Dear All,
An experiment was carried out, using as factors the temperature, the humidity and in addition, it was carried out for 6 different species. The total sample number of species analyzed is 6, analyzing 3 individuals of each, so the total N = 18. In my case, I would like to be able to test normality, but the following problem arises. As I must test within each group, I would finally have a N = 3 for the same temperature, humidity and species. It is an N too low for the power of the result of normality to be high.
Trying to see how to solve the problem, I found the following possibility: calculate the average of each group of 3 individuals (that is, of each species), for a certain temperature and humidity. Once calculated the means, we obtained the subtractions (or deviations) of each individual of a species, with respect to the average of the species. When calculating these subtractions or deviations, we could group the N = 18 data, that is, all the species together, so that we increase in sample size and on that, finally perform the Test of Normality.
The problem is that I read this in a book, and I do not find any more information that supports this technique. What do you think about the reliability of this method? What alternatives could I use?
What you did was essentially correct. You said that "As I must test within each group, [...]", what actually means that the conditional distribution of the response should be (approximately!) normal. In a linear model the conditional distribution is just the distribution of the residuals. And in fact, statisticiand do a residual analysis to see if (how well) data and model go together.
With your subtractions you actually calculated the residuals of a full-factorial model. You did this quite manually, but that doesn't make it wrong.
I am only slightly concerned with your wish to "test" the normal assumption. A formal test won't answer your important question, namely whether the normal model is sufficiently good to model your uncertainty associated with the data. If the test is not significant, it may simply be "blind" w.r.t. relevant deviations from the normal model, and if it is significant it may only because of entirely irrelevant deviations from the normal model. Ideally, the normal assumption is justified on theoretical grounds (or prior experience/data). If you think the normal assumption should be ok, it doesn't harm to confirm this using a diagnostic plot of the residuals. In your case, a normal quantile-quantile plot would be good.
https://en.wikipedia.org/wiki/Q%E2%80%93Q_plot
It is necessary to increase your sample size to use anova method and your data also must be normally distributed. Another solution is using a non-parametric alternative.
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