If your graduate statistical training was anything like mine, you've learned in a class ANOVA and linear regression in another. My professors often say things like "ANOVA is just a special case of regression," then make a lot of acting hand, when pressed to explain it.
It was not until I started, advice that I, as closely related ANOVA and regression can be realized. They are not only related, they are the same. Not one quarter and a nickel – the different sides of the sameMedal.
So, here is a very simple example that shows why. If someone showed me a light bulb went on, although I already knew both ANOVA and mulitple linear regression very well (and even gentlemen in the statistics!). I believe that the understanding was that little concept key to my understanding of the general linear model as a whole – the applications are far reaching.
As an example, I use a model with a single categorical independent variables – employment category – with3 categories: management, clerical and custodial sentences. The dependent variable is Prior experience in months. (This record is employment.sav, one of the records, which comes free with SPSS).
We can run them either ANOVA or a regression. Encoded in the ANOVA, the categorical variable effect, which means that each category is common to represent the large, is compared. In the regression is the dummy-coded categorical variable **, which means that intercept each category is comparedto listen to the reference group. Since the intersection is less than the median value when all other predictors = 0, and there are no other predictors, the three sections are only means.
In either analysis, a job category F = 69.192, with ap <.001. Of great importance.
In ANOVA, we find the mean of the three groups are:
Clerical: 85.039
Imprisonment: 298.111
Manager: 77.619
In the regression, we find these coefficients:
Intercept:77.619
Clerical: 7,420
Imprisonment: 220.492
The intersection is simply the average of the reference group manager. The coefficients for the other two groups, the differences are in the middle between the reference group and the other groups.
You'll notice for example that the regression coefficient for Clerical is the difference between the mean value for Clerical, 85.039, and the interception, or does this mean for managers (from 85.039 to 77.619 = 7.420). The same works for Custodial.
Thus, aANOVA reports each mean and a p-value indicates that at least two differ substantially. (A regression intercept reports only as a mean), and to evaluate the differences between one and any other means, but the p-values of the specific comparisons.
It's all the same model, the same information but presented in different ways. Understand what the model tells you in every way, and you are entitled.
I suggest you try this little exercise to add to each record, then in a secondcategorical variables, first without and then with an interaction. Go through the means and the regression coefficients and see how they add up.
** The dummy coding generates two 1 / 0 Variables: Clerical = 1 for the spiritual category, 0 otherwise; Custodial = 1 0. to detention category, otherwise Observations in the Management category have a value of 0 on these two variables, and this is known as the reference group.
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