CI for Difference of Two Means (t)
Computes the confidence interval for the difference between the means of two independent groups, using the t distribution with pooled variances. It's the natural companion to the two-sample t-test: instead of only saying whether the difference is significant, it shows the plausible range for the real size of that difference. If the interval doesn't contain zero, there's a significant difference at the chosen level. Enter the two samples of values and the confidence level.
Resultado
โ
CI for Difference of Two Means (t)
Computes the confidence interval for the difference between the means of two independent groups, using the t distribution with pooled variances. It's the natural companion to the two-sample t-test: instead of only saying whether the difference is significant, it shows the plausible range for the real size of that difference. If the interval doesn't contain zero, there's a significant difference at the chosen level. Enter the two samples of values and the confidence level.
How much, after all, does one group differ from the other?
The two-sample t-test answers a yes-or-no question: is there a significant difference between the groups? But that answer alone is poor. Knowing that two treatments differ doesn't say whether the difference is two points or twenty. The confidence interval for the difference of means fills that gap, delivering a plausible range for the real size of the effect.
The calculation combines the variances of the two groups into a single estimate, the pooled variance, under the assumption that both have similar spread. From it comes the standard error of the difference, and the critical value of the t distribution sets the margin. The center of the interval is the observed difference between the means; the width reflects the sample sizes and the variability of the data.
Enter the two samples and the confidence level. The tool returns the point difference and the interval bounds. There's a valuable reading shortcut: if the entire interval falls on one side of zero, the difference is significant at that level; if it crosses zero, you can't rule out that the groups are equal.
Related Tools
CI for the Difference of Two Proportions
Computes the confidence interval for the difference between two proportions, using the Wald method. It's the companion to the two-proportion z-test and the basis of any A/B test reading: beyond saying whether the difference is significant, it shows the plausible range for its real size. If the interval doesn't contain zero, there's a significant difference. For example: variant A converted 45 of 100 and B, 30 of 100 โ what's the interval for the difference? Enter the successes and the total of each group and the confidence level.
CI for the Ratio of Two Variances
Computes the confidence interval for the ratio between the variances of two normal populations, ฯโยฒ/ฯโยฒ. Instead of just testing whether the variances differ, it gives a plausible range for how many times one is larger than the other. If the interval contains the number 1, there's no evidence the spreads are different. The calculation uses the F distribution, and because it's asymmetric, the bounds come from F quantiles with the degrees of freedom swapped. Enter the two samples and the confidence level.
Wilson Interval (Proportion)
Computes the Wilson confidence interval for a proportion, the modern alternative to the Wald interval (the pฬ ยฑ zยทSE formula you learn first). The Wald interval fails badly with small samples or proportions near 0 or 1 โ it can even produce negative bounds. Wilson's fixes this by inverting the score test, which keeps it inside [0, 1] with much better coverage. It's the recommended interval for proportions. Enter the successes, the total and the confidence level.
Agresti-Coull Interval (Proportion)
Computes the Agresti-Coull confidence interval for a proportion, an elegant middle ground between the simplicity of the Wald interval and the accuracy of Wilson's. The almost folkloric idea is to add a few fictitious successes and failures to the sample before applying the Wald formula โ which fixes Wald's terrible behavior in small samples or extreme proportions. For 95% confidence, it's like adding two successes and two failures. Enter the successes, the total and the confidence level.
CI for Correlation (Fisher z Transform)
Computes the confidence interval for a correlation coefficient using the Fisher z transformation. The sampling distribution of r is skewed, especially near โ1 or +1, which prevents applying the usual symmetric margin. Fisher solved this with a transformation that makes the distribution approximately normal; you build the interval on that scale and then map back to r. The result is an asymmetric interval, narrower on the side near the extremes. Enter the coefficient r and the sample size.
Two-Proportion z-Test
Computes the two-proportion z-test statistic, which compares the success rates of two independent groups โ the backbone of any A/B test. For example: variant A converted 45 of 100 and B converted 30 of 100; is the difference real or noise? The statistic uses the pooled proportion of the two groups to estimate the standard error under the hypothesis that the proportions are equal. Enter the successes and the total of each of the two groups.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.