Using the Chi-Squared Test for Association Between Two Species
Definition
Chi-squared test
The chi-squared test is a statistical method used to assess whether the occurrences of two species in a given area are due to chance or due to some form of association, possibly from ecological interactions like competition or mutualism.
- The test essentially compares observed data with expected data under a given hypothesis.
- In ecology, it helps determine whether two species are:
- Independently distributed → No ecological relationship.
- Associated (positively or negatively) → Potential competition or mutualism.
Key Terms
- Null Hypothesis ($H_0$): The species are distributed independently, with no association between them.
- Alternative Hypothesis ($H_1$): There is an association between the species, they may be found together more often or less often than expected by chance.
Always define your hypotheses clearly before starting the analysis.
Steps to Perform a Chi-Squared Test
1. Collect Data Using Quadrat Sampling
- Select random quadrats across a study site.
- Record the presence or absence of both species in each quadrat.
2. Construct a Contingency Table
- Organize the collected data in a 2 × 2 table:
| Species B Present | Species A Absent | Total | |
|---|---|---|---|
| Species A Present | Observed (O₁) | Observed (O₂) | 50 |
| Species B Absent | Observed (O₃) | Observed (O₄) | 50 |
| Total | Column Total | Column Total | Overall Total |
3. Calculate Expected Values ($E$) for Each Category
Use the formula:
\[
E = \frac{\text{Row Total} \times \text{Column Total}}{\text{Overall Total}}
\]
4. Apply the Chi-Squared Formula
\[
\chi^2 = \sum \frac{(O - E)^2}{E}
\]
Where:
