Understanding the Two Sample Unpooled T-Test
A two sample unpooled t-test compares two independent averages. It is often called Welch's t-test. It does not assume equal population variances. That makes it useful when samples have different spread, different sizes, or both. The calculator uses each sample standard deviation directly. It then builds a standard error from both groups.
How the Test Works
The test begins with the mean of group one and group two. It subtracts the hypothesized difference. Most studies use zero. The result is divided by the Welch standard error. This gives the t statistic. A larger absolute t value means the observed difference is large, compared with sampling noise.
Degrees of Freedom
Degrees of freedom are not pooled. They come from the Welch-Satterthwaite equation. The value is often not an integer. This calculator keeps the decimal value, because it gives a more accurate p value. The p value depends on the selected alternative hypothesis. Choose two tailed when any difference matters. Choose greater or less when the direction was planned before testing.
Confidence and Meaning
Confidence intervals help explain practical size. The interval shows a likely range for the true mean difference. If a two sided interval excludes zero, the matching two sided test is usually significant at the same level. Still, practical judgment matters. A tiny difference can be significant with large samples.
Data Entry Advice
Use raw data when you have every observation. Use summary mode when a report gives sample size, mean, and sample standard deviation. Do not enter population standard deviations. The unpooled test expects sample standard deviations from independent observations.
Assumptions and Reporting
Check assumptions before trusting the answer. Observations should be independent inside and between groups. Each group should be roughly normal, especially with small samples. Larger samples are more forgiving. Strong outliers can distort the mean and standard deviation. In that case, inspect the data first.
This calculator is helpful for experiments, surveys, quality tests, classroom studies, and business comparisons. It returns the standard error, Welch degrees of freedom, p value, confidence interval, and a decision. The CSV and PDF options make it easier to save the result. Always report the inputs, test direction, confidence level, and conclusion together. When results guide important decisions, pair the calculation with study design details, subject knowledge, and clear notes about uncertainty too.