I have data of the following form:
Where 1 is a plant of top quality, 2 is a plant of lesser quality that USED TO BE top quality, and 3 is a plant of poor quality that USED TO BE of type 2 quality. The values listed are the counts of each type of plant from an untreated control group and with a treated group.
I had been using a simple chi-square test to determine whether these treatments had any effect, but I've come to learn that that test assumes no order to the categories, whereas my categories do have an order.
Can someone please help me to understand how to determine:
A) whether the control and treatment are statistically significantly different from one another while taking into account the ordering of the categories.
B) How to determine an effect size from these results to use in statistical power calculations to determine sample size requirements for future studies.
For example, ordinal regression has been suggested, but it's not clear to me how such a calculation would be performed in this case (What is the dependent variable? How does one determine the significance parameter? How is effect size determined?)
Another suggestion has been the Kruskal-Wallis test, but I'm not clear how the order of the values is represented in that test.
Thanks for any advice that you can provide.