# Nonparametric Statistics And Correlation

### Assessment Instructions

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

Question | Concept |
---|---|

Question 1 | SPSS: One-Variable Chi Square |

Question 2 | SPSS: One-Variable Chi Square |

Question 3 | Chi-Square as a Test of Independence |

Question 4 | SPSS: Two-Variable Chi-Square |

Question 5 | Measures of Effect Size |

Question 6 | Power and the Factors Affecting It |

Question 7 | Power and the Factors Affecting It |

Question 8 | Correlational Studies |

Question 9 | Correlation: Relationship Direction |

Question 10 | SPSS: Scatterplot |

Question 11 | SPSS: Pearson r |

Question 12 | SPSS: Pearson r |

#### Question 1

Complete the following steps:

- Open the SPSS file assessment5a.sav linked in the Resources under the Required Resources heading.
- At the top of the screen, click on Data, then select Weight Cases.
- 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.
- On the toolbar, click Analyze, then Nonparametric Tests, then Legacy Dialogs, the Chi Square.
- Click on Favorite Color, then click on the arrow to send to the Test Variable List window.
- Under Expected Values, select Value, then enter the following four values in order: 43, 58, 253, 414.
- 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.

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Complete the following:

- Identify the null hypothesis.
- What are the degrees of freedom (
*df*)? - Complete the table (complete in SPSS and paste the output into your Word document):

Question 2 Men Women Number Observed Number Expected Number Observed Number Expected - Calculate χ² in SPSS and paste the output into your Word document.
- 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:

- Open the SPSS file assessment5b.sav linked in the Resources under the Required Resources heading.
- At the top of the screen, click on Data, then select Weight Cases.
- 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.
- On the toolbar, click Analyze, then Descriptive Statistics, then Crosstabs.
- Click on Team Placement, then click on the arrow to send to the Rows window.
- Click on Gender, then click on the arrow to send to the Columns window.
- Click on the Statistics button, then check the box for Chi-Square. Click Continue.
- Click on the Cells button, then check the box for Expected. Click Continue.
- Click OK, and copy and paste the output to your Word document.
- 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).

- Calculate effect size using Cohen’s d and effect size
*r*. - 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:

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

#### Question 11

Complete the following:

- Open the SPSS file assessment5c.sav.
- At the top of the screen, click on Analyze, then select Correlation, then Bivariate.
- Click on Exam 1 (X), then click on the arrow to send it over to the Variables box.
- Click on Exam 2 (Y), then click on the arrow to send it over to the Variables box.
- 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:

- Create a scatterplot. Copy and paste the scatterplot output to your Word document.
- Based on the scatterplot, what is the expected strength and direction of the correlation?
- Identify the null hypothesis.
- Calculate Pearson r. Copy and paste the correlation output to your Word document.
- 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?
- 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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