introduction

1. introduction Statistical analysis of the Orielton field course data sets Peter Shaw

2. The basics of what we want • One of the main ideas of this course is to get you to write up your work in the format of a scientific paper. It has to be admitted that this is not a natural or comfortable format, but it is a standard that you need to come to terms with. So – always: • Abstract • Introduction • Methods • Results • Discussion • References

3. The universal model for this course The statistical model underlying most of the field work was the same: a transect of multiple ‘stations’ from which data were collected, and for which variation is estimated as between-student group variance. (This includes the woodland inverts, even though you only compared 2 sites) Here you can test whether ecosystem properties change along the transect (/differ between sites). To do this we need to examine the null hypothesis, and see whether we can reject it as being unlikely (=significant, here at p<0.05). H0: The distribution of (pH, Temperature, Species A) is random and independent of position along the transect.

4. H0: The distribution of (pH, Temperature, Species A) is random and independent of position along the transect. To test, use 1-way anova or (safer) Kruskal-Wallis non-parametric anova on each variable in turn. 1: Load into SPSS, checking that missing values are shown as dots not zeroes. 2: Ensure that ‘distance’ or ‘station’ is encoded by consecutive integers (station A = 1, station B = 2, C = 3). 3: Finally, Run Analyse – Non parametric tests – K independent samples, or if you are happy that the data approximate to a normal distribution Analyse – Compare means – 1 way anova Either way group by station (or rather the numeric variable coding for station) and examine the significance value generated. How to do it in SPSS

5. Analyse Non-parametric tests K independent samples

6. Voila!

7. Present data (selected variables, where H0 is rejected) as error bars or box plots

8. Diversity indices The idea of a diversity index is one number that is meant to encapsulate both the species richness of a sample, and the evenness of species distribution. Not surprisingly, no one index can actually do this! The simple index suggested is the Shannon index. This index uses logarithms, and gives different answers according to which log base you use. I use log base 10, but then say so in the write-up. Purists use log base 2, which gives the same answer but 3.3219 times bigger [=1/log10(2)] and means the information content of the sample in binary digits. To calculate this index, take each sample and add up the total number of animals then convert each observation into a proportion of the total:

9. You are referred to chapter 2 of Shaw PJA (2003): Multivariate statistics for the Environmental Sciences for more details on diversity indices. A demonstration of the Simpson index calculation on a contrived (ie fictitious) sample: 60 Chironomids, 40 caddis, 2 mayflies, sum = 102 animals. Proportions (called p1, p2,..pi): 60/102 = 0.588, 40/102 = 0.392, 2/102 = 0.020 (note Σ pi = 1) The Simpson diversity of this one sample (one diversity value per sample), is 1-Σpi*pi = 1-((0.588*0.588) + (0.392*0.392)+ (0.02*0.02) = 0.500

10. You are referred to chapter 2 of Shaw PJA (2003): Multivariate statistics for the Environmental Sciences for more details on diversity indices. A demonstration of the Shannon calculation on a contrived (ie fictitious) sample: 60 Chironomids, 40 caddis, 2 mayflies, sum = 102 animals. Proportions (called p1, p2,..pi): 60/102 = 0.588, 40/102 = 0.392, 2/102 = 0.020 (note Σ pi = 1) The Shannon diversity of this one sample (one diversity value per sample), is -Σpi*log(pi) = -((0.588*-0.2306) + (0.392*-0.4067)+ (0.02*-1.699) = 0.328 base 10 (1.09 base 2).