Unit 6: Non-Parametric Models Student Capella Universi ✓ Solved

Nonparametric methods are known as distribution-free tests because they assumptions are typically not required about population distribution. Thus, nonparametric methods may be used when parametric assumptions are not satisfied where ranks of observations are used instead of the measurements themselves. However, caution is advised as this method may cause some loss of information. Nonparametric methods mainly test the pre-set hypothesis, such as whether two data differ. As a result, nonparametric methods usually don't provide any useful parameter estimates. This document presents four sections of calculations using nonparametric testing.

Section A

This section provides information about the study and the tests to be conducted specifically including: the research question, the null and the alternative hypotheses; the levels of measurement used and the significance level; the selection process using the Decision Tree. For the dataset, the nominal variable is music, while offer is scale, with a Confidence Level =95% and Significance = .074. The research question explored was: Was there a significant difference between offers made while listening to Bon Scott compared to those listening to Brian Johnson? The null hypothesis states that the distribution of offers made in dollars is the same across categories of background music, while the alternative hypothesis states that the distribution of offers made in dollars is not the same across categories of background music.

Statistical analysis revealed that offers made by people listening to Bon Scott, with a median=30, were not significantly different from offers by people listening to Brian Johnson, with a median U = 218.50, z = 1.85, p = .074, r = .31.

Section B

When conducting a test, it is imperative to identify and address outliers. Using a box plot to remove them is an accepted method for further analysis. Thus, the variables could be recoded and re-plotted without the outlying values. Initial investigations revealed three outliers in scores for Brian Scott, while one was found for Brian Johnson.

Tests of normality indicated that the distribution in question was significantly different from a normal distribution. Specifically, the K-S tests for normality indicated significant deviations. Overall, the results suggested that the data are not normally distributed for all groups, leading to the rejection of the null hypothesis in favor of the alternative.

Section C

Following the nonparametric models that require no assumptions about the data, this section included relevant graphs for analysis, testing the null hypothesis, and interpreting results. Utilizing the dataset, the distribution was significantly non-normal with a confidence interval of 95%. Given these findings, the null hypothesis was retained, indicating that the distribution of offers is the same for both Bon Scott and Brian Johnson.

Section D

Statistical power is an essential parameter in detecting effects, highlighted in G*Power analysis, which illustrated that a total sample size of 162 was necessary for adequate power. The findings pointed out limitations due to the relatively small current sample size of 36.

Conclusively, the assumption of homogeneity has been met, and the analysis has substantiated the null hypothesis. With the G*Power result showing a 95% probability of detecting an effect, researchers are encouraged to ensure adequate sample sizes and conduct further tests where necessary to uphold the reliability of results.

Conclusion

This document was structured into four sections focusing on the Mann-Whitney test and its application. It included detailed hypotheses, measurement levels, decision trees, and assumptions related to nonparametric testing, ultimately demonstrating that significant differences between listener offers were not found.

References

• Cumming, G. (2014). The New Statistics: Why and How. Psychological Science, 25(1).
• Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics (4th ed.). SAGE Publications.
• Faul, F., Erdfelder, E., Buchner, A., & Lang, A-G. (2009). Statistical Power Analyses Using G*Power 3.1: Tests for Correlation and Regression Analyses. Behavior Research Methods, 41(4), 1149–1160.
• Oxoby, G. (2008). Offers Dataset.
• Saha, A., & Jones, S. (2016). Power Analysis for Nonparametric Tests. Statistical Procedures for Research Data.