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 as a general name refers to an overall or a global test. Other names include 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. at least one pair  µ_j≠µ_j' , 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   σ_j≠ σ_j'  in testing equality of variances in ANOVA; or regarding coefficients  β₁= β₂=….= β_k  vs. at least one pair β_j≠β_j'  in Multiple linear regression or in Logistic regression.