u09a1 – Nonparametric Statistics

Problem Set 9.1: One-Variable Chi-Square in SPSS (1)

• Criterion: Use SPSS for a chi-square analysis.
• Data: Tandy’s Ice Cream shop serves chocolate, vanilla, and strawberry ice creams. Tandy wants to plan for the future years. She knows that on average she expects to purchase 100 cases of chocolate, 75 cases of vanilla, and 25 cases of strawberry (4:3:1). This year, the ice cream sales increased and she purchased 125 cases of chocolate, 80 cases of vanilla, and 35 cases of strawberry.
• Instruction: Complete the following steps:

• Open SPSS and create a New DataSet.
• Go to the Variable View tab and type Flavor in the first row and Frequency in the second row. Adjust the decimal value to 0. Go to Values in the Flavor row and enter 1 for chocolate, 2 for vanilla, and 3 for strawberry and click OK.
• Go to the Data View tab and under the Flavor column, enter 1 in row 1, 2 in row 2, and 3 in row 3. Under the frequency column, enter 125 in row 1, 80 in row 2, and 35 in row 3.
• In the Toolbar, click Data, then select Weight Cases.
• Select Weight Cases By, select Frequency, and then click Arrow to send it over to the Frequency Variable box. Click OK.
• In the Toolbar, click Analyze, then Nonparametric Tests, then Legacy Dialogs, and then Chi-Square.
• Select Flavor and then click Arrow to send to the Test Variable List.
• Under Expected Values, select Values and then enter the following three values in the order: 100, 75, and 25.
• Click OK and copy and paste the output to the Word document.
• Answer this: Was Tandy’s distribution of proportions the same as expected?

(Assignment continues on next page.)

Problem Set 9.2: One-Variable Chi-Square in SPSS (2)

• Criterion: Calculate a chi-square analysis in SPSS and interpret the results.
• Data: There are 218 first graders in an elementary school. Of these first graders, 86 are boys and 132 are girls. School wide, there are 753 boys and 1063 girls.
• Instructions: The principal would like to know if the gender ratio in first grade reflects the gender ratio school wide. Complete the following:

a. Identify the hypothesis.

b. What are the degrees of freedom (df)?

c. Complete the table in SPSS and paste the output below to replace it:

d. Calculate χ² in SPSS and paste the output below.

e. Can you reject the null hypothesis at α = .05?Explain why or why not.

Problem Set 9.3: Identifying Variables

• Criterion: Identify variables for a study.
• Data: A magazine article states that professionals who attended college online tend to earn higher salaries than professionals who attended brick-and-mortar universities.
• Instruction: Identify the study’s two variables.

Problem Set 9.4: Alternative to Chi-Square as a Test of Independence

• Criterion: Identify an alternative to chi-square as a test of independence.
• Data: A chi-square test of independence could be used to examine the relationship between overhead light preference (on or off) and glasses use (wearing or not wearing).
• Instruction: Answer this: What other type of test could be used to measure the data? Explain.