Difference in Means Calculator
Compare the means of two independent groups with a two-sample t-test. Enter raw data or summary statistics to get the difference, t statistic, p-value, and a confidence interval for the difference.
- t statistic
- 4.3301
- df
- 12.0000
- Std. error
- 0.1155
- 95% CI
- [0.2484, 0.7516]
Test statistic & rejection area
p = 0.0010How to use this calculator
- Enter the data for both groups, or switch to summary statistics and type each group’s mean, standard deviation, and size.
- Choose the alternative hypothesis and whether to assume equal variances (pooled) or not (Welch, the default).
- Read the difference, t statistic, p-value, and the confidence interval for the difference.
What is a two-sample t-test?
A two-sample (independent-samples) t-test checks whether the means of two separate groups differ by more than would be expected from sampling variation alone. The null hypothesis is that the two population means are equal.
Welch vs. pooled t-test
The pooled t-test assumes the two groups have equal variances and combines them into one estimate. Welch’s t-test does not assume equal variances and adjusts the degrees of freedom accordingly. Welch’s test is the safer default and is recommended unless you have good reason to assume equal variances.
Welch's t statisticInterpreting the result
If the p-value is below your significance level (commonly 0.05), you conclude that the two group means are significantly different. The confidence interval for the difference gives the plausible range for how large that difference is — if it excludes zero, the difference is significant at the corresponding level.
This test assumes the two samples are independent. For before-and-after measurements on the same subjects, use a paired t-test instead.Frequently asked questions
When should I use Welch’s t-test instead of the pooled test?
Use Welch’s t-test when the two groups may have unequal variances or unequal sample sizes, which is most of the time. It is the safer default; the pooled test is only preferable when you are confident the variances are equal.
What does the confidence interval for the difference tell me?
It gives a plausible range for the true difference between the two population means. If the interval does not contain zero, the difference is statistically significant at the corresponding confidence level.
What is the difference between an independent and a paired t-test?
An independent (two-sample) t-test compares two separate groups. A paired t-test compares two measurements on the same subjects, such as before and after a treatment, and accounts for the pairing.
How do I calculate the difference in means in Excel?
Use =T.TEST(array1, array2, tails, type) with type 3 for Welch’s unequal-variance test or type 2 for the pooled equal-variance test to get the p-value.