Type of Anova test My daughter has gathered data relating to rock pool populations of various entities across 5 months, on two sites, one with a lot of human interaction and one with little.
She is starting to look at comparisons on a particular month between results in the two environments, so the data appears as:
Species             DisturbedMay    UndisturbedMay
Enteromorpha linza  22.30769        18.92857143
E. intestinalis     9.5             7.5
etc

Thanks to this site we have found out the coding for a Levene test and run it, now her attention is going towards Anova.  We are not sure a) if its one or two way we want (suspect the latter), and if so any hints on the R coding would be gratefully received (though please go easy on us, we understand little of R or stats) 
 A: welcome to Cross Validated. A question specifically on R coding is out of scope here, but a question on statistics would be appropriate. So, first of all, let's define exactly the goal of your analysis. I guess you have a population of algae in both environments, composed of different species. You are measuring some continuous variable for each of your algae species, say $y$, in both environments, during the month of May. Thus, for each species $i$ you have 2 measures $y_{iA},y_{iB}$ where $A$ and $B$ denote respectively the measure in the disturbed environment and the measured in the undisturbed environment. The goal of your analysis is to use your finite sample in order to test the hypothesis that the mean of $y$ for the overall population of algae of all species is the same between environment $A$ and environment $B$. In this case, ANOVA is not needed: you have only two groups, thus a paired t-test is sufficient. The paired t-test is valid under some assumptions:


*

*the pair differences are approximately normally distributed (have a
look at their histogram and at the QQ-plot to verify this
assumption). If you have difficulties with this point, have a look at the results of this search for the assumptions of a t-test on this site, and add the full data set in your question, or at least include the sample size, an histogram and a QQ-plot.

*the residuals are independent: this means that the difference of the two measures of $y$ for each species is independent of the difference of the two measures for any other species. I'm not exactly an expert in algae biology :) but I would think that unless these rock pools are really small and/or this measure is very invasive, the act of measuring $y$ for a given species, e.g., Enteromorpha linza, shouldn't influence the result of the measure of $y$ for other species, e.g. Enteromorpha intestinalis. Thus the independence assumption may be justified. Just for safety, though, you may either provide more details on the measurement process in your question, so that we can help you with deciding whether the samples are independent, or your daughter may check the existing literature on the subject/ask her tutor.


The paired t-test may lead you to reject your null hypothesis at a certain significance level, in which case you conclude that either a very unlikely event has happened, or human interaction has a significant effect on the mean of $y$. Or the test may fail to reject the null hypothesis (this doesn't mean that it's true).
PS two very important notes:


*

*I assumed that your population is made up of all the algae of each species. If you want to treat algae of different species as different populations, then you need more that one pair of measurements for each species. If you have them, you can consider the algae species as an additional factor, together with the type of environment. In this case you actually need two-way ANOVA. Have a look at the assumptions of two-way ANOVA to verify that it would lead to valid inferences in your case, then ask a question on Stack Overflow in order to get support with running two-way ANOVA in R.

*You specified that you were considering only measurements in May. If you are not performing other tests in different months, then the paired t-test (or the two-way ANOVA, if the algae species is to be considered a factor) is a valid tool, provided that the above assumptions are met. However, if later on you plan to perform the same test for other months, then the results of the paired t-test will be affected by the issue of multiple comparisons. In layman's terms, this means that by performing so many tests, one of them may result signficant just by chance, even if human interaction doesn't have an effect on algae population. ANOVA was born exactly to avoid this. If this is your case, please edit your question accordingly and I will modify (basically, delete and rewrite from scratch :) my answer.

