Is it possible to have a statistically significant ANOVA in which none of the pairwise comparisons are statistically significant answer yes or no and then state the reason for your answer?

Is it possible to have a statistically significant ANOVA in which none of the pairwise comparisons are statistically significant answer yes or no and then state the reason for your answer?

Yes it is possible. The exception is Scheffe’s test (which no GraphPad product offers). It is intertwined with the overall F test. If the overall ANOVA has a P value greater than 0.05, then the Scheffe’s test won’t find any significant post tests.

What is an omnibus statistical test?

Omnibus tests are statistical tests that are designed to detect any of a broad range of departures from a specific null hypothesis. For example, one might want to test that a random sample came from a population distributed as normal with unspecified mean and variance.

What is the null hypothesis for the omnibus F-test in ANOVA?

The null hypothesis in ANOVA is always that there is no difference in means. The research or alternative hypothesis is always that the means are not all equal and is usually written in words rather than in mathematical symbols.

What does it mean when omnibus test is not significant?

Your omnibus test (model, line 1 of output) is not significant, which means you do not have enough evidence to reject that hypothesis. Classically, people think that means you shouldn’t move forward with more specific analyses. However, omnibus test can non-significant for multiple reasons. It could be that all your means are in fact equal.

How to interpret the F-test of overall significance in?

Typically, you don’t interpret the F-value directly, but instead the p-value associated with it. For the F-test, your p-value of 0.000 indicates the model as a whole is statistically significant. Additionally, it looks like your independent variables are also significant. The R-squared is also high. It looks like good results overall.

How does the F test work in ANOVA?

Read my blog post about how F-tests work in ANOVA. To calculate the F-test of overall significance, your statistical software just needs to include the proper terms in the two models that it compares. The overall F-test compares the model that you specify to the model with no independent variables.

When to use ANOVA to test for statistical significance?

When you use ANOVA to test the equality of at least three group means, statistically significant results indicate that not all of the group means are equal. However, ANOVA results do not identify which particular differences between pairs of means are significant.