Chi-Squared Test: Skills

Tests for Interspecific Competition

To test if there is an association between species of if they co-exist independently of each other experimental tests can be performed

There are two possible hypotheses:

• H0: two species are distributed independently (null hypothesis)

--> there is no statistical significant association in the distribution of the two species

• H1: two species are associated (alternative hypothesis)

--> there is a statistical significant association between the distribution of the two species

These hypotheses can be tested using the chi-square test using random quadrat sampling to record the presence or absence of more than one species that is recorded in every quadrat

--> chi-square test is a statistical methods used to compare observed and expected frequencies in data

Stronger evidence for competition can by obtained by carrying out an experiment in a habitat:

• Field manipulation - one of two species could be removed form quadrats in grassland

• Laboratory experiment - species could be grown together and apart to investigate whether they compete for resources

Positive association: species found in the same habitat (e.g. predator - prey)

Negative association: species occur separately in differing habitats (e.g. due to competition)

No association: species occur as frequently apart as together

Testing for Association

Using quadrat sampling, the presence or absence of the two species in 200 quadrats was recorded. Of these quadrats there were 31 of only Bell heather present, 45 of only Ling present, 89 of Bell heather and Ling present, and 35 of neither of the two present. Is there an association between the two species?​

1. Define the hypothesis

2. Draw a contingency table of observed frequencies (the number of quadrats containing and not containing the species)

1. Calculate the expected values using the formula:

Expected values = (row total x column total)/grand total

(120 x 134)/200 = 80.4

1. Now you can calculate the Chi2 value using the following equation:

1. Calculate the degrees of freedom and compare the calculated Chi2 value to the critical one in the 0.05 confidence interval

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