Confidence Interval Paired T Test Calculator

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Mean of the Differences

The average difference between each pair's before and after values.

Standard Deviation of Differences

How spread out the individual pair differences are.

Sample Size

Number of paired observations (e.g. number of people measured before and after).

Confidence Level (%)

Common choices are 90, 95, or 99.

About This Test

What Is a Paired T Confidence Interval?

This builds a confidence interval for the true average difference between two related measurements on the same subjects — like before-and-after scores — rather than comparing two separate independent groups. Because each pair is linked, you work directly with the differences instead of the two original sets of numbers.

When to Use It

Before-and-after measurements on the same people (weight loss, test scores, blood pressure)
Matched-pairs experiments where each subject serves as their own control
Any two measurements taken on the same subject or matched unit

The Formula

\[ \bar{d} \pm t_{\alpha/2,\,df}\,\frac{s_d}{\sqrt{n}} \]

Worked Example

15 participants in a weight-loss program lost an average of 3.2 kg, with a standard deviation of differences of 1.5 kg. What's the 95% confidence interval for the true average weight loss?

\( \bar{d} = 3.2, \ s_d = 1.5, \ n = 15 \)
Degrees of freedom: \( df = n - 1 = 14 \)
Critical value: \( t_{0.025,\,14} \approx 2.145 \)
Standard error: \( 1.5/\sqrt{15} \approx 0.3873 \)
95% confidence interval: (2.37, 4.03) — since it doesn't include 0, the weight loss is likely real.

Your Results

Related Resources:

Understanding the Empirical Rule

Learn how confidence intervals relate to the 68-95-99.7 rule.

What Are Residuals?

Essential for understanding regression analysis.

Perfect for students, researchers, and professionals looking to build real statistical skills.

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