2 Sample T Interval Non Pooled Calculator

Example Data Table

Formula Used

The calculator uses the Welch, non pooled confidence interval for two independent means.

Difference = x̄1 - x̄2

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

df = ((s1^2/n1 + s2^2/n2)^2) / (((s1^2/n1)^2/(n1-1)) + ((s2^2/n2)^2/(n2-1)))

Interval = Difference ± t critical × SE

How to Use This Calculator

Enter summary statistics for both independent samples. You may paste raw values instead. Raw values override their matching summary fields. Choose a confidence level. Enter a hypothesized difference when you want an interval inclusion check. Press the calculate button. Use CSV or PDF buttons when you need a saved report.

Understanding the Non Pooled Two Sample T Interval

Purpose

A two sample t interval compares the mean of two independent groups. The non pooled version is useful when the group variances may differ. It is also called the Welch confidence interval.

Input Choices

This calculator supports summary entries and raw lists. You can enter means, standard deviations, and sample sizes. You can also paste comma separated observations. When raw values are supplied, the page calculates the summary statistics for you.

Method

The method estimates the difference between two population means. The estimate is sample one mean minus sample two mean. The standard error uses each group variance separately. That is why no pooled standard deviation is required. The degrees of freedom are estimated with the Welch Satterthwaite equation. This usually gives a decimal value. A decimal value is acceptable for interval work.

Confidence Level

The confidence level controls the width of the interval. A higher confidence level gives a larger critical value. That creates a wider interval. A lower confidence level gives a narrower interval. The result should be read as a plausible range for the true mean difference.

Assumptions

Use independent samples only. The method is not intended for paired before and after data. It also assumes each sample represents its population fairly. Very small samples need careful review. Strong skew or large outliers can affect the interval. Larger samples usually make the method more stable.

Interpretation

The calculator also checks a hypothesized difference. The default value is zero. If zero is inside the interval, the result does not show a clear mean difference at that confidence level. If zero is outside the interval, the groups appear separated by the interval estimate. This statement is practical guidance, not a full study conclusion.

Exports

The export buttons help with documentation. CSV is useful for spreadsheets. PDF is useful for reports and classroom notes. Keep the inputs with the output so the calculation can be reviewed later.

Review

This page is designed for fast statistical comparison. It shows the estimate, standard error, degrees of freedom, critical value, margin of error, and final interval. Each value supports transparent checking and clearer decisions. Good records also make repeated classroom checks, audit trails, and later model comparisons easier to complete without confusion again. Use it carefully, and verify assumptions before final decisions.

FAQs