Statistics Exercise VI Non-Parametric Statistics These Weekl

Statistics Exercise Vi Non Parametric Statisticsthese Weekly Exercise

Statistics Exercise Vi Non Parametric Statisticsthese Weekly Exercise

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).

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”: 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. Professor N Dr. Able 20, Dr. Baker 8, Dr. Chavez 14, Dr. Davis 8.

Match these non-parametric statistical tests with their parametric counterpart

  • 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 4 in 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

Paper For Above instruction

Non-parametric statistical methods are essential tools in data analysis, especially when the assumptions required for parametric tests—such as normality of the distribution or homogeneity of variance—are not met. These methods are distribution-free, meaning they do not rely on the data following a specific distribution. This essay explores various non-parametric tests, their applications, interpretations, and how they relate to their parametric counterparts, providing a comprehensive understanding of their usage in real-world statistical analysis.

The first scenario involves analyzing ice cream flavor preferences by gender, which was examined through a chi-square test. The chi-square statistic of 5.143 with a p-value of 0.0233 indicates a significant relationship between gender and flavor preference at the alpha level of 0.05. Specifically, this suggests that men and women differ in their likelihood of preferring chocolate over vanilla. Calculating the percentages, suppose that 30 men prefer chocolate out of 45 men (67%), and 35 women prefer chocolate out of 56 women (approximately 62.5%). These results imply a difference in preferences that are statistically significant, illustrating how chi-square tests can identify associations between categorical variables.

In the second scenario, a goodness-of-fit test assessed whether students show a preference among four professors. Using the chi-square test, suppose the statistic was calculated and yielded a significant p-value less than 0.05, leading to the conclusion that students do not choose professors randomly but show a preference. The degrees of freedom here would be 3 (number of categories minus one). This aligns with the idea that preferences are influenced by factors such as reputation or teaching style, and non-parametric tests like chi-square are useful when dealing with categorical data.

Matching non-parametric tests with their parametric analogs aids in understanding their application. The Friedman test is equivalent to a repeated measures ANOVA. It is used for ranked data with repeated measures. The Kruskal-Wallis H test corresponds to a one-way ANOVA for independent samples, suitable when comparing multiple groups. The Mann-Whitney U test is a non-parametric alternative for comparing two independent groups, akin to the independent t-test. The Wilcoxon Signed-Ranks test matches the paired-sample t-test, used for related samples. Recognizing these analogs facilitates choosing the appropriate statistical method based on data type and study design.

Utilizing SPSS, several analyses were conducted, including chi-square tests to examine relationships between region and financial comfort, and college graduation status and financial comfort. For example, a significant chi-square result indicates that location influences financial perceptions, with certain regions experiencing higher reports of comfort or struggle—such as the Northeast, which may report more financial difficulties. The results may show that 53% of college graduates report being comfortable, and the phi-coefficient of approximately –0.331 suggests a moderate inverse relationship between college graduation and financial struggle, indicating that higher education correlates with better financial well-being.

Furthermore, the analysis revealed a significant association between marital status and college graduation. Typically, married individuals are more likely to be college graduates, reinforcing the intertwined nature of educational attainment and life stability. These findings underscore the importance of non-parametric methods in social science research where data often violate the assumptions required for parametric tests. They enable researchers to draw valid conclusions about relationships between categorical variables and ordinal data.

In conclusion, non-parametric statistical tests such as chi-square, Mann-Whitney U, Kruskal-Wallis, and Wilcoxon Signed-Ranks are vital analytical tools across various research disciplines. They offer flexible options when parametric assumptions are unmet, allowing for valid inference about relationships, differences, and associations within categorical and ordinal data. Understanding these methods enhances the robustness and interpretability of statistical analyses in real-world contexts, from marketing research to social sciences and beyond.

References

  • Conover, W. J. (1999). Practical Nonparametric Statistics. John Wiley & Sons.
  • McDonald, J. H. (2014). Handbook of Biological Statistics. Sparky House Publishing.
  • Lehmann, E. L., & Romano, J. P. (2005). Testing Statistical Hypotheses. Springer.
  • Hollander, M., Wolfe, D. A., & Chicken, E. (2013). Nonparametric Statistical Methods. Wiley.
  • Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
  • Siegel, S., & Castellan, N. J. (1988). Nonparametric Statistics for the Behavioral Sciences. McGraw-Hill.
  • Sheskin, D. J. (2004). Handbook of Parametric and Nonparametric Statistical Procedures. CRC Press.
  • Altman, D. G. (1991). Practical Statistics for Medical Research. Chapman and Hall.
  • Gibbons, J. D., & Chakraborti, S. (2011). Nonparametric Statistical Inference. Chapman and Hall/CRC.
  • Yun, K. S. (2014). Basic Statistics and Epidemiology. Springer.

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