I have a data set from a two-choice rodent feeding trial. We were testing the effectiveness of 10 deterrents by coating them on seeds and offering them to rodents alongside control seeds that were uncoated. The explanatory variable is which of the 10 deterrents the treatment seed was coated with, and the response variable is the proportion of control seed and treatment seed consumed. The question we are asking is, "Is each deterrent effective at reducing seed consumption?". The 2-choice feedings were replicated with 6 different rodents for each deterrent (6 rodents X 10 treatments = 60 replicates) (60 replicates x 2 paired measurements{treated seed consumed/control seed consumed} = 120 data points), so very small sample size given the number of parameters we need (10, one for each deterrent). The data distribution for the treated seeds is right skewed and zero-inflated (31 zeroes) while the distribution for the control seeds is relatively normal with greater variance than the treated seeds, so I couldn't use normal statistics.
I choose to use generalized regression fit to a beta distribution because my understanding is that this distribution accounts for the non-normality and variance differences often found with proportion data and that the beta distribution can have an asymptote at 0 which allows for zero inflation. I just had to add a small constant to move the zeroes off of the asymptote (k =0.000001). I'm new to beta distributions, so If I have miss understood something, let me know.
I used JMP's Generalized Regression platform and selected beta as my distribution. I put proportion of seeds consumed as my y, treated/untreated as my x, and placed deterrent type in the 'by' window. This produced 10 different tests that give the results I expected
My questions are:
Have I followed correct procedures given the nature of my data? Like, am I violating an independence assumption because the control consumption and treatment consumption is paired because it came from the same rodent? If so, how do I remedy this?
Are the chi-square values that JMP gave me adjusted for multiple tests? (since I ran 10 of them with the 'by' function)
Is Chi-square even the way I should display my results? cuz the generalized regression output window allows me to do multiple comparisons with a students t that gives me p-values
