T-statistic

In statistics, the t-statistic is a ratio of the departure of an estimated parameter from its notional value and its standard error. It is used in hypothesis testing. For example, it is used in determining the population mean from a sampling distribution of sample means if the population standard deviation is unknown.

Let ${\displaystyle \scriptstyle {\hat {\beta }}}$ be an estimator of parameter β in some statistical model. Then a t-statistic for this parameter is any quantity of the form

where β₀ is a non-random, known constant which may or may not match the actual unknown parameter value β, and ${\displaystyle s.e.({\hat {\beta }})}$ is the standard error of the estimator ${\displaystyle \scriptstyle {\hat {\beta }}}$ for β. By default, statistical packages report t-statistic with β₀ = 0 (these t-statistics are used to test the significance of corresponding regressor). However, when t-statistic is needed to test the hypothesis of the form H₀: β = β₀, then a non-zero β₀ may be used.

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