1. Quadrat sampling & the Chi-squared test
4.1.S3 Testing for association between two species using the chi-squared test with data obtained by quadrat sampling

2. Quadrat Sampling
Quadrats are square sample areas, often marked by a quadrat frame
Quadrat sampling involves repeatedly placing a quadrat frame at random positions in a habitat and recording numbers of organisms present
Goal is to obtain realistic estimates of population sizes
Not useful for motile organisms

3. Quadrat Sampling
In our example, students wanted to see if the presence of ferns was statistically significantly larger in the shaded areas (the woodland) compared with the areas in direct sunlight (the prairie).
First we must state the “null hypothesis”
The null hypothesis basically says that there is a high probability that any deviation from the expected values can be attributed to chance
Null hypothesis: The two categories (presence of fern and presence of shade) are independent of each other.
Now we will use the data provided to do a statistical test called a chi-squared test to determine if shade and fern distribution are related.

4. Chi-Squared Testing Draw a contingency table of observed frequencies
Area Sampled
Shade
Sunlight
Presence of ferns
Present
Absent
Observed:
# of quadrats that had ferns present

5. Chi-Squared Testing Draw a contingency table of observed frequencies
Area Sampled
Shade
Sunlight
Presence of ferns
Present
Absent
Observed:
# of quadrats that had ferns absent

6. Chi-Squared Testing Draw a contingency table of observed frequencies
Area Sampled
Shade
Sunlight
Presence of ferns
Present
Absent
Observed:
Sum of the rows (ex: 14+7)

7. Chi-Squared Testing Draw a contingency table of observed frequencies
Area Sampled
Shade
Sunlight
Presence of ferns
Present
Absent
Observed:
Sum of the columns
(ex: 14+6)

8. Chi-Squared Testing Draw a contingency table of observed frequencies
Area Sampled
Shade
Sunlight
Presence of ferns
Present
Absent
Observed:
Total sample size (Grand total)

9. Chi-Squared Testing
Calculate the expected frequencies for each of the possible contingency table scenarios
(Row Total) x (Column Total) / Grand Total
Area Sampled
Shade
Sunlight
Presence of ferns
Present
Absent
Expected:
(20x21)/40 =
(20x21)/40 =
(20x19)/40 =
(20x19)/40 =
Column totals
Row totals
Total sample size (Grand total)

10. Chi-Squared Testing Calculate number of degrees of freedom
(# Rows – 1)(# Columns – 1) = df
(2 – 1)(2 – 1) =
Shade & Sunlight = 2
Present or Absent = 2 1

11. Chi-Squared Testing Calculate the Chi-Squared value: Area Sampled
Shade
Sunlight
Presence of ferns
Present 14 7
Absent 6 13
Observed:
( )2 + ……
10.5
X2 =
Area Sampled
Shade
Sunlight
Presence of ferns
Present
10.5
Absent
9.5
Expected:

12. Chi-Squared Testing
Find the critical value for the Chi-squared test (0.05)
Find the degrees of freedom (df) you calculated earlier
Find the p value of 0.05
Determine the critical value (3.841)

13. Chi-Squared Testing
Compare the Chi-squared value with the Critical Value
If the X2 < CV, then ACCEPT the Null Hypothesis
(i.e. there is NO Association between the variables)
If the X2 > CV, then REJECT the Null Hypothesis
(i.e. there is a significant Association between the variables)…aka ACCEPT the Alternative Hypothesis
Chi-squared vale = 4.91
Critical value = 3.841