TheCaseoftheCarelessZookeeper.pdf

# Group determine how they will gauge the damage

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group determine how they will gauge the damage suffered for an animal, but remind them to be consistent and unbiased throughout the process. The following table contains example data collected from this activity in an introductory statistics course. There were 15 pairs of students in this section. Table 1. Example class data. Damaged Carnivore Not Damaged Carnivore Damaged Herbivore Not Damaged Herbivore 3 4 5 11 1 4 2 13 4 3 1 9 1 4 3 12 4 5 6 8 0 5 1 14 2 4 2 12 1 5 2 13 2 5 1 13 1 4 3 12 3 6 2 10 0 3 2 15 8 14 1 8 0 3 2 15 2 3 6 10 To see how students should complete the remainder of the activity, the questions on the Activity Worksheet will be answered in parts III and IV using the first row of the table.

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_____________________________________________________________________________________________ ST atistics E ducation W eb: Online Journal of K-12 Statistics Lesson Plans 4 Contact Author for permission to use materials from this STEW lesson in a publication III. Analyze the Data Once the students have grouped the animals and assessed their injury status, they will need to fill out all 9 cells of the two-way table on the Activity Sheet. Using the first row of example data above, the table would look as follows. Table 2. Example individual two-way table. Injury Status Row Totals Type of Animal Damaged Not Damaged Carnivore (f) 3 (g) 4 (b) 7 Herbivore (h) 5 (i) 11 (c) 16 Column Totals (d) 8 (e) 15 (a) 23 Students are asked to identify certain attributes for the animal type and injury status variables. The animal type variable is categorical, nominal, and is the independent variable. The injury status is categorical, nominal, and is the dependent variable. Typically, the dependent is the column variable. The students should be aware that this analysis requires both variables to be categorical, so neither variable should be given a quantitative attribute. Questions 3 through 11 have already been answered in the two-way table above. The students simply sum across all rows and all columns to get the respective values. When students reach questions 12 through 15, they need to find the row percentages for animal type. This means that .429 (3/7) is the proportion of carnivores experiencing damage and .571 (4/7) is the proportion of carnivores experiencing no damage. Similarly, .313 (5/16) is the proportion of herbivores with damage and .688 (11/16) is the proportion of herbivores with no damage. Using these 4 proportions, the students should compare .429 to .313 and then .571 to .688 to answer question 16. If these proportions are deemed to be roughly the same, then no evidence exists to show that a relationship exists between type of animal and injury status. This would tell students that the proportion of damaged and not damaged is the same regardless of animal type, so the variables would be deemed independent. If students see that the proportion of damaged herbivores is low and the proportion of damaged carnivores is high, then there may be a relationship between injury status and animal type. To address this relationship statistically, have the students answer questions 17 to 21, which will outline a chi-square test of independence.
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