Hi, Despite my intense searches on the web, I unfortunately could not find any information explaining the Coefficient Estimates and Anova Tables that aoctool.m returns.
For the ?separate lines? options, the Coefficient Estimates table shows results for intercepts and slopes. The ?intercept? and ?slope? parameters belong to the common line and individual intercepts and slopes for each study group are listed separately.
I ran a linear regression on my data to obtain intercepts, slopes, R-squared, and p-values for each group. Then, I ran aoctool to determine whether the regression lines were different. The regression analysis (regress) returned a p<0.05 for one group. For, the same group aoctool showed p>0.05. Please note below that the slope of the common line had, however, a significant p-value.
1) In Anocova test with aoctool, each line has a p-value. What is the meaning of this p-value? Is it testing whether each intercept and slope is equal to zero?
2) How do you compare the results of the regress and aoctool? The intercept and slope of the individual lines are the same in both methods, but p-values are different.
3) What is the importance of p-values in the coeff table? If p is not significant and if this means that the slope or intercept is not different from zero, should it be eliminated from or assumed zero in the model formula. In other words, should the slope of Group1 and Group2 below equal to 0.2074 with p=0.0078? And if so, how would you reconcile this with the results of the linear regression analysis?
4) Aoctool also returns an anova table, which has p-values for ?group?, covariate parameter, and interaction of both. The ?group? parameter is actually categorical, ie, [1 1 1 ?. 1 1 2 2 2?.2 2]. Howcome does it have a p-value?
5) The covariate parameter (the horizontal axis in the regression) in the study is actually the same for both groups, which means a paired test, eg, various doses of a drug and two kinds of physiological response. So, What does the p-value in the second line of Anova table returned by aoctool, which belongs to the covariate, refer to?
The results of linear regression (regress.m) Group1 Group2 Slope 0.25 0.17 Intercept -0.07 0.04 P-value 0.04 0.10 R-squared 0.24 0.16
The Coeffients table of ANOCOVA test (aoctool.m) Estimates P-value Intercept -0.0164 0.9032 Group1 -0.0572 0.6719 Group2 0.0572 0.6719 Slope 0.2074 0.0078 Group1 0.0403 0.5852 Group2 -0.0403 0.5852