T Test Calculator Guide
A t test helps you judge a sample mean. It is useful when the population standard deviation is unknown. This calculator works with summary statistics. You do not need raw observations. You only need the mean, standard deviation, sample size, hypothesis value, and tail choice.
When This Tool Helps
Use the one sample option when one group is compared with a fixed value. A teacher may compare a class mean with a required score. A lab may compare a measured value with a standard. Use the paired summary option when each subject has two related readings. Enter the mean of the paired differences, the standard deviation of those differences, and the number of pairs.
Comparing Two Groups
The two sample option compares two independent means. Welch testing is the safer default because it does not require equal variances. The pooled option is suitable when equal variance is a reasonable assumption. Both methods estimate the standard error, degrees of freedom, t statistic, and p value.
Reading the Result
The t statistic shows how many standard errors separate the estimate from the hypothesized value. A larger absolute t value gives stronger evidence against the null hypothesis. The p value gives the probability of seeing evidence at least this strong, assuming the null is true. Compare the p value with alpha. If p is less than or equal to alpha, reject the null hypothesis.
Confidence and Effect Size
The confidence interval gives a practical range for the mean or mean difference. It is often more informative than a p value alone. The calculator also reports effect size. Cohen d shows the standardized difference. Hedges g adjusts d for smaller samples. These values help describe practical importance, not only statistical evidence.
Good Practice
Check that the study design matches the selected test. Confirm that samples are independent when using two sample mode. For paired data, summarize differences rather than separate groups. Report the test name, t statistic, degrees of freedom, p value, confidence interval, and conclusion. Save the result as CSV or PDF when you need clean documentation. Keep units consistent. Record assumptions clearly. Review outliers, because unusual values can change the mean, spread, standard error, and final inference outcome.