Understanding the T Test Null Hypothesis
A t test checks whether sample evidence disagrees with a stated claim. That stated claim is the null hypothesis. It often says that a mean equals a target value. It may also say that two means have no real difference.
This calculator supports common t test choices. You can test one sample mean. You can compare two independent groups. You can also test paired measurements. Each option uses the same core idea. It compares an observed difference with its standard error.
Why the Null Hypothesis Matters
The null hypothesis gives the test a clear reference point. Without it, a t value has little meaning. A small t value means the sample result is close to the claim. A large absolute t value means the sample result is far from the claim.
The p value measures how unusual the result is. It assumes the null hypothesis is true. A small p value suggests stronger evidence against the null. The alpha level is your cutoff for that judgment. Common alpha values are 0.05 and 0.01.
Choosing the Right Test
Use a one sample t test for one group. Use it when comparing a sample mean with a known target. Use a paired t test when each value has a matched partner. Before and after measurements are paired data. Matched patient results are also paired data.
Use an independent t test for two separate groups. The equal variance option assumes similar spread in both groups. Welch's option is safer when spreads or sample sizes differ. It is often preferred for real data.
Reading the Result
The calculator reports the t statistic, degrees of freedom, p value, and decision. It also gives a confidence interval. The interval estimates the likely range for the mean or mean difference. If the null value is outside a two sided interval, rejection is usually expected.
Results still need judgment. Check sample quality. Look for outliers. Confirm that the test matches the study design. A significant result does not prove importance. It only shows statistical evidence. Combine the result with context, effect size, and practical meaning. Document assumptions before sharing the result with teachers, clients, or supervisors. Keep raw data saved.