Math
T-Test Calculator
Run a one-sample or two-sample Student's t-test from raw data. Get the t statistic, degrees of freedom, two- and one-tailed p-values, and significance at p = 0.05 and p = 0.01.
Pick a test
Need at least 2 values.
t statistic
0.7276
df = 9
Not significant at p = 0.05
P-value (two-tailed)
0.485351
P-value (one-tailed)
0.242676
Mean 1
5.05
Std. dev. 1
0.2173
n1
10
Hypothesized mean
5
Frequently Asked Questions about the T-Test Calculator
What is the null hypothesis in a t-test?
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.
What does the p-value mean?
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.
When do I use one-tailed vs two-tailed?
Two-tailed is the standard choice: it tests for a difference in either direction. The calculator derives the one-tailed p-value by halving the two-tailed result, so choose one-tailed only when your hypothesis was directional before collecting data, for example you predicted the new drug would lower blood pressure, not just change it.
Equal variance or unequal variance (Welch)?
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.
Should I use a t-test or a z-test?
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.