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Skills 4.1
Quadrat Sampling
Chi-squared Test
Testing for association between
two species using the chi-squared
test with data obtained by
quadrat sampling.
General Set Up
• To obtain data for the chi-squared test, an
ecosystem should be chosen in which one or
more factors affecting the distribution of the
chosen species varies.
• Sampling should be based on random numbers.
• In each quadrat the presence or absence of the
chosen species should be recorded.
• The collection of raw data through quadrat
sampling will be done in Bamfield on the Beach
Quadrat sampling 101
The presence of two species within a given environment can be determined using quadrat
sampling
• In Workbook Activity 116 you learned about
Sampling as a way to measure the Diversity of
an Ecosystem. CAN YOU RECALL THE FOUR
SAMPLE TYPES?
• A quadrat is a rectangular frame of known dimensions that
can be used to establish population densities
– Quadrats are placed inside a defined area in either a random
arrangement or according to a design (e.g. belted transect)
– The number of individuals of a given species is either counted or
estimated via percentage coverage
– The sampling process is repeated many times in order to gain a
representative data set
Quadrat sampling is not an effective method for counting
motile organisms – it is used for counting plants and sessile
animals
• In each quadrat, the presence or absence of each species is
identified
• This allows for the number of quadrats where both species
were present to be compared against the total number
of quadrats
• Plot-based (quadrat)
methods are often used
to study populations of
different species within a
certain area.
• Quadrats are generally
square sample areas
marked out using a
framed structure.
• Quadrats are placed in a
marked out habitat
according to random
numbers obtained using a
random number table or
a random number
generator on a calculator
Quadrats for Population Estimations
Activity 118
• Discuss the questions
with your group and
share your responses
Activity 119
• Do this in a group of 4
and compare your
answers when you are
finished.
• What did you find?
What is the Chi-Squared Test
• Statistics is one of the most hated subjects by
biologists around the globe. In spite of its daily dose
of abuse, knowledge of statistics can be a life-saver.
T-test or Chi Square???
T-Test
χ2 test
• Looks at the difference
between two groups on
some variable of
interest
• Used for many
applications
• Compares observed
frequencies to expected
frequencies
• Used in Genetics and
Ecology
1. Goodness of Fit - Genetics
• The goodness of fit test is normally used in genetics
where the genotypic and phenotypic ratios have
already been established for a given test and
population.
• Ie. when the expected outcome has already been
established.
– For example: You want to understand
the outcome of an experiment that
in your field based on the
test cross given by Mendel.
you set
Chi-Squared Tests in Ecology
The presence of two species within a
given environment will be dependent
upon potential interactions between
them
Types of Association
POSITIVE
• If two species are typically found
within the same habitat, they
show a positive association
• Species that show a positive
association include those that
exhibit predatorprey or symbiotic relationships
NEGATIVE
• If two species tend not to occur
within the same habitat, they
show a negative association
• Species will typically show a
negative association if there
is competition for the same
resources
– One species may utilise the
resources more efficiently,
precluding survival of the other
species (competitive exclusion)
– Both species may alter their use of
the environment to avoid direct
competition (resource partitioning)
NO ASSOCIATION - If two species do not interact, there will be no association
between them and their distribution will be independent of one another
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.
A chi-squared test can be completed
by following five simple steps:
• Identify hypotheses (null versus alternative)
• Construct a table of frequencies (observed
versus expected)
• Apply the chi-squared formula
• Determine the degree of freedom (df)
• Identify the p value (should be <0.05)
Lets Try It
The presence or absence of two species of
scallop was recorded in fifty quadrats (1m2) on a
rocky sea shore
The following distribution pattern was observed:
• 6 quadrats = both species ; 15 quadrats =
king scallop only ; 20 quadrats = queen
scallop only ; 9 quadrats = neither species
Step 1: Identify hypotheses
A chi-squared test seeks to distinguish between
two distinct possibilities and hence requires two
contrasting hypotheses:
• Null hypothesis (H0): There is no significant
difference between the distribution of two
species (i.e. distribution is random)
• Alternative hypothesis (H1): There is a
significant difference between the distribution
of species (i.e. species are associated)
Step 2: Construct a table of
frequencies
A table must be constructed that
identifies expected distribution frequencies for
each species (for comparison against observed)
• Expected frequencies are calculated according
to the following formula:
• Expected frequency = (Row total × Column
total) ÷ Grand total
Step 3: Apply the chi-squared formula
• The formula used to calculate a statistical value
for the chi-squared test is as follows:
Where: ∑ = Sum ; O = Observed frequency ; E =
Expected frequency
These calculations can be broken down for each
part of the distribution pattern to make the final
summation easier
Based on these results the statistical value calculated by the chisquared test is as follows:
𝝌2 = (2.20 + 2.38 + 1.59 + 1.73) = 7.90
Step 4: Determine the degree of
freedom (df)
In order to determine if the chi-squared value is statistically
significant a degree of freedom must first be identified
• The degree of freedom is a mathematical restriction that
designates what range of values fall within each significance
level
• The degree of freedom is calculated from the table of
frequencies according to the following formula:
df = (m – 1) (n – 1)
Where: m = number of rows ; n = number of columns
When the distribution patterns for two species are being
compared, the degree of freedom should always be 1
Step 5: Identify the p value
• The final step is to apply the value generated
to a chi-squared distribution table to
determine if results are statistically significant
• A value is considered significant if there is less
than a 5% probability (p < 0.05) the results are
attributable to chance
When df = 1, a value of greater than 3.841 is required for
results to be considered statistically significant (p < 0.05)
• A value of 7.90 lies above a p value of 0.01, meaning
there is less than a 1% probability results are caused by
chance
• Hence, the difference between observed and expected
frequencies are statistically significant
As the results are statistically significant, the null
hypothesis is rejected and the alternate hypothesis
accepted:
• Alternate hypothesis (H1): There is a significant
difference between observed and expected
frequencies
• Because the two species do not tend to be present in
the same area, we can infer there is
a negative association between them
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.