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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Levene's test ： ウィキペディア英語版 Levene's test In statistics, Levene's test is an inferential statistic used to assess the equality of variances for a variable calculated for two or more groups. Some common statistical procedures assume that variances of the populations from which different samples are drawn are equal. Levene's test assesses this assumption. It tests the null hypothesis that the population variances are equal (called ''homogeneity of variance'' or ''homoscedasticity''). If the resulting ''p''-value of Levene's test is less than some significance level (typically 0.05), the obtained differences in sample variances are unlikely to have occurred based on random sampling from a population with equal variances. Thus, the null hypothesis of equal variances is rejected and it is concluded that there is a difference between the variances in the population. Some of the procedures typically assuming homoscedasticity, for which one can use Levene's tests, include analysis of variance and t-tests. Levene's test is often used before a comparison of means. When Levene's test shows significance, one should switch to more generalized tests that is free from homoscedasticity assumptions (sometimes even non-parametric tests). Levene's test may also be used as a main test for answering a stand-alone question of whether two sub-samples in a given population have equal or different variances. ==Definition== The test statistic, ''W'', is defined as follows: : $W\; =\; \backslash frac\; \backslash frac-Z\_)^2\}\; ^\; (Z\_-Z\_)^2\},$ where * $W$ is the result of the test, * $k$ is the number of different groups to which the sampled cases belong, * $N$ is the total number of cases in all groups, * $N\_i$ is the number of cases in the $i$th group, * $Y\_$ is the value of the measured variable for the$j$th case from the $i$th group, * |Y_ - \tilde_|, & \tilde_ \mbox \end\right. (Both definitions are in use though the second one is, strictly speaking, the Brown–Forsythe test – see below for comparison) * $Z\_\; =\; \backslash frac\; \backslash sum\_^\; \backslash sum\_^\; Z\_$ is the mean of all $Z\_$, * $Z\_\; =\; \backslash frac\; \backslash sum\_^\; Z\_$ is the mean of the $Z\_$ for group $i$. The significance of $W$ is tested against $F(\backslash alpha,k-1,N-k)$ where $F$ is a quantile of the F-test distribution, with $k-1$ and $N-k$ its degrees of freedom, and $\backslash alpha$ is the chosen level of significance (usually 0.05 or 0.01). 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「Levene's test」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.