A scientist has been studying the organisms colonising the pilings underneath a wharf in Sydney Harbour. He postulates two factors might make these communities of sponges, worms, anemones, starfish and other marine creatures different from what would be found on a natural rocky reef in these areas. One factor is the shade provided by the wharf. The other factor is the distance from the bottom. He designs an experiment to test the importance of these factors on these communities with the following factors and design:

Factor 1: Position, 2 levels (near (N) vs far (F) from the sea floor), fixed

Factor 2: Shade, 3 levels (open (O), shaded by opaque plexiglass (S) and a procedural control

(C), consisting of clear plexiglass), fixed

He measured the community diversity, using the Shannon diversity index (unitless), on each of n = 4 replicate surfaces per combination of the above two factors. The Shannon index (the response variable here) is defined as: pi log pi, where pi is the proportional abundance of the ith species in the community. Data are found in the file "Shannon.txt".

a. Analyse the data using a two-way ANOVA. Be sure to check the assumptions.

b. Given the ANOVA results, do appropriate pair-wise comparisons, using Tukey's HSD tests.

c. Summarise the results and give conclusions regarding the effects of these factors on the diversity of communities as measured by the Shannon index.