IB Biology HL C4.1.15 Chi Squared Test Questions

Use quadrat presence/absence counts for two species to test whether their distributions are associated. Calculate expected counts and degrees of freedom, then compare the chi-squared statistic with a critical value.

Exam points

Set up hypotheses for association between two species, then calculate expected quadrat counts from row and column totals and determine the degrees of freedom.
Calculate chi-squared from observed and expected counts, then compare it with the critical value to judge whether species presence/absence is 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 HL C4.1.15 Chi Squared Test Questions question 1 — IB Biology HL

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

a. in each quadrat determine the presence/absence «of plants» of each species
b. null hypothesis is that the presence of one is random 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
c. $x^{2}=\sum \frac{(O-E)^{2}}{E}$
d. 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 HL C4.1.15 Chi Squared Test Questions question 1