Data Analysis – Linear Regression: aov

From the curves: there is no interaction between the patients and the measurements, but there is difference in the measurements for each patient

aov.pat1 <- aov(pat_dat~Measure*Patient, pat.df)
summary(aov.pat1)
                 Df   Sum Sq Mean Sq
Measure    5    195.768  39.154
Patient       6     16.301     2.717
Measure:Patient 30  71.452   2.382
aov2.pat1 <- aov(pat_dat~Measure+Patient, pat.df)
summary(aov2.pat1)
                Df  Sum Sq Mean Sq   F value    Pr(>F)    
Measure   5  195.768    39.154   16.4391    8.162e-08 ***
Patient      6    16.301      2.717     1.1407    0.3634    
Residuals   30  71.452   2.382

The "*" before "Patient" means interaction between these factors, i.e., Measure depends upon Patient. The "+" before "Patient" means the difference between these factors, i.e., Measure is independent of Patient.

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Transcript

Now, the structure when we have when we do an ANOVA - we just have a simple function in R that is called aov(). We can use this function in two ways. We can say of the measurements - there's an interaction between the measurements and the patients. And we certainly want to know that that's independent.  And then we look at: Is there a difference between the factors? Is the measure itself independent of the patients?  And that's an important point because if it's not, then the inferences were going (to join) to infer from the data could be wrong.  In the first case, you can see that the summary of the ANOVA doesn't even give us an F value or p-value.  Whereas in the second case we see that the measurements are highly different and one would expect that because we're looking at a coronal angle, a sagittal angle, and an axial angle and three translations - so you would expect the measurements to be all different and the p-value is teeny tiny saying that they are independent. The patients, however, do not depend upon the measurements - as you can see - because the second line is _not_ significant. So, we are assured that the measurements are independent of the patients, and the patients are all the same [i.e.,] have all the same problem - so we expect that the patients will be somewhat alike.