Chi-Squared Tests in Ecology
The Chi-Squared Test (2)
• The chi-squared test is used to study differences between data sets.
• It is only used for frequencies (counts), never for measurements.
• It is used to compare an experimental result with an expected
theoretical outcome.
• It is not a valid test for small sample sizes (n<20)
• It tests the validity of the null hypothesis: no difference between
groups of data.
• In ecology, chi-squared tests are used to study habitat preference.
Mangrove (Avicennia marina var. resinifera)
Mangroves are
doing well in USA
these days…
Mangrove forests vs shrimp farming
Pneumatophores
• Some plants have aerial roots – pneumatophores
• These can come in handy in waterlogged soil where oxygen levels are
very low…
Soil porosity is related to the average size of
soil particles…
• Larger particles, like sand, have larger spaces for air
• Clay soils have very tiny particles, much smaller spaces for air
Experimental Design
• 1 m x 1 m quadrats were placed
around many mangroves in
numerous locations.
• Pneumatophores were counted.
• Chi-squared test was use to
compare observed results for
pneumatophore density.
• Null hypothesis: no difference in
density between substrates (soils)
The Flat Periwinkle
(Littorina littoralis)
Periwinkles feed on a number of seaweed species
Food preference is a form of animal behavior
• Using quadrats, the
number of periwinkles
associated with each
seaweed species was
recorded.
State your null hypothesis for this investigation (H0)
• H0: There is no difference between the
numbers of periwinkles associated with
different species.
• What is the alternative hypothesis (HA)?
• HA : There is a real difference between
numbers of periwinkles associated with
different species.
Use the chi-squared test to determine if the
observed differences are significant or if they can
be attributed to chance alone.
Enter the observed values
and calculate the chisquared value
Here’s how you do it…
• The expected value (E)
would be the mean
number of periwinkles
associated with the
four seaweed species.
Now Complete the Chart…
• Calculate the degrees of freedom:
• 4-1 = 3
Check your Chi-square table for 3 degrees of
freedom.
• 57.4 >> 7.82, 11.34
• Is H0 accepted or rejected?
• There is a significant difference in feeding preferences of periwinkles.
Woodlice (Pillbugs) Experiment
Category
Dry
Humid
O
15
35
E
25
25
O-E
-10
+10
(O-E)2
100
100
Chi-squared value is 8 for 1DF
(O-E)2/E
4
4
Chi-Square Homework Worksheet
• A marketing analyst wishes to
see whether consumers have
any preference among five
flavors of a new fruit candy.
• A random sample of 100
people provided the
following data.
Flavor
Preference
Cherry
32
Strawberry
28
Orange
16
Lime
14
Grape
10
What is the null hypothesis?
• How do you calculate your expected value?
• How many degrees of freedom do you have?
• Show your chi-square calculations below, and state whether the null
hypothesis is accepted or rejected.
Flavor
Preference
Cherry
32
Strawberry
28
Orange
16
Lime
14
Grape
10
A science teacher living in the desert noticed that
native mesquite trees differed in terms of number
of parasitic mistletoe plants they contained.
Mesquite trees in residential neighborhoods
tended to have fewer parasitic plants than trees
found in undisturbed areas.
• RESEARCH QUESTION: Is there really more mistletoe in the
undisturbed areas than in his neighborhood?
• What is his hypothesis?
Mesquite and Mistletoe
Tree
#
1
2
3
4
5
6
7
8
9
10
“wild”
trees
26
11
16
9
3
14
5
8
14
15
Residential
trees
6
8
1
0
0
0
3
3
3
1
Here is his data. Calculate the chi-squared
value for the null hypothesis.