Advanced T Test Stats Guide
A t test helps compare a sample mean with a target mean. It also compares two sample means. This calculator supports one sample, paired sample, equal variance, and Welch tests. It accepts raw values, so you do not need precomputed summaries. You can paste numbers separated by commas, spaces, or new lines.
When you submit the form, the tool cleans the data and counts each valid value. It then finds the mean, standard deviation, standard error, degrees of freedom, t statistic, p value, and confidence interval. The result also gives a plain decision. That decision uses your chosen alpha level and tail direction.
The one sample test checks whether one group differs from a known value. It is useful for quality checks, classroom marks, lab readings, or survey scores. The paired test compares matched observations. Use it for before and after data, repeated measures, or matched subjects.
Independent tests compare two unrelated groups. The equal variance version assumes both groups have similar spread. Welch testing is safer when spreads or sample sizes differ. Many analysts prefer Welch as a default choice because it adjusts degrees of freedom.
The p value shows how unusual your result is under the null claim. A small p value means the observed difference is unlikely if the null claim is true. The confidence interval shows a likely range for the mean difference. If a two sided interval excludes zero, the result usually matches a significant two tailed test.
Cohen's d gives effect size. It helps judge practical strength, not just statistical significance. A larger absolute value means a stronger difference. Still, context matters. Small effects can matter in large systems. Large effects may be unstable with tiny samples.
Use clean data and check assumptions. T tests work best with independent observations. They also expect roughly normal data, especially for small samples. With larger samples, they are often robust. Always review outliers before trusting the result. Export the table when you need records, audits, or shared reports.
The report layout is designed for quick reading. Start with the decision, then review the estimates. Finally, inspect the sample details. This order helps both beginners and analysts avoid common interpretation mistakes during reviews.