Before I respond to your question, I have a question of my own: When you say you did your experiment in triplicates, does that mean there are 3 independent observations in each of the 8 cells? Thanks for clarifying.

Re your question, there is no point in using a statistical test of normality. For all OLS models (including two-way ANOVA), normality of the errors is a sufficient normality condition, but the necessary normality condition is that the sampling distributions of the parameter estimates are approximately normal. (And as n increases, those sampling distributions approach the normal distribution.) The problem with statistical tests of normality is that they have too little power when n is small and too much power when n is large(r). I.e., they fail to detect important departures from normality when n is small, and they detect unimportant departures from normality when n is large(r). Instead of testing for normality, I suggest that you just ask yourself if it is both sensible and defensible to use means and SDs for description of your data. If the answer is yes, then ANOVA is also sensible and defensible, IMO.

Finally, the issue of testing for normality prior to using some kind of OLS model has been discussed many times. Here are a couple of those old discussions you might find helpful.

• https://www.researchgate.net/post/How_to_assume_normality_for_my_dataset
• https://www.researchgate.net/post/Can_the_use_of_a_parametric_test_ANOVA_after_a_failed_normality_test_be_justified

Thanks, Jochen Wilhelm

Thanks Jochen Wilhelm

I'm not sure if I can consider the 3 replicates as truly independent because they measure the same condition (same adsorbent and temperature) under repeated experimental runs. They are meant to capture the variability within a single condition, rather than providing completely independent observations.

I'll also review the shared answers and available literature to understand it clearly. Thanks

I myself find it unlikely that these types of examples can be considered a mixed model. Perhaps because there is no such thing as a random effect in these examples and studies.

However, I think it would be appropriate to think of a Generalized Linear Models (Generalized Estimating Equations or GEE).

In this model, the subject variable can be entered into the model and, given the model's response, a gamma function with log link can be used (given that all responses are positive numbers).