Dependent Sample T Test Calculator

Calculator

Example Data Table

Formula Used

The dependent sample t test uses differences from paired observations.

d = second score - first score

Mean difference = sum of differences / n

Standard error = standard deviation of differences / square root of n

t = (mean difference - hypothesized mean difference) / standard error

Degrees of freedom = n - 1

Cohen dz = mean difference / standard deviation of differences

How to Use This Calculator

Choose paired rows when each line contains both measurements.

Choose separate lists when before and after values are pasted separately.

Select the difference order that matches your research question.

Enter the hypothesized mean difference. Most tests use zero.

Select the test direction and confidence level.

Press calculate. The result appears above the form.

Use CSV or PDF buttons to save the output.

Dependent Sample T Test Guide

What This Test Measures

A dependent sample t test studies two scores from the same subject, item, or matched pair. It is also called a paired t test. The method checks whether the average difference is far from a chosen value, usually zero. It is useful when measurements are linked. The link removes extra noise from person to person variation.

When It Fits

Use this test for before and after scores. Use it for matched twins, paired machines, repeated lab readings, or two methods used on the same sample. Do not use it for two unrelated groups. Independent groups need another test.

How It Calculates

The calculator works from raw paired data. It first builds a difference for each pair. Then it finds the mean difference, standard deviation of differences, standard error, degrees of freedom, and t statistic. The p value is based on the selected tail. A two tailed test checks any change. A right tailed test checks whether the mean difference is greater. A left tailed test checks whether it is smaller.

Reading the Output

Confidence intervals show a practical range for the mean difference. If a zero value is outside a two sided interval, the result often supports a change at that confidence level. Still, context matters. A tiny change can be statistically significant with many pairs. A large change can be uncertain with few pairs.

Effect Size

Effect size helps explain importance. Cohen's dz divides the mean difference by the standard deviation of differences. Values near 0.2 are often small. Values near 0.5 are often moderate. Values near 0.8 are often large. These labels are only guides. Your field may use different standards.

Data Checks

Check the data before trusting the result. Pairs must be correctly matched. The differences should not contain extreme errors. The distribution of differences should be reasonably symmetric for small samples. Larger samples are more forgiving. For very unusual differences, use plots or a nonparametric method.

Reporting

This page also supports exports. CSV is useful for spreadsheets. PDF is useful for reports. Keep the original data with your output. That makes review easier later. For formal work, report the sample size, test direction, t statistic, degrees of freedom, p value, confidence interval, and chosen alpha. Add units for each score. State the difference order clearly every time.

FAQs

What is a dependent sample t test?

It is a test for paired measurements. It checks whether the average difference between matched scores is different from a hypothesized value.

Is this the same as a paired t test?

Yes. A dependent sample t test is commonly called a paired t test. Both names describe the same paired data method.

How many pairs do I need?

You need at least two valid pairs. More pairs usually give a more stable standard error and more reliable result.

What should I enter as the hypothesized difference?

Most users enter zero. Use another value only when your null hypothesis states a specific expected mean difference.

Which tail should I choose?

Use two tailed for any change. Use greater or less only when your research question clearly predicts one direction before analysis.

What does Cohen dz mean?

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

Can I paste data from a spreadsheet?

Yes. Paste two columns into paired rows, or paste each column into separate before and after boxes.

Why does the result use differences?

The test focuses on within-pair change. Using differences removes much unmatched variation and tests the paired effect directly.