Nonparametric Procedures

Guidance for discussion.

Some researchers do not believe nonparametric procedures are robust enough to yield reliable results. This may hold true if a sample is small or variances between groups are unequal. But does that make the procedures themselves unreliable, or are they simply as reliable as the data themselves?

For this discussion, consider a small, hypothetical quantitative case study, and develop an original response as follows:

Describe the hypothetical study, and name two variables to compare or correlate.

Propose a sample size. Which nonparametric statistical procedures would you apply and why?

Respond to each post in a paragraph:

Post 1

My hypothetical study would explore if there was a connection between students who drop out of graduate school and their race. The study would use a sample of 75 students. For this study I would use the Chi-Square Test of Independence.

A Chi-Square Test of Independence is used to determine if two nominal variables are related (Wagner & Gillespie, 2019). In this study the two nominal variables would be race and drop out status. The null hypothesis for this study would be that there is no connection between race and drop out status. The Chi-Square Test of Independence cannot show causality, but it can show if there is a correlation between the two variables.

Post 2

Describe the hypothetical study, and name two variables to compare or correlate.

Hypothetical Study: The study will adopt a cross-sectional design, collecting data on daily caffeine intake and sleep quality from participants representing diverse age groups (18-65 years) and lifestyles. Participants will self-report their caffeine consumption over a week, and sleep quality will be assessed using a standardized questionnaire.

Variables: Daily caffeine intake (in mg) and sleep quality (measured on a scale from 1 to 10).

Propose a sample size.

Sample Size: 150 participants.

Which nonparametric statistical procedures would you apply and why?

Nonparametric Statistical Procedure: Spearman's rank correlation coefficient. This method is appropriate for assessing the strength and direction of a monotonic relationship between two variables, which suits the nature of caffeine intake and sleep quality. Spearman's rank correlation coefficient will be applied due to the ordinal nature of sleep quality data and the likely non-linear relationship with caffeine intake.

Post 3

For a sample size of around 150, there are several nonparametric tests that can be appropriate depending on the nature of your data and research question. Here are a few commonly used nonparametric tests that could be suitable for your study involving 150 teachers:

Wilcoxon Signed-Rank Test: This test is used when you have paired or matched data and want to determine if there is a significant difference between two related variables. For example, if you have data on the pre- and post-intervention performance of teachers and want to assess if there is a significant change, the Wilcoxon signed-rank test can be used.

Mann-Whitney U Test: If you have two independent groups of teachers and want to compare their medians or distributions for a continuous outcome variable, the Mann-Whitney U test can be appropriate. It is a nonparametric alternative to the independent samples t-test.

Kruskal-Wallis Test: If you have more than two independent groups and want to compare their medians or distributions for a continuous variable, the Kruskal-Wallis test can be used. It is a nonparametric alternative to the one-way ANOVA test.

Spearman's Rank-Order Correlation: If you want to assess the strength and direction of the relationship between two variables, both of which are measured on an ordinal or continuous scale, Spearman's rank-order correlation can be used. It assesses the monotonic relationship between variables.

These nonparametric tests do not assume a specific distribution of the data and can be robust against violations of normality assumptions. They are suitable for a variety of research questions and data types. However, it's important to ensure that the assumptions of each specific test are met and that the choice of test aligns with your research objectives and data characteristics. Thoughts?