On-line statistics

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Petersons Homogeneity Index

Suppose three samples are taken from a garden. How similar are they? The way in which you assess this will depend on the format of your data. If you hve counted the numbers of individuals of each species present in each sample you can use Peterson's Homogeneity Index. If not you should use something like Søerensen's Quotient

Similarity or homogeneity within a community or batch of samples can be quantified with Peterson's Homogeneity Index (I ) .

where ai = the proportion of species i in Sample A

bi = the proportion of species i in Sample B.

Steps :

Convert the sample data into proportions

Calculate I for each pair of samples :

= 0.357

The mean homogeneity of the community can be taken as the mean of all I's calculated in a pair by pair comparison.

Now check that you understand by completing the following:

  Question #1:
What is the value of Peterson's Homogeneity index if Sample B and Sample C are compared? :

Question #2:
What is the overall community homogeneity? :

Correct Answers

Petersons Homogeneity Index is influenced by :

a) Sample size
b) Differences in diversity between samples
c) Sampling error

To get a homogeneity value with these biases removed, a Monte Carlo simulation must be carried out to calculate an Adjusted Similarity Index. To do this:

1) Calculate the mean Peterson Homogeneity Index for the community.
2) By pooling the data and randomly associating species numbers from each sample work out a simulated value for Petersons Homogeneity Index. Work out the mean I for the same number of simulated samples as there were in the original sample
3) Work out a simulated Index five times and calculate the median.
4) The index of homogeneity is then the mean I for the community divided by the median of 5 simulated mean similarity indices and homogeneity is maximum when I = 1.

Source : Bakus (1990)

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Descriptive Stats

Diversity Indices

Comparisons

Correlations

Regression