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

F-test

An F-test is any statistical test in which the test statistic has an F-distribution under the null hypothesis.It is most often used when comparing statistical models that have been fit to a data set, in order to identify the model that best fits the population from which the data were sampled. ...

 in the analysis of variance

Analysis of variance

In statistics, analysis of variance is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation...

. 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

Contrast (statistics)

In statistics, particularly analysis of variance, a contrast is a linear combination of two or more factor level means whose coefficients add up to zero. A simple contrast is the difference between two means...

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