1. BUG’S LIFE
A Comparison of the Insect Species Richness Between Forest and Pasture Ecosystems in Sao Paulo, Brazil

2. CONTINGENCY TABLES
Contingency Tables: are tabulation of data that permits you to test for differences in frequencies between samples
Hypothesis Testing: Start with a NULL hypothesis, which in this case is “the frequency of species does NOT differ between habitats and ecosystems”

3. HOW TO TEST THIS HYPOTHESIS?
A contingency table does that by estimating the probability that the frequency of species between habitats and ecosystems DOES NOT vary.
In our case we could think that all four possible ecosystem/habitat combination would support the same # of species (i.e. there would be no difference between them).
Another way of putting it: the # of species is completely independent of any kind of ecosystem/habitat combination.

4. GOODNESS OF FIT
Performing a statistical test, the null hypothesis is tested by comparing the data (OBSERVED values) to statistical tables, which represent the EXPECTED probabilities (they represent known frequency distributions).
The measure of how well our data fit the expected probabilities is called “goodness of fit”. In other words, this measure tells you how much your data DEVIATE from the expected probabilities.

5. SUMMARY
So, when you compare your observed frequencies with the expected frequencies, two results are possible:
1) If the departure is large (observed differs from expected), then the null hypothesis is probably wrong;
2) If the departure is small, then possibly the null hypothesis fits your data.

6. Ecosystems: Forest vs. Pasture Habitats: Canopy vs. Ground level
Total
Canopy 14 28 42
Ground 6 12 20 34 54

7. ANALYSIS of RESULTS
We used the “G” test of goodness of fit, and found the following:
Calculated (our) G = 1.08
Critical value (tabled) G = 3.84
Since the calculated value of the G statistic is smaller than the critical value, we can say that there is a very good chance that the null hypothesis is true.