Hello everyone! I am looking for some statistical help!
I am working in in vitro micropropagation and one of the aspects that I am studying is the rooting of plants in 10 different growing media. For that, I categorize the rooting of the plants as 0 (no roots) or 1 (rooting). Therefore, I have one categorical independent variable (rooting medium) with 10 different categories and one categorical dependent variable with two variables. My sample size is 30 plants per medium.
From those numbers, I obtain a rooting percentage for each medium and I would like to now if this parameter differs significantly between the different media.
I would like to know how I should compare my data. These are the tests I have done but do not know which one to use:
- 2x10 contingency table in SPSS and Chi-2 test. This gives me a p value for the whole experiment. For post hoc, I have used a Z-test.
- I have also tried a univariate GLM in SPSS with a tukey post hoc test.
I do not know if both are valid or if I should just stick to the contingency table.
Any help would be appreciated
Thanks!
Since you knnow the denominator (of the percentages), you should use a binomial GLM (aka logistic regression).
+1 for Jochen Wilhelm 's suggestion. A simple chi-square test will give a significance, but is missing an important piece of information: effect size and confidence interval (how biologically meaningful is the size of the difference and what is the uncertainty around that).
The Generalized Linear Model (GLM) with a Binomial distribution will provide all this. You can also easily do post-hoc comparisons using the package emmeans.
Hope that helps!
Maybe I am reading this differently from Jochen Wilhelm and others, so am taking a different tact (but am certainly willing to be convinced that I am wrong ... and this is not my substantive area, so ... ). My concern is with a statistical approach that has 9 values that are the focus and the power of post hoc tests with this many categories. In order to offer guidance, I have a question.
Do you have any ideas/theories/hunches about the relationships among the 10 categories?
If yes, use these ideas in you model to focus what you are looking at.
If not (so these are just random categories that were picked), presumably your interest is just whether there is more variability among these categories than expected if the categories don't make a difference. Then, you'd probably want to allow the intercept to vary by category, and might assume the distribution of these intercepts is random, and then just have a single number (the variance) that you are focused on.
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