IB Biology SL C4.1.15 Chi Squared Test Questions

Use quadrat presence/absence counts for two species to test whether their distributions are associated. Compare observed and expected counts, calculate chi-squared, and use the critical value to interpret the result.

Exam points

From quadrat presence/absence data for two species, state hypotheses about association and explain how expected counts are calculated under the null hypothesis.
Calculate chi-squared from observed and expected counts, then compare it with the critical value to conclude whether the species distributions are associated.

[Maximum number: 3]

White sage (Salvia apiana) is a native Californian shrub. Slender oat (Avena barbata) is a grass, originally from the Mediterranean, which was introduced to California. The map shows the distribution of the two species in relation to one another in an area near Santa Ynez, California.

Figure for Question IB Biology SL C4.1.15 Chi Squared Test Questions question 1 — IB Biology SL

Using the scale bar, determine the area of quadrat A1, giving the units.

Outline how chi-squared can be used to test for an association between the distributions of the two species.

in each quadrat determine the presence/absence «of plants» of each type
null hypothesis is that the presence of one is random/independent in relation to the presence of the other plant
OR
alternate hypothesis is that the presence of one is associated with the presence or absence of the other
$x^{2}=\sum \frac{(O-E)^{2}}{E}$
accept alternative hypothesis / reject null hypothesis if the difference between observed and expected is statistically significant / p<0.05 / calculated $X^{2}$ higher than tabulated $X^{2} /$ critical value
OR
it supports the association between the two species if the difference between observed and expected is statistically significant / p<0.05 / calculated $X^{2}$ higher than tabulated $X^{2} /$ critical value

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IB Biology SL C4.1.15 Chi Squared Test Questions question 1