The F statistic is calculated by comparing the Variation Among Sample Means to

the Variation Within Groups.

If the Variation Among Sample Means wins out, the p value will be less than,

or equal to, 0.05 and we have a significant finding.

This would allow us to reject the null hypothesis and

say that the explanatory and response variables are associated.

The model sass syntax for conducting an analysis of variance is the following.

PROC ANOVA; CLASS CAT_EXPLANATORY;

MODEL QUAN_RESPONSE =

CAT_EXPLANATORY;.

And then finally the MEANS, which includes the CAT_EXPLANATORY variable.

If your explanatory variable has more than two levels or groups,

you'll also need to conduct a post hoc test.

To conduct a Duncan multiple range test, you include a forward slash followed by

the word Duncan at the end of the means statement and before the semi-colon.

Now you're ready to test a categorical to quantitative relationship.

If your own research question does not include these types of variables,

you might want to test the procedure with variables from your data set that

do require ANOVA.

For example, you could look at mean age differences according to any categorical

variable in the NESARC.

Or treating the grade level variable and add health as quantitative.

You could look at mean differences in grade level,

again, by any categorical variable that you choose.

For both Gap Minder and the Marsh Crater data,

there are many quantitative variables, so

you might choose to categorize one of them for inclusion in an ANOVA.

Whatever types of variables you have,

you'll be able to test the association with the right tool.

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