IB Biology HL C4.1.15 Chi Squared Test Questions

Use quadrat contingency tables to calculate expected frequencies and degrees of freedom, compare chi-squared with a critical value and conclude species association in IB Biology HL C4.1.15.

Exam points

Set null and alternative hypotheses for association between two species, calculate expected frequencies from row and column totals, and determine degrees of freedom.
Calculate or interpret chi-squared against a critical value to accept or reject the null hypothesis and conclude whether 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 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