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# Descriptive Statistics For Nonparametric Model

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## Question:

State a hypothesis.

List and explain the variables you would collect in this study. There must be a minimum of three variables and two must meet the assumptions for a correlational analysis.

Create a fictitious data set that you will analyze. The data should have a minimum of 30 cases, but not more than 50 cases.

Conduct a descriptive data analysis that includes the following:

a measure of central tendency

a measure of dispersion

at least one graph

Briefly interpret the descriptive data analysis.

Conduct the appropriate statistical test that will answer your hypothesis. It must be a statistical test covered in this course such as regression analysis, single t-test, independent t-test, cross-tabulations, Chi-square, or One-Way ANOVA. Explain your justification for using the test based on the type of data and the level of measurement that the data lends to for the statistical analysis.

### Introduction

Every college have their college placement tests, which helps the students of that college to find their job after completing their college education. Various such tests take place in the colleges of the United States of America. Students had been attending these tests over the years and eventually they are placed from their college (McMillan & Schumacher, 2012). With time, some of these students change their jobs while some stick to the jobs they got from their college placement.

Within a span of ten years, the income of these students’ changes from the income they had during their time of joining the job (Bickel & Lehmann, 2012). In this assignment, the dependency of the income of these students on the scores of their college placement test would be analysed. Data would be collected for this analysis and these collected data would be analysed using various statistical tools. Interpretation of these analyses would the result of the desired hypothesis. Graphs and charts would accompany these analyses in order to give a better interpretation of the collected data.

### Discussion

#### Data collection

Data had been collected by the methods of survey. The ex-students of the colleges of the United States of America were selected for the survey of this report. The students who had been working for at least ten years had been selected as the category of this assignment. Thirty such ex-students had been randomly selected from the chosen category of samples. These thirty ex-students of the United States of America were asked about their scores at their college placement tests, their income during the first job and their income ten years after the college placement tests. Quantitative data had been collected from the survey (McMillan & Schumacher, 2012). Thus, primary research was used to collect the data for this assignment. Both male and female ex-students of the United States of America participated in the survey.

### Hypothesis

The hypothesis of this survey is given below.

H0 : scores of the students in their college placement test do not affect their income after ten years of college

H1: scores of the students in their college placement test affect their income after ten years of college

### Analysis and interpretation

On analysing the collected data for the survey, it was seen that among the thirty samples of the survey, 19 respondents were male and 11 respondents were female. The responses of these respondents showed that the average score of the standardized college placement test out of 100 was 83.06 (Bickel & Lehmann, 2012). This shows that the average scores of the ex-students were above average. The standard deviation of the score of the standardized college placement test out of 100 was found to be 9.013. The variance of the scores of the tests was found to be 81.2368. This shows that the scores of the test varied widely among the students. The range of the scores of the tests was found to be 40. It can be interpreted that there was huge variation among the scores of the students. The maximum score of the test was found to be 99 and the minimum score was found to be 59. The mode of the score was found to be 90 (Kock, 2013). It can be interpreted that many students scored 90 in their college placement test out of 100.

Figure 1: Graph of scores on a standardized college placement test (out of 100)

(Source: created by author)

On analysing the data of the variable, “level of income immediately after college placement (per year in \$)”, it was seen that the average level of income for the students was \$928.67. It can be interpreted that the average income level of the students just after completing their college was good. The standard deviation of this variable was found to be 235.0309 and the variance was 55239.5403 (McEwen & Dean, 2015). This shows that there was huge variation among the income of the students. The range of the level of income for the selected samples was found to be \$1100. The maximum income by any student of the sample was \$1500 and the minimum income of a student of the sample was \$400 (Samuels et al., 2012). This shows a high variability among the income level of the samples. It can be interpreted that the students who gave the college placement test, were placed in different companies that had different pay scale from each other. It can be possible that the students were placed according to their scores in the college placement test and they got their companies and pay scale according to this test. The mode of “level of income immediately after college placement (per year in \$)” was found to be \$800 (Weiss & Weiss, 2012). This shows that the income of most of the students after their placement was \$800.

Figure 2: Graph of level of income immediately after college placement (per year in \$)

(Source: created by author)

The data given by the ex-students of the colleges of the United States of America shows the “level of income a person makes 10 years after college (per year in \$)”. The data shows that the average value of “level of income a person makes 10 years after college (per year in \$)” is \$ 87133.33 (Qiao et al., 2015). This shows that there is a high level of income among the ex-students of the colleges of the United States of America. The standard deviation of the “level of income a person makes 10 years after college (per year in \$)” was found to be 23105.057 and the variance was found to be 533843678.2 (Kleinbaum et al., 2013). This shows that there was huge variability among the income of the ex-students of the colleges of the United States of America. There is a huge difference among the salary of the ex-students after ten years of their college placement. The highest salary of the ex-students after ten years of their college life is \$ 150000 and the lowest salary of the ex-students after ten years of their college life is \$ 30000 (Cameron & Trivedi, 2013). The range of the salary is \$ 120000. This suggests that there was huge difference in the salaries of the ex-students after ten years of their college placement. However, this does not show that this difference in the income of the students after ten years of their college placement test. The mode of the “level of income a person makes 10 years after college (per year in \$)” was \$ 80000 (Draper & Smith, 2014). This shows that most of the ex-students of the colleges of the United States of America had their salary as \$ 80000 after ten years of their college placement examination.

Figure 3: Graph of level of income a person makes 10 years after college (per year in \$)

(Source: created by author)

Regression analysis was done for the dependent variable, “level of income a person makes 10 years after college (per year in \$)”. The independent variables for this regression analysis are “scores on a standardized college placement test (out of 100)” and “level of income immediately after college placement (per year in \$)” (Montgomery et al., 2015). On performing the regression analysis, the value of R square was found to be 0.64 (Chatterjee & Hadi, 2015). This shows that the data is moderately fitted in the regression line. It also suggests that the variability of the data is 68% around its mean.

The value of the f-statistic is 24.30419 and the value of “Significance F” is 9.17732E-07. Considering the “level of significance” as 0.05, is was seen that the p-value of the regression is less than 0.05 (Fox, 2015). This leads to the rejection of “null hypothesis”. It can be stated that the scores of the students in their college placement test affect their income after ten years of college. It can be interpreted that the students who got their jobs from the college placement might not have changed their jobs over the years. They had stuck to the job, which had influenced their salary in a negative way. It can also be interpreted that the merits of the students who had scored less marks in their college placement examination were less than those who have scored higher marks in the examination. Thus, it is seen that the income of the students was affected by the marks of the college placement examination.

## Conclusion

The effect of the marks secured any student in the college placement examination on the income level of those students after ten years of their college life was analysed in this assignment. Data was collected by primary survey method. The quantitative data collected for the research was analysed and interpreted to draw a conclusion of the hypothesis test. Statistical methods of descriptive statistics and regression analysis were performed on the collected data set. It was seen that both male and female employees participated in this survey. The survey result shows that the average score of the college placement examination was above average for the selected samples. The income of the selected samples just after the completion of their college was found to be good as a fresher. As the years passed by, after ten years of their college placement examination, it was seen that the salary level of the respondents was good. However, regression analysis suggested rejection of “null hypothesis” and it was seen that the marks in the examination of placement at their college had affected their income ten years hence. It could be concluded that the types of jobs the respondents got due to their college placement examination had influenced their jobs in the near future. This might have affected their income level ten years after the college placement examination.

## References

Bickel, P. J., & Lehmann, E. L. (2012). Descriptive statistics for nonparametric models IV. Spread. In Selected Works of EL Lehmann (pp. 519-526). Springer US.

Cameron, A. C., & Trivedi, P. K. (2013). Regression analysis of count data(Vol. 53). Cambridge university press.

Chatterjee, S., & Hadi, A. S. (2015). Regression analysis by example. John Wiley & Sons.

Draper, N. R., & Smith, H. (2014). Applied regression analysis. John Wiley & Sons.

Fox, J. (2015). Applied regression analysis and generalized linear models. Sage Publications.

Kleinbaum, D. G., Kupper, L. L., Nizam, A., & Rosenberg, E. S. (2013).Applied regression analysis and other multivariable methods. Nelson Education.

Kock, N. (2013). Using WarpPLS in E-Collaboration Studies: Descriptive Statistics, Settings. Interdisciplinary Applications of Electronic Collaboration Approaches and Technologies, 62.

McEwen, W., & Dean, I. E. (2015). Riverside City College Descriptive Statistics for Math Placement and Math Success 2014-2015.

McMillan, J. H., & Schumacher, S. (2014). Research in education: Evidence-based inquiry. Pearson Higher Ed.

Montgomery, D. C., Peck, E. A., & Vining, G. G. (2015). Introduction to linear regression analysis. John Wiley & Sons.

Qiao, Y., Liu, L., Zhang, Y., Anwar, Z., Mirbagheri, S., Xie, Y. Y., ... & Suri, F. (2015). Abstract T P108: MRI measurements of intracranial atherosclerosis in the ARIC neurocognitive study: methods, reliability and descriptive statistics. Stroke, 46(Suppl 1), ATP108-ATP108.

Samuels, M. L., Witmer, J. A., & Schaffner, A. (2012). Statistics for the life sciences. Pearson education.

Seber, G. A., & Lee, A. J. (2012). Linear regression analysis (Vol. 936). John Wiley & Sons.

Weiss, N. A., & Weiss, C. A. (2012). Introductory statistics. London: Pearson Education.

### Cite This Work

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