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2605
2605
Level III

Difference in degrees of freedom in ANOVA report and effect test

Jul 23, 2019 07:14 AM (3396 views)

I am running Three way anova with interaction and I am unable to understand the difference in the values of degrees of freedom. One of my variable is continuous with 84 observations and other is a nominal variable with 2 levels.

In ANOVA report table for the model DF is 3, Error is 80 and C.Total is 83. 

Whereas, in effect test DF for both variables is 1.

 

How do I interpret this? Also, when I say main effect of one variable was found significant I write it as F(1,83) = 63.4054. What does 1 and 83 account for? How is the F-ratio reported in research papers?

 

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1 REPLY 1
Mark_Bailey
Staff Mark_Bailey
Staff

Re: Difference in degrees of freedom in ANOVA report and effect test

Created: Jul 23, 2019 07:47 AM  |  Last Modified: Jul 23, 2019 4:53 AM (3392 views)  |  Posted in reply to message from 2605 07-23-2019

Your continuous variable requires one parameter (i.e., the slope). Your two-level categorical variable requires one parameter because of the 'effect coding.' Your intercept requires one parameter. So there are three degrees of freedom in the whole model that is tested by the analysis of variance but there is only one DF associated with the individual test for each estimate.

 

The symbol F( 1, 83 ) indicates that the F ratio (i.e., MS Model / MS Error) has 1 DF in the numerator and 83 DF in the denominator.

 

Have you studied linear models or linear regression? These topics are basic lessons in these subjects. Either way, these reports are explained by selecting Help > Books > Fitting Linear Models or by using search in the Help system.