**Statistics Exercise VI: Non-parametric statistics**

**These weekly exercises provide the opportunity for you to understand and apply statistical methods and analysis. Unless otherwise stated, use 5% (.05) as your alpha level (cutoff for statistical significance).**

Ice Cream Flavor Preference by Gender

**MenWomen****Marginal Row Totals****Vanilla**151025**Chocolate**30535* Marginal Column Totals*451560 (Grand Total)

The chi-square statistic is 5.143. The

*p*-value is .0233. This result is significant at

*p*< .05.

**#1**. The chart above shows male and female preferences for vanilla vs. chocolate ice cream among men and women.

- What percent of men prefer chocolate over vanilla? ________
- What percent of women prefer chocolate over vanilla? ________
- Report the results of the statistical test in plain language:

**#2**. The calculator at this link will allow you to perform a one-way chi-square or “goodness of fit test”:

http://vassarstats.net/csfit.html

Fifty students can choose between four different professors to take Introductory Statistics. The number choosing each professor is shown below. Use the calculator above to test the null hypothesis that there is no preference for professors — that there is an equal chance of choosing each of them. Report your results including chi-square, degrees of freedom, p-value and your interpretation. Use an alpha level of .05. Be careful not to over interpret – state only what the test result tells you.ProfessorNDr. Able20Dr. Baker8Dr. Chavez14Dr. Davis8 **#3**. Match these non-parametric statistical tests with their parametric counterpart by putting the corresponding letter on the line.

_____ Friedman test

_____ Kruskal-Wallis H test

_____ Mann-Whitney U test

_____ Wilcoxon Signed-Ranks T test

A: Paired-sample t-test

B: Independent-sample t-test

C: One-way ANOVA, independent samples

D: One-way ANOVA, repeated measures

**Use SPSS and the data file found in syllabus resources (DATA540.SAV) to answer the following questions. Round your answers to the nearest dollar, percentage point, or whole number. **

**#4. ** Perform a chi-square test to look at the relationship between region of the country (REGION) and financial comfort (FCOMFORT). Using alpha = .05, what would you conclude from your test:

a. Financial comfort differs depending on the area one lives in.

b. People living in less expensive areas are more likely to report that they are financially comfortable.

c. There is not a significant relationship between region and financial comfort. d. People living in the northeast region are most likely to report that they are financially struggling.**Click TRANSFORM –> COMPUTE VARIABLE. Type COLLEGE in the “Target Variable” box and type****EDUC1 GE 4in the “Numeric Expression” box. Then click “OK.” This will create a new variable, COLLEGE, that is “1” for college graduates and “0” for those with less education.****#5. ** Perform a chi-square test to look at the relationship between college graduation (COLLEGE) and financial comfort (FCOMFORT). Notice how FCOMFORT is coded, 1=Comfortable, 2=Struggling. Using alpha = .05, what would you conclude from your test?

- College graduates are more likely to be financially comfortable than non-graduates
- College graduates are less likely to be financially comfortable than non-graduates
- There is not a significant difference between college graduates and non-graduates with regard to financial comfort
- Graduating college will generally increase your income

**#6**. Looking at the results of your chi-square test and the associated crosstabs table, what percentage of college graduates report that they are financially comfortable?

- 41%
- 47%
- 53%
- 59%

**#7**. What is the phi-coefficient for the relationship between college graduation and financial comfort?

- -.470
- -.331
- -.255
- -.118

**#8**. Now look at the relationship between marital status (MSTAT) and college graduation using a chi-square test. What would you conclude?

- Married people are more often college graduates than singles
- College graduates are more often married than non-graduates
- There is not a significant relationship between marital status and college graduation
- Both “a” and “b” are true