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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 in the Student’s ''t''-test, in the augmented Dickey–Fuller test, and in bootstrapping. ==Definition== Let be an estimator of parameter ''β'' in some statistical model. Then a ''t''-statistic for this parameter is any quantity of the form : where ''β''0 is a non-random, known constant, and is the standard error of the estimator . By default, statistical packages report ''t''-statistic with (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 , then a non-zero ''β''0 may be used. If is an ordinary least squares estimator in the classical linear regression model (that is, with normally distributed and homoskedastic error terms), and if the true value of parameter ''β'' is equal to ''β''0, then the sampling distribution of the ''t''-statistic is the Student's ''t''-distribution with degrees of freedom, where ''n'' is the number of observations, and ''k'' is the number of regressors (including the intercept). In the majority of models the estimator is consistent for ''β'' and distributed asymptotically normally. If the true value of parameter ''β'' is equal to ''β''0 and the quantity correctly estimates the asymptotic variance of this estimator, then the ''t''-statistic will have asymptotically the standard normal distribution. In some models the distribution of ''t''-statistic is different from normal, even asymptotically. For example, when a time series with unit root is regressed in the augmented Dickey–Fuller test, the test ''t''-statistic will asymptotically have one of the Dickey–Fuller distributions (depending on the test setting). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「T-statistic」の詳細全文を読む スポンサード リンク
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