Difference of Means Confidence Interval Calculator

How it is calculated

The difference is d = mean₁ − mean₂. Its standard error combines the spread of both groups: SE = √(sd₁²/n₁ + sd₂²/n₂). The interval is d ± z × SE, with z fixed at 1.645 for 90 percent, 1.96 for 95 percent and 2.576 for 99 percent confidence. The confidence field accepts only 90, 95 or 99 (blank means 95); any other value, such as 80, shows no result. Results are shown to four decimals.

The tool uses these normal-distribution (z) values, not Student's t, so with small samples the true interval is wider than shown: roughly 45% wider at 3 per group. It assumes two independent groups, takes each SD as a sample standard deviation (not negative), and needs each group size to be at least 2.

Common mistakes

• Entering the standard error instead of the standard deviation. The SD describes spread among individuals; the tool computes the standard error itself, so using the SE would give an interval far too narrow.
• Using it for paired data, such as before and after measurements on the same people. The formula assumes independent groups, so paired data need an interval on the within-pair differences.
• Reading a 95 percent interval as a 95 percent chance that the true difference lies inside it for this particular study. It describes the long-run behaviour of the method, not the probability for one result.
• Typing a confidence level such as 80 or 97 and expecting a result. Only 90, 95 and 99 are recognised; anything else leaves the result empty.
• Concluding that no difference exists because the interval contains 0. It means the data are compatible with no difference, but equally compatible with differences up to the upper limit.