T-Test Calculator

The null hypothesis is the default claim that no real difference exists. In a one-sample test it states that the population mean equals your hypothesized value; in a two-sample test it states that the two population means are equal. The p-value measures how likely your data would be if that claim were true.

It is the probability of observing a t statistic at least as extreme as yours, assuming the null hypothesis is true. A p-value below 0.05 is conventionally considered significant; below 0.01 is stronger evidence. The p-value is not the probability that the null is true, and a small p-value does not measure the size of an effect.

Use a two-tailed test for a difference in either direction. Use one-tailed only when you specified a direction before collecting data. The calculator evaluates the selected direction: an observed t statistic in the opposite direction produces a one-tailed p-value above 0.5, not half the two-tailed value. The significance verdict follows that selected one-tailed test.

Use Welch's t (unequal variance) by default. It uses the Welch-Satterthwaite formula for degrees of freedom, which handles unequal sample sizes and unequal spreads without inflating your false-positive rate. Switch to pooled (Student's t) only when you have a strong prior reason to believe the population variances are the same.

Use a t-test when you estimate the standard deviation from your data, which is almost always the case. A z-test requires knowing the true population standard deviation in advance. When your sample has more than about 30 observations, the t and z distributions converge and the choice makes little practical difference.