**u05a1** **–** **Nonparametric Statistics** **and** **Correlation**

Complete the following problems within this Word document (do not submit other files). Show your work for problem sets that require calculations. Ensure that your answer to each problem is clearly visible. (You may want to highlight your answer or use a different type of color to set it apart.)

**Problem** **Set 5.1**: **One-Variable Chi-Square** **in** **SPSS** **(1)**

• **Criterion**: Calculate a chi-square analysis in SPSS.• **Data**: Tandy’s Ice Cream shop serves chocolate, vanilla, and strawberry ice creams. Tandy wants to examine planning 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, her sales increased and she purchased 125 cases of chocolate, 80 cases of vanilla, and 35 cases of strawberry. • **Instruction**: Complete the following steps:a. Open SPSS and create a **New DataSet**.b. Go to the **Variable View** tab and enter Flavor in row 1and Frequency in the row 2. 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**.c. 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.d. In the Toolbar, click **Data**, and then select **Weight Cases.**e. Click **Weight Cases By**, click **Frequency**, and then click **Arrow** to send it over to the **Frequency Variable**box. Click **OK**.f. In the Toolbar, click **Analyze**, then **Nonparametric Tests**, then **Legacy Dialogs**, and then **Chi-Square**.g. Click **Flavor** and then click **Arrow** to send to the **Test Variable List** window.h. Under **Expected Values**, select **Value**, and then enter the following three values in the given order: 100, 75, 25.i. Click **OK** and copy and paste the output to your Word document.j. Answer this: Was Tandy’s distribution of proportions the same as expected?

**Problem** **Set 5.2**: **One-Variable Chi-Square** **in** **SPSS** **(2)**

• **Criterion**: Perform 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*)?

*(Assessment* *continues on next page.)*

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

**Men**

**Women**

**No. Observed**

**No. Expected**

**No. Observed**

**No. Expected**

d. Calculate *χ*² in SPSS and paste the output below.

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

**Problem** **Set 5.3**: **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 5.4**: **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 this data? Explain.

**Problem** **Set 5.5**: **Correlational Studies**

• **Criterion**: Determine if a correlation is the appropriate analysis for a study.• **Instruction**: Answer this: Which of the following scenarios might be analyzed using a correlation?

a. The effectiveness of training A versus training B in raising skill level.

b. Minutes spent exercising per week and physical fitness score.

c. Income level and number of visits to a financial planner.

d. Beer brand preference among college students.

**Problem** **Set 5.6**: **Correlation: Relationship Direction**

• **Criterion**: Differentiate between positive, negative, and neutral relationships among variables.• **Instruction**: For each of the following, answer this: Do you expect the relationships between the variables to be negative (-), positive (+), or zero (0):

a. Size of yard and size of landscaping bill.

b. Years of education and income level.

c. Hours of TV watched per week and physical fitness level.

d. Number of siblings and number of pets.

e. Hours spent studying and exam scores.

*(Assessment* *continues on next page.)*

**Problem** **Set 5.7**: **Scatterplot** **in** **SPSS**

• **Criterion**: Create a scatterplot using SPSS.• **Data**: Dr T wanted to see if mindfulness training is related to stress levels. He recruited 10 participants to undergo mindfulness training and examined their reported stress levels on the DRT Stress Inventory. These were his results:

**Minutes of Mindfulness Training**

**DRT Stress InventoryScore**

61

8

122

6

201

3

33

9

55

7

329

1

10

9

1

10

93

7

144

5

• **Instruction**: Complete the following steps:a. Open SPSS and create a **New** **DataSet**.b. Click the **Variable View** tab and enter Mindfulness in row 1 and **Stress** in row 2.c. Click the **Data View** tab and enter the data.d. In the Toolbar, click **Graphs**, then select **Legacy Dialogs**, and then **Scatter** or **Dot.**e. Click **Simple Scatter** and select **Define.**f. Click **Mindfulness (X)** and then click **Arrow** to send it over to the **X-Axis** box.g. Click **Stress (Y)** and then click **Arrow** to send it over to the **Y-Axis** box.h. Click **OK** and copy and paste the scatterplot output below.i. Answer this: Based on the scatterplot, what is the expected strength and direction of the correlation?

*(Assessment* *continues on next page.)*

**Problem** **Set 5.8**: **Pearson** **r****in** **SPSS** **(1)**

• **Criterion**: Calculate a Pearson *r* using SPSS.• **Data**: Use the same data set from Problem Set 5.7 in SPSS.• **Instruction**: Complete the following steps:a. In the Toolbar, click **Analyze**, then select **Correlation**, andthen select **Bivariate**.b. Click **Mindfulness** and then click **Arrow** to send it over to the **Variables** box.c. Click **Stress** and then click **Arrow** to send it over to the **Variables** box.d. Click **OK** and copy and paste the correlation output into thisWord document below.

**Problem** **Set 5.9**: **Pearson** **r****in** **SPSS** **(2)**

• **Criterion**: Complete hypothesis testing and interpret correlational data.• **Data**: Use the same data set from Problem Set 5.7.• **Instruction**: Complete the following:

a.Identify the null hypothesis.

b.Answer this: Based on the correlation output (two-tailed test), can the null hypothesis be rejected? If the null can be rejected, how confident can you be that the results are not due to chance?

c.Report the results as you might see them in a journal (i.e., in APA Style).

**Problem** **Set 5.10**

• **Criterion**: Apply results of a Pearson *r* to a real-world scenario.• **Data**: Consider the results of Dr T’s Mindfulness study from Problem Set 5.3 and Problem Set 5.5.• **Instruction**: **Answer the following:**o If you worked in a stress reduction clinic, what conclusions might you share with your clients about the effects of mindfulness training on stress levels?o What conclusions might you share with other clinicians or researchers at the clinic?

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