should not replace study judgment. Statistical significance depends on sample size and variation. A tiny change may become significant with many pairs. A useful change may be nonsignificant with few pairs. Report the mean difference, confidence interval, p value, and design context together. This makes the conclusion clearer and more defensible.

FAQs

What is a dependent means t test?

It tests whether the average difference between two related measurements is statistically different from a chosen value, usually zero.

When should I use this test?

Use it for before-after studies, repeated measures, matched pairs, or any design where observations are naturally linked.

What does the calculator use as the difference?

It uses second score minus first score. A positive mean difference means the second condition is higher on average.

Can I use summary statistics only?

Yes. Choose summary mode when you know sample size, mean difference, and standard deviation of paired differences.

What if I only know both means and correlation?

Use correlation mode. It estimates the standard deviation of differences from both standard deviations and the paired correlation.

What does p value mean here?

The p value measures how unusual the observed mean difference is if the null hypothesis is true.

What does effect size dz show?

It standardizes the paired change by the standard deviation of differences. It helps describe practical size beyond significance.

Does the test require normal original scores?

No. The main assumption is that the paired difference scores are approximately normal, especially for small samples.