{"id":5507,"date":"2022-09-19T16:56:16","date_gmt":"2022-09-19T16:56:16","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5507"},"modified":"2022-10-04T19:11:56","modified_gmt":"2022-10-04T19:11:56","slug":"15e-inclass","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/15e-inclass\/","title":{"raw":"15E InClass","rendered":"15E InClass"},"content":{"raw":"
\r\n
The International Union for Conservation of Nature\u2019s Red List (IUCN Red List)wasestablished in 1964. Since then, ithas evolved to become \u201cthe world\u2019s most comprehensive information source on the global extinction risk of animal, fungus, and plant species.\u201d[footnote]The IUCN Red List of Threatened Species. (n.d.). Background & history. https:\/\/www.iucnredlist.org\/about\/background-history[\/footnote]<\/div>\r\n
\"A<\/div>\r\n
\r\n
\r\n

Question 1<\/h3>\r\n1) 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\u2019s Exact Test instead.Youwill be able to:Check the conditions for Fisher\u2019s Exact Test. Use Fisher\u2019s Exact Test to determine whether there is a relationship between two qualitative binary variables.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
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:[footnote]The IUCN Red List of Threatened Species. (n.d.). Frequently asked questions. https:\/\/www.iucnredlist.org\/about\/faqsCredit: iStock\/Cheryl Ramalho[\/footnote]<\/div>\r\n
\"A<\/div>\r\n
\r\n
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:<\/div>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\nLeast concern<\/strong><\/td>\r\nNear threatened<\/strong><\/td>\r\nVulnerable<\/strong><\/td>\r\nEndangered<\/strong><\/td>\r\nCritically endangered<\/strong><\/td>\r\n<\/tr>\r\n
Plants in forest, subarctic<\/strong><\/td>\r\n33<\/td>\r\n15<\/td>\r\n3<\/td>\r\n3<\/td>\r\n1<\/td>\r\n<\/tr>\r\n
Plants in grassland, subarctic<\/strong><\/td>\r\n27<\/td>\r\n10<\/td>\r\n4<\/td>\r\n1<\/td>\r\n0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n
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.<\/div>\r\n<\/div>\r\n
\r\n
\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\nLeast concern<\/strong><\/td>\r\nNear threatened<\/strong><\/td>\r\nVulnerable<\/strong><\/td>\r\nEndangered<\/strong><\/td>\r\nCritically endangered<\/strong><\/td>\r\n<\/tr>\r\n
Plants in forest, subarctic<\/strong><\/td>\r\n34.0<\/td>\r\n14.2<\/td>\r\n4.0<\/td>\r\n2.3<\/td>\r\n0.57<\/td>\r\n<\/tr>\r\n
Plants in grassland, subarctic<\/strong><\/td>\r\n26.0<\/td>\r\n10.8<\/td>\r\n3.0<\/td>\r\n1.7<\/td>\r\n0.43<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n
\r\n
\r\n

Question 2<\/h3>\r\n2) 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.\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Question 3<\/h3>\r\n3) 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.\r\n\r\n<\/div>\r\n<\/div>\r\n
<\/div>\r\n
This is acontext-drivenfirst step into simplifying the categories in an attempt to satisfy the conditions of the chi-square test.<\/div>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\nLeast concern<\/strong><\/td>\r\nNear threatened<\/strong><\/td>\r\nThreatened<\/strong><\/td>\r\n<\/tr>\r\n
Plants in forest, subarctic<\/strong><\/td>\r\n33<\/td>\r\n15<\/td>\r\n7<\/td>\r\n<\/tr>\r\n
Plants in grassland, subarctic<\/strong><\/td>\r\n27<\/td>\r\n10<\/td>\r\n5<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n
\r\n
\r\n

Question 4<\/h3>\r\n4) 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.\r\n\r\n<\/div>\r\n<\/div>\r\n
Suppose now the scientists replicated the study in the Subantarctic.\u00a0<\/span><\/div>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\nLeast concern<\/strong><\/td>\r\nNear threatened<\/strong><\/td>\r\nVulnerable<\/strong><\/td>\r\nEndangered<\/strong><\/td>\r\nCritically endangered<\/strong><\/td>\r\n<\/tr>\r\n
Plants in forest, subantarctic<\/strong><\/td>\r\n20<\/td>\r\n10<\/td>\r\n2<\/td>\r\n1<\/td>\r\n0<\/td>\r\n<\/tr>\r\n
Plants in grassland, subantarctic<\/strong><\/td>\r\n12<\/td>\r\n7<\/td>\r\n2<\/td>\r\n1<\/td>\r\n0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n
\r\n

Question 5<\/h3>\r\n5) 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.\r\n\r\n<\/div>\r\n<\/div>\r\n
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.<\/div>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\nLeast concern<\/strong><\/td>\r\nNear threatened<\/strong><\/td>\r\nThreatened<\/strong><\/td>\r\n<\/tr>\r\n
Plants in forest, subantarctic<\/strong><\/td>\r\n20<\/td>\r\n10<\/td>\r\n3<\/td>\r\n<\/tr>\r\n
Plants in grassland, subantarctic<\/strong><\/td>\r\n12<\/td>\r\n7<\/td>\r\n3<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nNote that while we are unable to use the chi-square test for independence, we can use Fisher\u2019s Exact Test. This test can be done on a 2\u00d72 contingency table when the expected frequencies do not meet the conditions for the chi-square test. For Fisher\u2019s 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\u00d72 contingency table.<\/div>\r\n<\/div>\r\n
\r\n
\r\n
\r\n

Question 6<\/h3>\r\n6) Fill in the following 2\u00d72 table.\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\nLeast concern<\/strong><\/td>\r\nThreatened levels<\/strong><\/td>\r\n<\/tr>\r\n
Plants in forest, subantarctic<\/strong><\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Plants in grassland, subantarctic<\/strong><\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe null and alternative hypotheses for Fisher\u2019s 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.\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Question 7<\/h3>\r\n
\r\n
7) Using the DCMP Fisher\u2019sExact Test toolat https:\/\/dcmathpathways.shinyapps.io\/FisherExact\/, enter the frequencies of the2\u00d72contingency table and obtain the test statistic and P-value. For the alternative hypothesis, select \u201cOdds ratio not equal to 1 (association).\u201dAt 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.<\/div>\r\n
Part A: Verify the assumptions of Fisher\u2019s Exact Test.<\/div>\r\n
Part B: Write the null hypothesis.<\/div>\r\n
Part C: Write the alternative hypothesis.<\/div>\r\n
Part D: What is the resulting test statistic?<\/div>\r\n<\/div>\r\n
\r\n
Part E: What is the P-value?<\/div>\r\n
Part F: At the 5% significance level, can the null hypothesisbe rejected?<\/div>\r\n
Part G: Write your conclusion in a sentence.<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"
\n
The International Union for Conservation of Nature\u2019s Red List (IUCN Red List)wasestablished in 1964. Since then, ithas evolved to become \u201cthe world\u2019s most comprehensive information source on the global extinction risk of animal, fungus, and plant species.\u201d[1]<\/sup><\/a><\/div>\n
\"A<\/div>\n
\n
\n

Question 1<\/h3>\n

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\u2019s Exact Test instead.Youwill be able to:Check the conditions for Fisher\u2019s Exact Test. Use Fisher\u2019s Exact Test to determine whether there is a relationship between two qualitative binary variables.<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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]<\/sup><\/a><\/div>\n
\"A<\/div>\n
\n
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:<\/div>\n
\n\n\n\n\n\n
<\/td>\nLeast concern<\/strong><\/td>\nNear threatened<\/strong><\/td>\nVulnerable<\/strong><\/td>\nEndangered<\/strong><\/td>\nCritically endangered<\/strong><\/td>\n<\/tr>\n
Plants in forest, subarctic<\/strong><\/td>\n33<\/td>\n15<\/td>\n3<\/td>\n3<\/td>\n1<\/td>\n<\/tr>\n
Plants in grassland, subarctic<\/strong><\/td>\n27<\/td>\n10<\/td>\n4<\/td>\n1<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
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.<\/div>\n<\/div>\n
\n
\n\n\n\n\n\n
<\/td>\nLeast concern<\/strong><\/td>\nNear threatened<\/strong><\/td>\nVulnerable<\/strong><\/td>\nEndangered<\/strong><\/td>\nCritically endangered<\/strong><\/td>\n<\/tr>\n
Plants in forest, subarctic<\/strong><\/td>\n34.0<\/td>\n14.2<\/td>\n4.0<\/td>\n2.3<\/td>\n0.57<\/td>\n<\/tr>\n
Plants in grassland, subarctic<\/strong><\/td>\n26.0<\/td>\n10.8<\/td>\n3.0<\/td>\n1.7<\/td>\n0.43<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
\n
\n

Question 2<\/h3>\n

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.<\/p>\n<\/div>\n<\/div>\n

\n
\n

Question 3<\/h3>\n

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.<\/p>\n<\/div>\n<\/div>\n

<\/div>\n
This is acontext-drivenfirst step into simplifying the categories in an attempt to satisfy the conditions of the chi-square test.<\/div>\n
\n\n\n\n\n\n
<\/td>\nLeast concern<\/strong><\/td>\nNear threatened<\/strong><\/td>\nThreatened<\/strong><\/td>\n<\/tr>\n
Plants in forest, subarctic<\/strong><\/td>\n33<\/td>\n15<\/td>\n7<\/td>\n<\/tr>\n
Plants in grassland, subarctic<\/strong><\/td>\n27<\/td>\n10<\/td>\n5<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
\n
\n

Question 4<\/h3>\n

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.<\/p>\n<\/div>\n<\/div>\n

Suppose now the scientists replicated the study in the Subantarctic.\u00a0<\/span><\/div>\n
\n\n\n\n\n\n
<\/td>\nLeast concern<\/strong><\/td>\nNear threatened<\/strong><\/td>\nVulnerable<\/strong><\/td>\nEndangered<\/strong><\/td>\nCritically endangered<\/strong><\/td>\n<\/tr>\n
Plants in forest, subantarctic<\/strong><\/td>\n20<\/td>\n10<\/td>\n2<\/td>\n1<\/td>\n0<\/td>\n<\/tr>\n
Plants in grassland, subantarctic<\/strong><\/td>\n12<\/td>\n7<\/td>\n2<\/td>\n1<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n
\n
\n

Question 5<\/h3>\n

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.<\/p>\n<\/div>\n<\/div>\n

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.<\/div>\n
\n\n\n\n\n\n
<\/td>\nLeast concern<\/strong><\/td>\nNear threatened<\/strong><\/td>\nThreatened<\/strong><\/td>\n<\/tr>\n
Plants in forest, subantarctic<\/strong><\/td>\n20<\/td>\n10<\/td>\n3<\/td>\n<\/tr>\n
Plants in grassland, subantarctic<\/strong><\/td>\n12<\/td>\n7<\/td>\n3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Note that while we are unable to use the chi-square test for independence, we can use Fisher\u2019s Exact Test. This test can be done on a 2\u00d72 contingency table when the expected frequencies do not meet the conditions for the chi-square test. For Fisher\u2019s 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\u00d72 contingency table.<\/p><\/div>\n<\/div>\n

\n
\n
\n

Question 6<\/h3>\n

6) Fill in the following 2\u00d72 table.<\/p>\n\n\n\n\n\n
<\/td>\nLeast concern<\/strong><\/td>\nThreatened levels<\/strong><\/td>\n<\/tr>\n
Plants in forest, subantarctic<\/strong><\/td>\n<\/td>\n<\/td>\n<\/tr>\n
Plants in grassland, subantarctic<\/strong><\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

The null and alternative hypotheses for Fisher\u2019s 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.<\/p>\n<\/div>\n<\/div>\n

\n
\n

Question 7<\/h3>\n
\n
7) Using the DCMP Fisher\u2019sExact Test toolat https:\/\/dcmathpathways.shinyapps.io\/FisherExact\/, enter the frequencies of the2\u00d72contingency table and obtain the test statistic and P-value. For the alternative hypothesis, select \u201cOdds ratio not equal to 1 (association).\u201dAt 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.<\/div>\n
Part A: Verify the assumptions of Fisher\u2019s Exact Test.<\/div>\n
Part B: Write the null hypothesis.<\/div>\n
Part C: Write the alternative hypothesis.<\/div>\n
Part D: What is the resulting test statistic?<\/div>\n<\/div>\n
\n
Part E: What is the P-value?<\/div>\n
Part F: At the 5% significance level, can the null hypothesisbe rejected?<\/div>\n
Part G: Write your conclusion in a sentence.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
  1. The IUCN Red List of Threatened Species. (n.d.). Background & history. https:\/\/www.iucnredlist.org\/about\/background-history ↵<\/a><\/li>
  2. The IUCN Red List of Threatened Species. (n.d.). Frequently asked questions. https:\/\/www.iucnredlist.org\/about\/faqsCredit: iStock\/Cheryl Ramalho ↵<\/a><\/li><\/ol><\/div>","protected":false},"author":23592,"menu_order":14,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-5507","chapter","type-chapter","status-publish","hentry"],"part":5479,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5507","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/23592"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5507\/revisions"}],"predecessor-version":[{"id":5616,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5507\/revisions\/5616"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/5479"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5507\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5507"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5507"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5507"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5507"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}