Understanding T-Test P-Values
A t-test checks whether an observed difference is large enough to question a null claim. The p-value shows how unusual the result is, assuming the null claim is true. A small p-value does not measure practical importance. It measures evidence against the tested claim.
What This Calculator Handles
This calculator supports direct t input, one sample summaries, paired summaries, raw samples, pooled two sample tests, and Welch two sample tests. That range helps students, analysts, and researchers compare means without switching tools. It also reports degrees of freedom, standard error, confidence interval, critical value, and effect size.
Choosing the Right Method
Use a one sample test when one group is compared with a known target. Use a paired test when two values belong to the same subject or matched item. Use a pooled two sample test when both independent groups have similar spread. Use Welch when spreads or sample sizes differ. Welch is often safer for real data.
Reading the Output
The t statistic measures the estimated difference in standard error units. The degrees of freedom control the shape of the t distribution. The p-value changes with the chosen tail. A two-tailed test checks any difference. A left-tailed test checks whether the estimate is lower. A right-tailed test checks whether it is higher.
Using Results Carefully
A decision line compares the p-value with alpha. Rejecting the null means the data looks unlikely under that claim. Failing to reject does not prove equality. It only means the sample did not provide enough evidence. Always review sample design, outliers, independence, and measurement quality.
Common Assumptions
The test works best when observations are independent. Data should be numeric and measured on a consistent scale. Small samples need roughly normal differences or group values. Larger samples are more forgiving, but extreme outliers can still distort results. When assumptions look weak, inspect plots and consider robust checks before making a final claim. Document every choice before reporting results.
Why Exports Help
CSV export is useful for spreadsheets and audit trails. PDF export is useful for reports and classroom submissions. Keep the formula, inputs, and decision together. That makes the result easier to review later. It also reduces mistakes when sharing statistical work.