Discussion Question: Discuss The Differences Between Non-Par

Discussion Questiondiscuss The Differences Between Non Parametric And

Discuss the differences between non-parametric and parametric tests. Provide an example of each and discuss when it is appropriate to use the test. Next, discuss the assumptions that must be met by the investigator to run the test. Conclude with a brief discussion of your data analysis plan. Discuss the test you will use to address the study hypothesis and which measures of central tendency you will report for demographic variables.

Paper For Above instruction

Introduction

The selection of appropriate statistical tests is a fundamental step in research methodology, directly impacting the validity and reliability of study findings. Two broad categories of statistical tests are parametric and non-parametric tests, each with specific assumptions, applications, and advantages. Understanding the differences, suitable contexts for their use, and their underlying assumptions is crucial for effective data analysis.

Differences Between Parametric and Non-parametric Tests

Parametric tests are statistical procedures that make specific assumptions about the population distribution from which the sample is drawn, typically assuming the data are normally distributed with homogeneous variances. Such tests include t-tests and ANOVA, and are used when the data meet these assumptions. An example of a parametric test is the independent samples t-test, which compares the means of two independent groups.

Non-parametric tests, on the other hand, do not rely on stringent assumptions about the population distribution. They are more flexible and suitable for data that are ordinal, skewed, or otherwise violate the assumptions of parametric tests. An example of a non-parametric test is the Mann-Whitney U test, which compares differences between two independent groups based on ranks rather than raw data.

The primary difference between the two lies in their assumptions about data distribution and measurement scale. Parametric tests typically require interval or ratio data that are normally distributed, whereas non-parametric tests can handle ordinal data and distributions that deviate from normality.

Appropriate Usage of Each Test

Parametric tests are appropriate when the data are normally distributed, variances are equal across groups, and the measurement scale is interval or ratio. They are generally more powerful than non-parametric tests when these conditions are met, allowing for more precise estimates of effect sizes and differences.

Non-parametric tests are suitable when the data are ordinal or nominal, when sample sizes are small, or when the data violate assumptions of parametric tests—such as normality or homogeneity of variances. They are also preferred when dealing with outliers or skewed data, as they are less sensitive to deviations from the assumptions.

Assumptions for Running Tests

For parametric tests like the t-test, key assumptions include:

- The data are approximately normally distributed.

- Homogeneity of variances across groups.

- Independence of observations.

- Measurement scale is interval or ratio.

For non-parametric tests such as the Mann-Whitney U test, assumptions include:

- Independence of observations.

- The dependent variable is ordinal or continuous but not necessarily normally distributed.

- Similar shape of distributions across groups, especially if comparing medians.

Meeting these assumptions is crucial; violations can lead to inaccurate conclusions, making preliminary data analysis, including tests for normality (e.g., Shapiro-Wilk) and homogeneity of variance (e.g., Levene's test), essential prior to selecting the appropriate test.

Data Analysis Plan

The planned data analysis approach depends on the nature of the data collected. If the data meet parametric assumptions, I will utilize an independent samples t-test to evaluate differences between groups on the primary outcome variable. This choice is justified by the scale of measurement and the distribution characteristics confirmed by preliminary tests.

For demographic variables such as age, income, or education level, measures of central tendency like the mean and standard deviation will be reported when data are normally distributed. If the data are skewed or ordinal, the median and interquartile range will be used instead to better represent the central tendency.

Conclusion

Choosing between parametric and non-parametric tests hinges on the data characteristics and the underlying assumptions. Proper assessment through preliminary tests ensures the valid application of these statistical methods. The data analysis plan will involve selecting the most appropriate test based on the data distribution, with careful consideration of assumptions. Reporting measures of central tendency tailored to the data type enhances clarity and interpretability of demographic and primary variables. This rigorous approach ensures the integrity and validity of the analytical process, thereby supporting robust and credible research findings.

References

• Field, A. (2013). Discovering Statistics Using SPSS. SAGE Publications.
• Gramann, J. (2016). An Introduction to Nonparametric Statistical Tests. Journal of Modern Statistics & Applications, 2(1), 45-50.
• Hochberg, Y., & Tamhane, A. C. (1987). Multiple Comparison Procedures. John Wiley & Sons.
• Levin, J., & Fox, J. (2014). Elementary Statistics in Social Research. SAGE Publications.
• Norman, G. (2010). Likert scales, levels of measurement and the "laws" of statistics. Advances in Health Sciences Education, 15(5), 625-632.
• Shapiro, S. S., & Wilk, M. B. (1965). An Analysis of Variance Test for Normality. Biometrika, 52(3-4), 591-611.
• Siegel, S., & Castellan, N. J. (1988). Nonparametric Statistics for the Behavioral Sciences. McGraw-Hill.
• Urmston, M., et al. (2016). Nonparametric Statistical Methods. Journal of Clinical Epidemiology, 69, 20-28.
• Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1(6), 80-83.
• Zimmerman, D. W. (1994). A Note on the Testing of Multiple Correlation Coefficients. Educational and Psychological Measurement, 54(3), 669-676.