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# Chi square test for association

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Explanation and completion of 2.1, 2.2, & 2.3.

PART 2: Problems

Answer the questions in Part 2. Be sure to show every step of your work clearly and completely. Explain
your conclusions in clear language for someone who is not statistically numerate.
CASE # GNDR TRAK ADV LIKE STDY GPA HIGH SCHOOL SENIORS
1 1 1 19 2 5.5 0.55
2 1 1 17 4 5.8 0.63 GNDR = Gender
3 0 1 16 8 3.3 0.67 F = 1
4 0 1 17 6 4.7 0.71 M = 0
5 1 2 14 6 4.2 0.72 TRAK = Course of Study
6 1 1 15 8 6.7 0.76 1 = remedial
7 1 3 11 7 3.8 0.75 2 = vocational
8 0 2 20 7 3.5 0.79 3 = mainstream
9 1 2 12 6 5.7 0.79 4 = college prep
11 1 2 7 7 6.3 0.88 ranked index of
12 0 2 7 8 5.1 0.91 resources
13 0 3 7 4 4.4 0.90 for education
14 1 3 6 5 5.6 0.92 LIKE = Attitude Toward Teachers
15 1 3 4 4 6.1 0.95 1 = does not like teachers
16 0 2 4 5 5.7 0.94 10 = likes teachers a lot
17 0 3 7 5 5.1 0.96 STDY = Study time
18 0 3 3 10 6.2 0.98 hours per week
19 1 1 21 3 2.9 0.50 GPA = Average Grades
20 1 4 21 8 4.5 0.50 as percentage
21 0 4 2 10 4.1 0.99
22 0 4 1 10 2.2 1.00
2.1 Analyze the relation between GNDR and LIKE using Chi-square.

A. Construct a 2x2 table for these data using "female" and "male' as the categories on GNDR, and "dislike" and "like" as the categories on LIKE (by collapsing 1-5 into "dislike" and 6-10 in "like"). Include the marginals in your table.

B. Is there a statistically significant relation between gender and attitude toward teachers? Explain and justify your answer.

C. Compute the column percents for the table in order to determine the pattern of this relation. Explain your analysis in natural language for a non-technical audience.

2.2 Analyze the relation between TRAK and STDY.

A. Construct a table for these data using the existing categories on TRAK, and collapsing the continuous values of STDY into four categories (<2.0, 2.0-3.9, 4.0-5.9, and >5.9). Include the marginals in your table.

B. Calculate the percentages for the table so that they illustrate the effects of TRAK on STDY.

C. Is there an association? What are the strength and direction of the relation?

2.3 A. Calculate phi for the data in the table you constructed for 2.1.

B. Calculate lambda for the data in the table you constructed for 2.1.

C. Interpret phi and lambda. Explain how these statistics increase your understanding of these data.