Activity 9: Non-Parametric Tests
4Non-Parametric Tests
While you have learned a number of parametric statistical techniques, you are also aware that if the assumptions related to the tests are violated, then the tests are not valid. Because many phenomenon examined in business are not normally distributed, it is critically important to understand the role of non-parametric tests. It is possible you will need to use one or more of the methods covered in this chapter in your dissertation.
NOTE: You may experience an error message when attempting to run the analysis using SPSS of the .sav file used in this assignment. The error message says:
If you experience this error, click on the data view tab of the opened .sav file, then click on the line separating the labels of the first and second column. Drag the width of the first column out approximately 25% from its initial width. Save the file. The analysis should now work as intended.
Read Chapter 15 in the text. It will be to your advantage to have SPSS open on your computer as you work through chapter 15. While you are reading consider your area of research interest and when you have seen non-parametric methods applied. How might you use these analytical strategies in your dissertation research?
Complete the Self-Tests within each chapter. Answers are available on the companion web site under the heading Additional.
Complete Smart Alex's Quizzes. Be sure to take Smart Alex's Quiz at the end of the Chapter and spend time learning the concepts related to questions you answered incorrectly.
Optional Preparation for Activity #9
After completing the above activities, if you feel you need additional instruction on the concepts covered, please choose from any of the following activities that will assist you in mastering the core concepts.
Activity 9
You will submit one Word document for this activity. In the first part your activity #9 document, provide short answers to the following questions (250 words or less).
Part A. Questions about non-parametric procedures
1. What are the most common reasons you would select a non-parametric test over the parametric alternative?
2. Discuss the issue of statistical power in non-parametric tests (as compared to their parametric counterparts). Which type tends to be more powerful? Why?
3. For each of the following parametric tests, identify the appropriate non-parametric counterpart:
a. Dependent t-test
b. Independent samples t-test
c. Repeated measures ANOVA (one-variable)
d. One-way ANOVA (independent)
e. Pearson Correlation
Part B. SPSS Activity
In this part of Activity #9, you will perform the non-parametric version of the tests you used in Activities 6, 7, and 8. In each case, assume that you opted to use the non-parametric equivalent rather than the parametric test. Using the data files from earlier activities, complete the following tests and paste your results into the assignment Word document:
1. Activity 6A: non-parametric version of the dependent t-test
2. Activity 6B: non-parametric version of the independent t-test
3. Activity 6C: non-parametric version of the single factor ANOVA
4. Activity 7: non-parametric version of the factorial ANOVA
Part C. Contingency tables
Sometimes a researcher is only interested in the following: Whether or not two variables are dependent on one another, (e.g. are death and smoking dependent variables; are SAT scores and high school grades independent variables?)
To test this type of claim a contingency table could be used, with the null hypothesis being that the variables are independent. Setting up a contingency table is easy; the rows are one variable the columns another. In contingency table analysis (also called two-way ANOVA) the researcher determines how closely the amount in each cell coincides with the expected value of each cell if the two variables were independent.
The following contingency table lists the response to a bill pertaining to gun control.
| |
In favor
|
Opposed
|
|
Northeast
|
10
|
30
|
|
Southeast
|
15
|
25
|
|
Northwest
|
35
|
10
|
|
Southwest
|
10
|
25
|
Notice that cell 1 indicates that 10 people in the Northeast were in favor of the bill.
Example: In the previous contingency table, 40 out of 160 (1/4) of those surveyed were from the Northeast. If the two variables were independent, you would expect 1/2 of that amount (20) to be in favor of the amendment since there were only two choices. We would be checking to see if the observed value of 10 was significantly different from the expected value of 20.
To determine how close the expected values are to the actual values, the test statistic chi-square is determined. Small values of chi-square support the claim of independence between the two variables. That is, chi-square will be small when observed and expected frequencies are close. Large values of chi-square would cause the null hypothesis to be rejected and reflect significant differences between observed and expected frequencies. This part of the activity is not included in the text book. See the tutorial Chi-square pdf file in the additional resources section of the course room for details on how to perform a chi-square test in SPSS.
For part C, examine the relationship between education (degree) and perception of life (life). Can you reject the null that education and perception of life are independent? Make a bar chart that graphically summarizes your findings. Be sure to include the relevant portions of the chi-square test output in your explanation.
Submit your files in the Course Work area below the Activity screen.
Learning Outcomes: 5, 6, 7, 9, 10, 11
- Apply appropriate statistical tests based on level of measurement.
- Calculate, interpret, and understand the appropriate use of inferential statistical analysis. Evaluate the results of the analysis.
- Demonstrate how population, sampling, and statistical power are related to inferential analysis.
- Evaluate the difference between parametric and non-parametric data analysis and how to apply the correct statistical procedure.
- Demonstrate proficiency in the use of SPSS.
- Demonstrate proficiency in reporting statistical output in APA format.