Transcript BUG’S LIFE - Columbia University

BUG’S LIFE
A Comparison of the Insect Species
Richness Between Forest and Pasture
Ecosystems in Sao Paulo, Brazil
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”
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.
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.
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.
Ecosystems: Forest vs. Pasture
Habitats: Canopy vs. Ground level
FOREST
PASTURE
Total
Canopy
14
28
42
Ground
6
6
12
Total
20
34
54
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.