求助：关于F检验

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伍德.里奇《现代观点》第四章中提到F检验的备择假设是“双侧”假设，F分布不是单侧的吗？

请问如何理解？？

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关键词：F检验 备择假设 现代观点 如何理解 在线等 检验

F Test

In comparing two independent samples of size N₁ and N₂ the F Test provides a measure for the probability that they have the same variance. The estimators of the variance are s₁² and s₂². We define as test statistic their ratio T = s₁²/ s₂², which follows an F Distribution with f₁= N₁-1 and f₂= N₂-1 degrees of freedom. One can formulate the F test for three different hypotheses, defined by:

Tables of the quantiles , etc., of the F distribution can be found in the literature

[此贴子已经被作者于2005-9-27 7:44:43编辑过]

The test of a given statistical hypothesis in which only a value of the statistic that is, for example, sufficiently large will lead to rejection of the hypothesis tested.

The statistical tables for F, for [S-squared x over Sigma squared x] and for Chi. Sq. provide the critical values for a one-tailed test in which the entire alpha region is assigned to the upper end of the sampling distribution when the hypothesis tested is true.

The test of a given statistical hypothesis in which a value of the statistic that is either sufficiently small or sufficiently large will lead to rejection of the hypothesis tested.

The statistical tables for Z and for t provide criticaal values for both one and two tailed tests. That is, they provide the critical values that cut off an entire alpha region at one or the other end of the sampling distribution as well as the critical vfalues that cut off the 1/2 alpha regions at both ends of the sampling distribution

[此贴子已经被作者于2005-9-27 7:43:25编辑过]

One-Tailed versus Two-Tailed Tests

If you are interested in testing two directional parameter hypotheses against each other (e.g., H0: mu1 <= mu2; H1: mu1 > mu2), a one-tailed test is more appropriate than a two- tailed test. Limiting the region of rejection to one tail of the sampling distributions of H1 provides greater power with respect to an alternative hypothesis in the direction of that tail. The figure below tries to illustrate this.

[此贴子已经被作者于2005-9-27 7:50:16编辑过]

要是用中文讲解会更好。