One-Sample T-Test Calculator

The t-test is a parametric statistical test used to determine whether the sample mean differs significantly from an expected value. It was developed by William Sealy Gosset under the pseudonym "Student".

Use it when you want to compare the mean of a single sample against a known or hypothesized population mean. The test assumes normality or a sufficiently large sample (n≥30).

The t-statistic measures how many standard errors the observed mean is away from the expected value. A larger absolute t indicates a stronger departure from the null hypothesis.

Degrees of freedom (df=n−1) define the shape of the t-distribution used to assess significance. More degrees of freedom bring the t-distribution closer to the normal distribution.

It means that the probability of observing such an extreme t-statistic, assuming H₀ is true, is less than 5%. We reject the null hypothesis.

The 0.01 level is more stringent and requires a stronger effect. The 0.05 level is the standard threshold in most scientific research.

At least 30 observations are recommended. With smaller samples, the data should be approximately normally distributed.

Yes — outliers can distort the mean and standard deviation. Check your data before testing and consider non-parametric alternatives if extreme values are present.

Random sampling, independent observations, and normality of the variable (or n≥30). Violating these assumptions reduces the reliability of results.

The calculator provides an interpretation based on critical thresholds (1.96 and 2.576). For the exact p-value, consult t-distribution tables or statistical software.