Understanding Hypothesis T Tests
A hypothesis t test checks whether a sample mean is unusual under a stated null value. It is useful when population standard deviation is unknown. This calculator supports one sample, paired sample, Welch two sample, and pooled two sample methods. Each method estimates standard error from sample variation.
Null and Alternative Ideas
The test begins with a null hypothesis. It may say that a mean equals zero, a target value, or a stated difference. The alternative hypothesis sets the direction. A two tailed test looks for any difference. A left tailed test checks for a lower value. A right tailed test checks for a higher value.
Choosing Data Entry
Good inputs matter. Raw data lets the calculator compute every statistic directly. Summary data is faster when you already know sample size, mean, and sample standard deviation. Paired testing should use matched observations, such as before and after scores. Independent testing should use separate groups.
Variance and Method Choice
Welch testing is usually safer when variances differ. It adjusts degrees of freedom using the Welch Satterthwaite equation. Pooled testing assumes equal population variances. It combines both sample variances into one pooled estimate. Use pooled testing only when that assumption is reasonable.
Reading the Output
The p value measures how extreme the test statistic is under the null hypothesis. A small p value gives evidence against the null. The alpha level is your chosen cutoff. Common choices are 0.05, 0.01, and 0.10. If p is below alpha, reject the null. If not, do not reject it.
Confidence and Effect Size
The confidence interval gives a practical range for the mean or difference. It is built from the estimate, critical t value, and standard error. It helps judge size, not only significance. Effect size adds more context. It describes distance in standard deviation units.
Responsible Reporting
Use this tool for classwork, audits, experiments, surveys, and quality checks. Always review assumptions before reporting results. Independence, paired matching, outliers, and distribution shape can affect conclusions. The calculator gives clear numbers. Sound judgment gives meaning to them.
Reproducible Results
Before sharing results, write the test type, tail choice, alpha level, degrees of freedom, t value, p value, and interval. Also note whether raw data or summaries were used. This makes the work reproducible. It also helps readers see the exact decision path clearly for review.