Difference of Means Confidence Interval
Estimate an interval for one population mean minus another.
How the difference of means confidence interval works
A two-sample difference-of-means interval estimates how far one population mean lies above or below another. The point estimate is mean one minus mean two. Independent standard-error contributions are each sample variance divided by its size; their sum’s square root is multiplied by the selected z critical value to create a symmetric margin around the difference.
The defaults use means 52 and 48, standard deviations 10 and 8, and sample sizes 100 each. The difference is 4 and standard error is the square root of 1.64, approximately 1.280625. At 95 percent, the verified margin is 2.510025 and the interval runs from 1.489975 to 6.510025.
Reading difference of means confidence interval results privately
This formula uses a z critical value and treats the supplied standard deviations as adequate large-sample estimates. Small samples normally require a Welch t interval with estimated degrees of freedom. The groups must be independent; paired observations need an interval on within-pair differences. An interval excluding zero is not automatically practically important. This difference of means confidence interval calculation runs entirely in your browser, so the numbers you enter never leave your device.
Frequently Asked Questions
What determines the sign of the interval?
The point estimate is mean one minus mean two, so reversing group order reverses every endpoint sign.
When should I use a t interval instead?
Use a t-based method when population spread is unknown and sample sizes are not large enough for a z approximation.
Is the difference of means confidence interval private?
Yes. Its inputs and results stay in your browser. Bushe.co does not upload or store the values used in this calculation.
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