Nonparametric Statistics and Correlation

Assessment Instructions

Answer the questions below, following the Submission Requirements as specified at the end of the assessment.

Assessment ConceptsQuestionConceptQuestion 1SPSS: One-Variable Chi SquareQuestion 2SPSS: One-Variable Chi SquareQuestion 3Chi-Square as a Test of IndependenceQuestion 4SPSS: Two-Variable Chi-SquareQuestion 5Measures of Effect SizeQuestion 6Power and the Factors Affecting ItQuestion 7Power and the Factors Affecting ItQuestion 8Correlational StudiesQuestion 9Correlation: Relationship DirectionQuestion 10SPSS: ScatterplotQuestion 11SPSS: Pearson rQuestion 12SPSS: Pearson r

Question 1

Complete the following steps:

1. Open the SPSS file assessment5a.sav linked in the Resources under the Required Resources heading.
2. At the top of the screen, click on Data, then select Weight Cases.
3. Click on Weight Cases By, click on Count, then click on the arrow next to Frequency Variable to send it over to the Test Variable box.
4. On the toolbar, click Analyze, then Nonparametric Tests, then Legacy Dialogs, the Chi Square.
5. Click on Favorite Color, then click on the arrow to send to the Test Variable List window.
6. Under Expected Values, select Value, then enter the following four values in order: 43, 58, 253, 414.
7. Click OK and copy and paste the output to your Word document.

Question 2

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. The principal would like to know if the gender ratio in first grade reflects the gender ratio across the school.

Complete the following:

1. Identify the null hypothesis.
2. What are the degrees of freedom (df)?
3. Complete the table (complete in SPSS and paste the output into your Word document):Question 2MenWomenNumber ObservedNumber ExpectedNumber ObservedNumber Expected    
4. Calculate χ² in SPSS and paste the output into your Word document.
5. Can you reject the null hypothesis at α = .05?

Question 3

You recently read a magazine article stating that professionals who attended college online tend to earn higher salaries than professionals who attended brick-and-mortar universities. Identify this study’s two variables.

Question 4

Complete the following steps:

1. Open the SPSS file assessment5b.sav linked in the Resources under the Required Resources heading.
2. At the top of the screen, click on Data, then select Weight Cases.
3. Click on Weight Cases By, click on Count, then click on the arrow next to Frequency Variable to send it over to the Test Variable box.
4. On the toolbar, click Analyze, then Descriptive Statistics, then Crosstabs.
5. Click on Team Placement, then click on the arrow to send to the Rows window.
6. Click on Gender, then click on the arrow to send to the Columns window.
7. Click on the Statistics button, then check the box for Chi-Square. Click Continue.
8. Click on the Cells button, then check the box for Expected. Click Continue.
9. Click OK, and copy and paste the output to your Word document.
10. Highlight the chi-square and significance values in the output. Write the chi-square results as you might see them in a journal.

Question 5

Group A (n = 12) has a mean score of 7.42. Group B (n = 12) has a mean score of 6.00. Standard deviation for scores across all participants is 1.369. Group A’s mean is significantly higher than Group B’s mean ( t = 2.84, α < .01).

1. Calculate effect size using Cohen’s d and effect size r.
2. Based on the effect size, it there a practical difference between Groups A and B?

Question 6

Assume Cohen’s d to be approximately .40. If conducting an independent samples t test (two-tail, α= .05), how many participants will you need in each group to achieve 90 percent (.90) power?

Question 7

Assume effect size η to be approximately .29. If conducting a one-way ANOVA (three groups, α = .05), how many participants will you need in each group to achieve 80 percent (.80) power.

Question 8

Which of the following scenarios might be analyzed using a correlation?

• The effectiveness of training A versus training B in raising skill level.
• Minutes spent exercising per week and physical fitness level.
• Income level and the number of visits to a financial planner.
• Beer brand preference among college students.

Question 9

Indicate if you expect the relationship between the following variables to be negative (-), positive (+), or zero (0):

• Size of yard and size of landscaping bill.
• Years of education and income level.
• Hours of TV watched per week and physical fitness level.
• Number of siblings and number of pets.
• Hours spent studying and exam scores.

Question 10

Complete the following steps:

1. Open the SPSS file assessment5c.sav linked in the Resources under the Required Resources heading.
2. At the top of the screen, click on Graphs, then select Legacy Dialogs, then Scatter/Dot.
3. Click on Simple Scatter, and select Define.
4. Click on Exam 1 (X), then click on the arrow next to X Axis to send it over to the X Axis box.
5. Click on Exam 2 (Y), then click on the arrow next to Y Axis to send it over to the Y Axis box.
6. Click OK, then copy and paste the scatterplot output to your Word document.

Question 11

Complete the following:

1. Open the SPSS file assessment5c.sav.
2. At the top of the screen, click on Analyze, then select Correlation, then Bivariate.
3. Click on Exam 1 (X), then click on the arrow to send it over to the Variables box.
4. Click on Exam 2 (Y), then click on the arrow to send it over to the Variables box.
5. Click OK, then copy and paste the correlation output to your Word document.

Question 12

Complete the following steps after opening the SPSS file assessment5d.sav linked in the Resources under the Required Resources heading:

1. Create a scatterplot. Copy and paste the scatterplot output to your Word document.
2. Based on the scatterplot, what is the expected strength and direction of the correlation?
3. Identify the null hypothesis.
4. Calculate Pearson r. Copy and paste the correlation output to your Word document.
5. 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?
6. Report the results as you might see them in a journal.

Submission Requirements

• Submit all answers in one Word document (do not submit multiple files).
• Show your work for questions that require calculations.
• Ensure your answer to each problem is clearly visible (you may want to highlight your answer, or use a different font color, to set it apart).

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