0.10 Writing up nonparametric anova

Writing up your nonparametric one-way anova

About the Authors

• John R. Slate is a Professor at Sam Houston State University where he teaches Basic and Advanced Statistics courses, as well as professional writing, to doctoral students in Educational Leadership and Counseling. His research interests lie in the use of educational databases, both state and national, to reform school practices. To date, he has chaired and/or served over 100 doctoral student dissertation committees. Recently, Dr. Slate created a website, Writing and Statistical Help to assist students and faculty with both statistical assistance and in editing/writing their dissertations/theses and manuscripts.
• Ana Rojas-LeBouef is a Literacy Specialist at the Reading Center at Sam Houston State University where she teaches developmental reading courses. She recently completed her doctoral degree in Reading, where she conducted a 16-year analysis of Texas statewide data regarding the achievement gap. Her research interests lie in examining the inequities in achievement among ethnic groups. Dr. Rojas-LeBouef also assists students and faculty in their writing and statistical needs on the Writing and Statistical website, Writing and Statistical Help

The following is an example of how to write up (in manuscript text) your Nonparametric ANOVA test Statistics. This module is used with a larger Collection (Book) authored by John R. Slate and Ana Rojas-LeBouef from Sam Houston State University and available at: Calculating Basic Statistical Procedures in SPSS: A Self-Help and Practical Guide to Preparing Theses, Dissertations, and Manuscripts

Differences in Hispanic Student Enrollment as a Function of School Level

Research question

The following research question was addressed in this study:

• What is the difference in Hispanic student enrollment as a function of school level?

Results

Descriptive statistics for the percent of Hispanic students enrolled in Texas elementary schools, middle schools, and high schools are depicted in Table 1. Prior to conducting an inferential statistical procedure to address the research question previously delineated, checks of the normality of the data were conducted. In particular, the standardized skewness coefficients (i.e., the skewness value divided by its standard error) and the standardized kurtosis coefficients (i.e., the kurtosis value divided by its standard error) were calculated for the percent of Hispanic students enrolled in Texas elementary schools, middle schools, and high schools. As can be seen in Appendix B, all of these values were far outside of the boundaries of normally distributed data (i.e., -3 to +3) (Onwuegbuzie&Daniel, 2002). Thus, a nonparametric analysis of variance (ANOVA) procedure was used. Specifically, the Kruskal-Wallis test was employed.

The nonparametric ANOVA revealed a statistically significant difference in the percent of Hispanic students enrolled in Texas schools as a function of school level, Χ 2 = 75.72, p <.001. The effect size associated with this difference, as measured by Cramer’s V , was .07. Using Cohen’s (1988) criteria, this coefficient was indicative of a small effect. A series of nonparametric pairwise follow-up tests at the Bonferroni (Vogt, 2005) adjusted level (i.e., .05 divided by 3 analyses) of .0167 indicated that a statistically significantly higher percentage of Hispanic students were enrolled in elementary schools than in either middle or high schools. Similarly, a higher percentage of Hispanic students were enrolled in middle school than were enrolled in high schools. Readers are directed to Table 1 for the descriptive statistics for Hispanic student enrollment as a function of school level.

References

• Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.) . Hillsdale, NJ: Lawrence Erlbaum.
• Onwuegbuzie, A. J.,&Daniel, L. G. (2002). Uses and misuses of the correlation coefficient. Research in the Schools, 9 (1) , 73-90.
• Vogt, W. P. (2005). Dictionary of statistics and methodology: A nontechnical guide for the social sciences (3rd ed.). Thousand Oaks, CA: Sage.

Nonparametric ANOVA and Effect Size Formulae

• The chi-square value can be used to compute the effect size. Specifically, Cramer’s V is used, which is defined as Cramer’s V = √{χ ² / (df x n)}
• Where χ ² is the value extracted from the Kruskal-Wallis test, df = degrees of freedom, and n = the sample size.
• For the above data, we have Cramer’s V = √{75.72 / (2 x 7842)} = .07

Spss statistical output

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