First of all, I am very new to statistics, so this might be a very basic question but I could not find any answers to my question in other topics here.
I have a data set on microbial growth (Glob_mu_h) assessed in incubation experiments. Those incubation experiments were conducted once per season (Winter, Spring, Summer, Autumn) and per site in triplicates. Sites were two streams (one that goes in and the other goes out of the lake) and three depths inside the lake.
So in summary:
- Growth rate: continuous response variable
- Site: categorical predictor variable with 5 levels
- Season: categorical predictor variable with 4 levels
Now the question is whether there is a difference in the microbial growth rate dependent on season and the site.
When looking for potential statistical tests, I got a little confused which of the tests to use. First, I thought that season is a repeated measures design, so I conducted a linear mixed model approach, however, this gives me only a difference in the Seasons but not in Sites. And I guess it only compares all seasons with winter.
seaModel<-lme(Glob_mu_h ~ Season,
random = ~1|Site/Season, data = sum, method = "ML")
Output of summary()
Fixed effects: Glob_mu_h ~ Season
Value Std.Error DF t-value p-value
(Intercept) -0.001251552 0.0009999966 12 -1.251556 0.2346
SeasonSpring 0.004160010 0.0013194851 12 3.152752 0.0083
SeasonSummer 0.006340499 0.0013194851 12 4.805282 0.0004
SeasonAutumn 0.005689040 0.0013194851 12 4.311561 0.0010
So, I defined contrasts as described in the Book "Discovering statistics using R" by ANDY FIELD, JEREMY MILES and ZOË FIELD. Which enabled me to test the hypotheses regarding the seasons.
However, I am still missing the comparison between the sites as with this approach they are apparently pooled together.
An approach that evaluates both predictors might be a two-way ANOVA, but I was wondering whether I am not violating the assumption of independence because those are the same sites across seasons. Even though the experiments were of course independently run.
In the case, that I am not violating the independence, can I still conduct a two-way ANOVA if normal distribution within groups are not fulfilled? I was examining some QQ Plots to see whether the triplicates are normally distributed and for some predictor-combinations this is unfortunately not true. I've read in the same book as cited above, that if group sizes are equal the F-statistics are quite robust even when normality is violated. However, my group sizes are not equal (4 seasons, 5 sites).
To my understanding there isn't a non-parametric equivalent to two-way ANOVAs that are robust. So I am a little unsure how to proceed.
Any help is very much appreciated.
