What This Calculator Does
A pooled variance test statistic compares two independent sample means. It is useful when both populations are assumed to share one variance. The calculator combines the two sample standard deviations. Then it builds a pooled standard error. It also reports the t statistic, degrees of freedom, p value, confidence interval, and effect size.
Why Pooled Variance Matters
Separate samples often have different spreads. Pooled variance gives one weighted estimate. Larger samples receive more influence. Smaller samples still contribute through their degrees of freedom. This method can improve precision when the equal variance assumption is reasonable.
Interpreting the Test Statistic
The t statistic measures distance from the hypothesized difference. A larger absolute value gives stronger evidence against the null claim. The p value converts that distance into probability under the null model. Use the selected alternative to choose a two tailed, left tailed, or right tailed result.
Confidence Interval Use
The confidence interval estimates the likely range for the true mean difference. It uses the pooled standard error and a critical t value. If a two sided interval excludes the hypothesized difference, the test often rejects at the matching level.
Practical Reporting Tips
Report sample means, sample standard deviations, sample sizes, pooled variance, degrees of freedom, t statistic, p value, and decision. Add the alternative hypothesis. Include confidence level and effect size. Mention that the calculation assumes independent samples and equal population variances.
Assumption Checks
Before using this test, check the study design. The two groups should be independent. Measurements should be numeric. Severe outliers can distort means and variances. Equal variance should be plausible. When spreads are very different, Welch's test may be safer.
Best Use Cases
This tool helps with lab reports, business testing, classroom exercises, and quality comparisons. It also supports quick sensitivity checks. Change the alpha level or confidence level. Then compare how the decision and interval respond.
Reading the Output
Focus on the sign and size of t. A positive value means sample one is higher, after the hypothesized gap is considered. A negative value means sample two is higher. The decision line gives a quick guide. Still, interpret results with subject knowledge and data quality. Document each assumption before final reporting.