# Nonparametric Test

Essay by 24 • January 20, 2011 • 1,438 Words (6 Pages) • 1,330 Views

**Page 1 of 6**

Nonparametric Test

Education is even more important than ever today for anyone interested in entering the world of employment with either large international corporations, or even local vendors serving the community within the area where one lives. In an ongoing effort by our research team to determine if the difference in the wages from our sample population of men and women, who have various levels of education, does in fact make the difference. We are looking to use an additional test to discover whether or not we can inconclusively state that from our previous test conclusion that our team believes that there is a difference in the wages of the sample population.

In our investigation, the team will hope to convince the audience of the hypothesis chosen by the team through introducing our statement regarding the research issue, performing the five step hypothesis testing procedure on the data, explain the nonparametric test the team chose to analyze the data and why we chose this particular test. We will then interpret the results of the test; explain the differences that were observed from the teams week three paper. We have also included the raw data tables and results of this weeks test in Appendix A-D. The key is using the right data at the beginning to make the difference in how the test results will turn out.

Data

The data chosen by the team used in this research paper is the same as what was used for the previous two or more sample hypothesis running the One Factor ANOVA test (Doane & Seward, 2007), called Wages and Wage Earners Data Set. To help the team determine the significance between wages earned by men and women of different educational levels, the team needed to convert the data from the tabular format as seen in Appendix A, to a layout of merged data that would assist the team in setting up the nonparametric test as shown in Appendix B. Because the test chosen uses the sum of the rank and the sample size to compare the independent data groups, the team had to format the data into a worksheet of sum ranks as seen in Appendix C. Finally, it was considered necessary of the team to setup the data to be able to run the nonparametric test that we chose for this paper.

Formulate the Hypothesis

For this weekÐ²Ð‚™s research paper, the team chose to use the population median as part of our hypothesis statement. The reason for this is that the type of nonparametric test selected by the team deals with rank instead of a precise statistical assessment. The research question still remains the same as it did last week; is there a significant difference in the position of the executive management team seeking to hire new employees, as to whether or not the amount of years spent in school and the sexual characteristics of the that applicant has an affect on the wages earned by that group. Looking at the median of the data in the five different groups in our study it still consistently shows a recognizable distinction. The only way to determine whether the group medians are the same in our original study is by running the nonparametric test chosen by the team, which is the Kruskal-Wallis test.

Perform the Hypothesis Test

In doing our research, the team remembers the importance of performing the five-step hypothesis test on the data. In doing so, we can be assured that our test is not biased and that the results will overwhelmingly state our stance for the hypothesis we have chosen. Again, stating the hypothesis that H0: all c population medians are the same and H1: not all the population medians are the same will lead us to our next step of choosing a significant level. Because we used the Ð¿‚µ = .05 in the previous One Factor ANOVA test, we will use the same in this test to ensure that there is no partiality in our research.

The next step in the hypothesis test is to state the decision rule, which was determined by using the degree of freedom for the columns of our five different groups. The team used the tabular data from table 1 in the Appendix of this paper and Appendix E of Doane & Seward to determine that ÐžÐ... = c Ð²?' 1 = 5 Ð²Ð‚" 1 = 4, and at Ð¿‚µ = .05 which results in the team rejecting H0 if the Doane & Seward Chi-square Appendix E value was higher than 9.488 (2007). After that, the team had to calculate the test statistic by using the Appendix B worksheet rank sum sample size and rank sum from each group. The following formula gives the results of that worksheet

Our team then made our decision that because the test statistic of 18.51 is far greater then that of the Chi-square value at v = 4, Ð¿‚µ = .05 in Appendix E, we must reject the null hypothesis that all c populations are the same (2007). These results can be viewed in Appendix D, where at the significance level of .05, it shows the Chi-square of 25.75, which is still far above the level for the team to reject the null hypothesis that all c population

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