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Mon 21 Jul, 2014 11:22 pm
Hello stats guru,
With regard to an ANCOVA with two treatment groups (climbed/unclimbed) and a set of 10 potential environmental covariates I want to ensure statistically that there is no possibility that the environment was confounded with climbing treatment. If it was, then this would suggest that the apparent impacts of climbing on the response variable may have been due to environment, or may have been due to climbing.
Specifically, I'm wondering if a preliminary MANOVA of the 10 covariates by treatment group can indicate the potential confounded nature of these two variables (climbing treatment and environment).
I found no significance difference in the mean environment by group (climbed and unclimbed treatment) in a MANOVA. Does this imply that there is no mathematical possibility that these covariates, when used in an ANCOVA model with the treatment groups, could be confounded with the climbing impact? In other words, their inclusion in the ANCOVA model would not be able to negate the statistical significance of climbing impact?
I got this idea by reading the following from a blog post:
"Whenever a covariate is affected by the treatments, covariance analysis will fail to show some (or much) of the effects that the treatments had on the response, so that..." (Kutner 5th edition).
[I interpret this mathematically to mean whenever the covariate is correlated with the factor levels.] I thought the inverse of this mathematical relationship was: if environment does not differ significantly among climbing treatment, then there will be no mathematical ability for environmental covariates to be "confounded" with the treatments, and thereby no ability for the covariates to remove the significance of climbing treatment.
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I recognize this is not how covariates are typically used, but that is the primary goal of our research, enabling us to more confidently conclude a significant impact of climbing, despite environmental variability (we did do a paired design, but in the field such pairing does not create identical environments for the two treatments).
Thank you for your time!
T