# Nonparametric Analysis

**PSY 520: Module Nine Problem Set**

**Nonparametric Analysis**

Use the data set in the Problem Set Data document.

1. First we are going to see if males and females differ in their choice of college major. Since both variables are measured on a categorical scale, we have to use a chi-square test to address this question. You can learn about chi-squares on pp. 735-46 of the textbook.

Using *college major* and *sex* as your variables, perform a chi-square analysis. To do this, go to Analyze—Descriptive Statistics—Crosstabs. Enter Gender in the box labeled “Row(s)” and Major in the box labeled “Column(s).” Click on Statistics, and then on Chi-Square. Click “Continue,” then hit “OK” to run the analysis.

Paste the tables labeled “Gender*Major Crosstabulation” and “Chi-Square Tests” here. *(5 points)*

Gender * Major Crosstabulation |
|||||||

Count | |||||||

Major | Total | ||||||

1 | 2 | 3 | 4 | 5 | |||

Gender | 1 | 19 | 11 | 11 | 12 | 4 | 57 |

2 | 10 | 14 | 10 | 3 | 6 | 43 | |

Total | 29 | 25 | 21 | 15 | 10 | 100 |

Chi-Square Tests |
|||

Value | df | Asymp. Sig. (2-sided) | |

Pearson Chi-Square | 7.181a | 4 | .127 |

Likelihood Ratio | 7.467 | 4 | .113 |

Linear-by-Linear Association | .063 | 1 | .802 |

N of Valid Cases | 100 | ||

a. 1 cells (10.0%) have expected count less than 5. The minimum expected count is 4.30. |

The results of the chi-square analysis will be listed in the row labeled “Pearson chi-square” in the “Chi-Square Tests” table. Explain your results using APA formatting. See section 18.5.7 on p. 746 of the SPSS book for how to do this *(10 points: 2 points for type of test, 1 point for df, 2 points for the correct chi-square value, 1 point for the correct p value, and 4 points for correctly interpreting the results of the test.)*

2. Next, we are going to compare coffee drinkers and non-coffee drinkers on the amount of coffee they consume. The grouping variable is labeled *Coffee* (1 = coffee drinker, 2 = non-coffee drinker), and the outcome variable is labeled *Num_cups*.

a) First state the name of the parametric test that would typically be used to compare the results of two groups. *(1 point)*

b) Then look at the distribution of the data to determine if the assumptions of this test are met. An easy way to do this would be to go to Analyze—Descriptive Statistics—Frequencies. Enter the outcome variable (*Num_cups*) in the “Variable(s)” box. Then click on Charts and then on Histograms. Click Continue, then OK to run the analysis. Paste the histogram here *(2 points)*

c) After taking a look at the distribution of the data, state why these data violate a key assumption of parametric tests. *(2 points)*.

d) Find the medians of the 2 groups. One way to do this is to go to Analyze-Descriptive Statistics–Explore. Enter *Coffee* under Factor List and *Num_cups* under Dependent List. Click OK to run the analysis. List the medians of the coffee and non-coffee groups here. *(2 points)*

e) Now conduct a Mann-Whitney U test to see if the two groups differ in the amount of coffee consumed. You can learn more about the Mann-Whitney U test on pp. 217-228 of the SPSS book.

To conduct the test, go to Analyze—Nonparametric Tests—Independent Samples. Under the Objective tab, click on “Customize Analysis.” Under the Fields tab, drag Coffee to the box labeled Groups and Num_cups to the box labeled Test Fields. Under the Settings tab, click on Customize Tests, then on Mann-Whitney U (2 samples).

Click Run to run the analysis. Paste here the table labeled “Hypothesis Test Summary.” *(2 points)*

f) Explain your results using APA formatting. See section 6.4.6 in the SPSS book for an example, but don’t worry about effect sizes (r).

To write up the results, you’ll need to double click on the Hypothesis Test Summary table to see the value of the Mann-Whitney U statistic and the Standardized Test Statistic (z), but you don’t need to paste these detailed results here.

If the groups differed, please don’t just state that they differed significantly; instead, explain which group drank significantly more coffee than which other groups

*(6 points: 1 point for correctly stating the name of the test, 1 point for including the medians, 1 point for the correct value of the Mann-Whitney U statistic, 1 point for the correct value of the z statistic, 1 point for the correct p value, and 1 point for correctly interpreting the result).*