I must sadly say that Kou Hayakawa

@Bruce Weaver has an excellent answer to a related question here : https://www.researchgate.net/post/Is_linear_regression_valid_when_the_outcome_dependant_variable_not_normally_distributed

I'd just add that many processes can be modelled by approximations that seem laughably simple but which approximate well. My students are always impressed by the linearity of the relationship between the baby's weight and the mother's height. The humble logistic regression is at the basis of a vast number of clinical prediction systems used daily in health care.

So of course, the normal distribution is not the only distribution available in the world of generalised linear models either. Some processes have perfectly definable distributions – radioactive decay, for example. But many others can be modelled well using distributions that approximate well to their data generation process – I'm thinking of negative binomial, Poisson, gamma and Weibull models.

The trouble with many nonparametric models is their difficulty in returning interpretable measures of effect size, and of making useful predictions.

Beware, then, of simple answers. I hesitate to quote George Box yet again, but it seems like the place to honour his maxim : all models are wrong, but some models are useful.

Thanks Ronán Michael Conroy. I made a second post in that same thread where I went a bit further by arguing that normality of the errors is a sufficient, but not a necessary condition. Because you have to click Show previous answers several times to find that post in the original thread, I'll copy it here.

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March 14, 2018

Since I posted my earlier response 4 years ago, my thoughts on the normality requirement for OLS regression have changed a bit, and I think they are probably in line with the views expressed by Javed Iqbal and Athanasios Dermanis. I have been influenced by Jeffrey Wooldridge's book, Introductory Econometrics. What he says about the assumptions for OLS linear regression is summarized in the attached PDF. Note especially this excerpt (from p. 168 of the book) on slide 9:

• "One practically important finding is that even without the normality assumption (Assumption MLR.6), t and F statistics have approximately t and F distributions, at least in large sample sizes."

This suggests to me that normality of the errors is really a sufficient condition, but not a necessary condition. Sufficient for what? Sufficient to ensure (approximate) normality of the sampling distributions of the model parameters (i.e., the coefficients). And it is those sampling distributions, at the end of the day, that really need to be (approximately) normal.

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I hope this helps.

https://en.wikipedia.org/wiki/Spherical_cow

Returning to Rinaldi Gotama's question, it looks to me like a two-factor mixed design ANOVA. The between-subjects factor is Site (with 7 levels), and the within-subjects (or repeated measures) factor is Season (summer vs winter). The "three replicate sampling locations" within each site are the "subjects" in the vernacular I learned. (I.e., they are the independent units of observation.) You can find plenty of examples of how to estimate this kind of ANOVA model with R if you Google
. Here are some of the hits I found:

• https://personality-project.org/r/r.guide/r.anova.html
• https://www.alexanderdemos.org/ANOVA13.html

HTH.

Jochen Wilhelm – do you have a terriffic reference for absolutely everything? If often seems you do.

:)