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Omnibus tests are a kind of statistical test. They test whether the explained variance in a set of data is significantly greater than the unexplained variance, overall. One example is the F-test in the analysis of variance. There can be legitimate significant effects within a model even if the omnibus test is not significant. For instance, in a model with two independent variables, if only one variable exerts a significant effect on the dependent variable and the other does not, then the omnibus test may be non-significant. This fact does not affect the conclusions that may be drawn from the one significant variable. In order to test effects within an omnibus test, researchers often use contrasts. In addition, Omnibus test is a general name refers to an overall or a global test and in most cases omnibus test is called in other expressions such as: F-test or Chi-squared test. Omnibus test as a statistical test is implemented on an overall hypothesis that tends to find general significance between parameters' variance, while examining parameters of the same type, such as: Hypotheses regarding equality vs. inequality between k expectancies µ1=µ2=…=µk vs. at least one pair µj≠µj' , where j,j'=1,...,k and j≠j', in Analysis Of Variance(ANOVA); or regarding equality between k standard deviations σ1= σ2=….= σ k vs. at least one pair σj≠ σj' in testing equality of variances in ANOVA; or regarding coefficients β1= β2=….= βk vs. at least one pair βj≠βj' in Multiple linear regression or in Logistic regression. Usually, it tests more than two parameters of the same type and its role is to find general significance of at least one of the parameters involved. Omnibus tests commonly refers to either one of those statistical tests: * ANOVA F test to test significance between all factor means and/or between their variances equality in Analysis of Variance procedure ; * The omnibus multivariate F Test in ANOVA with repeated measures ; * F test for equality/inequality of the regression coefficients in Multiple Regression; * Chi-Square test for exploring significance differences between blocks of independent explanatory variables or their coefficients in a logistic regression. Those omnibus tests are usually conducted whenever one tends to test an overall hypothesis on a quadratic statistic (like sum of squares or variance or covariance) or rational quadratic statistic (like the ANOVA overall F test in Analysis of Variance or F Test in Analysis of covariance or the F Test in Linear Regression, or Chi-Square in Logistic Regression). While significance is founded on the omnibus test, it doesn't specify exactly where the difference is occurred, meaning, it doesn't bring specification on which parameter is significally different from the other, but it statistically determine that there is a difference, so at least two of the tested parameters are statistically different. If significance was met, none of those tests will tell specifically which mean differs from the others (in ANOVA), which coefficient differs from the others (in Regression) etc. ==Omnibus Tests in One Way Analysis of Variance== The F-test in ANOVA is an example of an omnibus test, which tests the overall significance of the model. Significant F test means that among the tested means, at least two of the means are significantly different, but this result doesn't specify exactly what means are different one from the other. Actually, testing means' differences is made by the quadratic rational F statistic ( F=MSB/MSW). In order to determine which mean differ from another mean or which contrast of means are significantly different, Post Hoc tests (Multiple Comparison tests) or planned tests should be conducted after obtaining a significant omnibus F test. It may be consider using the simple Bonferroni correction or other suitable correction. Another omnibus test we can find in ANOVA is the F test for testing one of the ANOVA assumptions: the equality of variance between groups. In One-Way ANOVA, for example, the hypotheses tested omnibus F test are: H0: µ1=µ2=….= µk H1: at least one pair µj≠µj' These hypotheses examine model fit of the most common model: yij = µj + εij, where yij is the dependant variable, µj is the j-th independent variable's expectancy, which usually is referred as "group expectancy" or "factor expectancy"; and εij are the errors results on using the model. The F statistics of the omnibus test is: Where, is the overall sample mean, is the group j sample mean, k is the number of groups and nj is sample size of group j. The F statistic is distributed F(k-1,n-k),(α) under assuming of null hypothesis and normality assumption. F test is considered robust in some situations, even when the normality assumption isn't met. 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「Omnibus test」の詳細全文を読む スポンサード リンク
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