Why a t test matters
A t test helps compare a sample mean with a claim. It also compares two related or independent means. This calculator supports common research cases. It works with summary statistics or raw values. That makes it useful for homework, lab work, surveys, audits, and quality checks.
What the result means
The t statistic shows how far the observed difference sits from the null value. It measures that distance in standard error units. A large absolute t value often gives stronger evidence. The p value shows how unusual the result is under the null hypothesis. Compare it with alpha. If p is less than or equal to alpha, reject the null hypothesis.
Supported test choices
Use the one sample option when one group is checked against a known value. Use the paired option when measurements belong together. Examples include before and after scores. Use the independent option when two separate groups are compared. The Welch choice is safer when group spreads differ. The pooled choice assumes equal variances.
Confidence and effect size
A confidence interval gives a likely range for the mean difference. It adds practical context to the p value. A result can be significant but still small. The effect size helps show practical strength. Cohen d is used for one sample, paired, and independent comparisons. Hedges style correction is also shown for independent groups.
Good input practice
Use sample standard deviation, not population deviation. Enter sample size carefully. For raw data, separate values with commas, spaces, or new lines. Paired data must have equal counts in both boxes. Check units before comparing values. Use a two tailed test unless the direction was planned before collecting data. Report the test type, degrees of freedom, t statistic, p value, confidence interval, alpha, and conclusion.
Limitations to remember
A t test assumes numeric data. It also works best when samples are random and observations are independent. For small samples, strong outliers can distort the answer. A histogram or box plot can help before final reporting. The calculator gives statistical guidance, not study design approval. Strong conclusions still need sound sampling, clear hypotheses, and honest interpretation. Always keep original data notes with every reported calculation for audit review.