15E InClass

The International Union for Conservation of Nature’s Red List (IUCN Red List)wasestablished in 1964. Since then, ithas evolved to become “the world’s most comprehensive information source on the global extinction risk of animal, fungus, and plant species.”^[1]

Question 1

1) Is itimportant to keep track of this information? Explain.Objectivesfor the activityYouwill understand:The chi-square test for independence has its limitations,but it may be possible to use Fisher’s Exact Test instead.Youwill be able to:Check the conditions for Fisher’s Exact Test. Use Fisher’s Exact Test to determine whether there is a relationship between two qualitative binary variables.

A researcher is interested in determining whether there is an association between where plants live in the subarctic region and their extinction levels, based on the IUCN classifications. The IUCN Red List consists of nine extinction levels, as presented in the following picture:^[2]

A depiction of the IUCN’s extinction levels. On the far left is all species, which branches into evaluated and not evaluated (NE). From evaluated, the tree branches into data deficient (DD) and adequate data. Adequate data then splits into 7 groups, which are, in order of lowest to highest extinction risk: least concern (LC), near threatened (NT), vulnerable (VU), endangered (EN), critically endangered (CR), extinct in the wild (EW), extinct (EX). Vulnerable, endangered, and critically endangered are all also labeled “threatened categories.”

Note that once a species is evaluated and adequate data are available, it may be classified as Least Concern, Near Threatened,Vulnerable, Endangered, Critically Endangered, or Extinct.Suppose, for example, the researcher specifically looks at a random sample of plants living in the subarctic forest and in the subarctic grassland.Consider the following data:

	Least concern	Near threatened	Vulnerable	Endangered	Critically endangered
Plants in forest, subarctic	33	15	3	3	1
Plants in grassland, subarctic	27	10	4	1	0

In this study, there are two variables: where the subarctic plants growand what their extinction classificationsare. Both of these are categoricalvariables. The following table contains the expected counts.

	Least concern	Near threatened	Vulnerable	Endangered	Critically endangered
Plants in forest, subarctic	34.0	14.2	4.0	2.3	0.57
Plants in grassland, subarctic	26.0	10.8	3.0	1.7	0.43

Question 2

2) Based onthetable, do you think it would be appropriate to perform a chi-square test for independence to determine if there is evidence of anassociation between where the plant lives and what its extinction level is? Explain.

Question 3

3) What would be a good way to combine some of the categoriesgiven the structure of the IUCN Red List? Refer to the figure. Note from the figure that the classifications Critically Endangered, Endangered,and Vulnerable are considered to be Threatened categories.

This is acontext-drivenfirst step into simplifying the categories in an attempt to satisfy the conditions of the chi-square test.

	Least concern	Near threatened	Threatened
Plants in forest, subarctic	33	15	7
Plants in grassland, subarctic	27	10	5

Question 4

4) Do you think it would be appropriate to perform a chi-square test for independence to determine if there is evidence of an association between where the plant lives and what its extinction level is? If so, conduct the testand write your conclusion.

Suppose now the scientists replicated the study in the Subantarctic.

	Least concern	Near threatened	Vulnerable	Endangered	Critically endangered
Plants in forest, subantarctic	20	10	2	1	0
Plants in grassland, subantarctic	12	7	2	1	0

Question 5

5) In this study, there are two variables: where the subantarctic plants growand what their extinction classificationsare. Do you think it would be appropriate to perform a chi-square test for independence to determine if there is evidence of an association between where the plant lives and what its extinction level is? Explain.

Unfortunately, the strategy that we used in Question 4 will not work. If we combine the Threatened categories into one, there are still not sufficient cell counts to conduct the chi-square test.

	Least concern	Near threatened	Threatened
Plants in forest, subantarctic	20	10	3
Plants in grassland, subantarctic	12	7	3

Note that while we are unable to use the chi-square test for independence, we can use Fisher’s Exact Test. This test can be done on a 2×2 contingency table when the expected frequencies do not meet the conditions for the chi-square test. For Fisher’s Exact Test, we require a simple random sample from the population and two categorical variables, each with two possible values. This will result in a 2×2 contingency table.

Question 6

6) Fill in the following 2×2 table.

	Least concern	Threatened levels
Plants in forest, subantarctic
Plants in grassland, subantarctic

The null and alternative hypotheses for Fisher’s Exact Test mirror those for the test for independence. Much like the other hypothesis tests, it uses a P-value to decide if there is evidence that the two variables are not independent. The P-value is calculated as the exact probability of observing cell counts that are as inconsistent with the hypotheses of independence as the counts in the table that were constructed from the sample data. The probability calculated is beyond the scope of what is covered in this course, but fortunately we can rely on technology to obtain calculations for us. In the end, remember that the smaller the P-value is, the stronger the evidence is against the null hypothesis.

Question 7

7) Using the DCMP Fisher’sExact Test toolat https://dcmathpathways.shinyapps.io/FisherExact/, enter the frequencies of the2×2contingency table and obtain the test statistic and P-value. For the alternative hypothesis, select “Odds ratio not equal to 1 (association).”At the 5% significance level, the researcher wants to establish whether there is an association between where a plant lives in the subantarctic (forest or grassland) and its extinction level.

Part A: Verify the assumptions of Fisher’s Exact Test.

Part B: Write the null hypothesis.

Part C: Write the alternative hypothesis.

Part D: What is the resulting test statistic?

Part E: What is the P-value?

Part F: At the 5% significance level, can the null hypothesisbe rejected?

Part G: Write your conclusion in a sentence.

The IUCN Red List of Threatened Species. (n.d.). Background & history. https://www.iucnredlist.org/about/background-history ↵
The IUCN Red List of Threatened Species. (n.d.). Frequently asked questions. https://www.iucnredlist.org/about/faqsCredit: iStock/Cheryl Ramalho ↵