Omnibus Test

Omnibus Test

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=…=µ_k vs. µ₁≠µ₂≠...≠ µ_k in Analysis Of Variance(ANOVA) ;

or regarding equality between k standard deviations σ₁= σ₂=….= σ _k vs. σ₁≠ σ₂≠...≠ σ_k in testing equality of variances in ANOVA ;

or regarding coefficients β₁= β₂=….= β_k vs. β₁≠ β₂≠...≠ β_k 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 there 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 different from the other (in ANOVA), which coefficient differ from the other (in Regression) etc.