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Formulas: One-Sample t-Test

One-Sample t-Test Formulas

Below you will find descriptions and details for the 5 formulas that are used to compute the results for a one-sample t-test.

Beta function:
Beta function formula
Lower incomplete beta function:
Lower incomplete beta function formula
Regularized lower incomplete beta function:
Regularized lower incomplete beta function formula
where the numerator is the lower incomplete beta function, and the denominator is the beta function.
t-distribution cumulative distribution function (CDF):
t-distribution cumulative distribution function (CDF) formula
where v is the degrees of freedom, t is the upper limit of integration, and I is the regularized lower incomplete beta function.
t-statistic and degrees of freedom:
t-statistic and degrees of freedom formula
where x is the sample mean, μ is the hypothesized mean, s is the sample standard deviation, n is the sample size, and df is the degrees of freedom.
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