I am running an ANCOVA to measure differences in an allometric relationship between tree height (dependent variable) and diameter (covariate) among one nutrient treatment with 4 levels. One of the levels doesn´t have a significant diameter vs height relationship (is not linear), so I am dropping it from the analysis and will only test the treatment levels that do have a significant linear relationship. One of the assumptions of ANCOVA is that the relationship between X (covariate) and Y is linear. Is it ok to drop the non-significant level?
Hello Gerardo Avalos. Can you show us scatter-plots with X = diameter and Y = height for each of the 4 groups? And what are the sample sizes in the 4 groups? Thanks.
Additive models might be useful for you.
I wouldn't use which side of .05 a p value is to determine what groups to compare.
Figure 1 summarizes the results with and without the control, which is the treatment without a significant linear relationship between DBH and H. I appreciate your feedback. Best, GA
I don't understand why you would want to drop one level of your independent variable. Don't you want to know the effect of that treatment on height, whether or not diameter is a significant covariate ?
Thank you Salvatore, the main goal was to see the effect of nutrients on the shape of the DBH vs H relationship... there is one practical aspect to this since adding the level doesn´t influence that much the fit of the model. Likewise, dropping it doesn´t affect that much the outcome either. I wanted to know if on statistical grounds it is justified to drop this level since one of the assumptions of ANCOVA is that the covariate and the IV should have a linear relationship...
Hi Gerardo Avalos. The names of your 4 groups make we think that they are really the 4 cells of a 2x2 combination of variables N and P as follows:
- Control: N=0, P=0
- N: N=1, P=0
- NP: N=1, P=1
- P: N=0, P=1
Is that right? If so, I would include N, P, and N*P in the model in place of your Treatment variable.
Gerardo Avalos , thank you for including those results. They are helpful when considering the question.
1) Bruce Weaver makes a good suggestion about the coding for the treatment variable.
2) I don't think it's desirable from a practical point of view to drop the control. And I don't think there's a statistical reason to force you to drop the control.
2b) Here's the way I see it. You are constructing a general linear model. Instead of focusing on the assumptions of ancova per se, look at the assumptions of a general linear model.
There is a linearity assumption with a general linear model. But this doesn't equate to --- in your case --- that there would have to be a linear association between DBH vs. H for each level of your treatment. If you found a strong curvilinear relationship, you might re-think your model. But there being no relationship at one level of treatment, I don't think violates any assumption.
The following document has a pretty useful explanation of linearity in general linear models, and of the other assumptions in general linear models.
http://psych.colorado.edu/~carey/Courses/PSYC5741/handouts/GLM%20Theory.pdf
2c) When you have four treatments --- or a factorial of treatments, like Bruce suggests --- it's difficult to tease out of the model what the DBH vs. H line is for each treatment. When you have two treatments, it's pretty easy to tease out what the intercept and slope would be for each line. But beyond this, it gets tricky. At least for me.
Given this --- for your purposes --- I'm wondering if you'd be just as happy to construct a linear model of DBH vs. H for each treatment, perhaps with confidence intervals for each of the intercepts and the slopes. This might be a way to tease out which lines are different from which other lines.
Dear all: thank you all for the feedback. I decided to include the control group in the ANCOVA even though it had no significant effect in terms of the regression. The fit of the model changed from r2 = 0.45 to r2 = 0.42. Obviously, it did not affect the interpretation of the model, although the control group had a significant effect at the treatment level. It is important to consider that the sum of squares type III is used for the calculation of the F test.
- Badges
- Science topic
- Similar topics
- Phytochemistry
- Extracts