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Nonparametric independent samples t-test:

For a writeup of a nonparametric independent samples t -test (i.e., mann-whitney U ) results, please see:

  • 1. Williams, J. S., Beken, J. A., Combs, J. P.,&Slate, J. R. (2010). Graduation and attendance rates of at-risk students at traditional and academic alternative high schools: A two-year statewide study. International Journal of Education Leadership Preparation, 5 (2). Retrieved from (External Link)&issueID=74
  • In their study, Williams, Beken, Combs, and Slate (2010) have four research questions in which they analyzed for differences between groups. After determining that their data were not normally distributed, they then conducted several nonparametric independent samples t -tests. In this study, Williams et al. (2010) reported their statistical results in a manner compliant with APA, as well as provide APA compliant tables.
  • 2. Clark, D., Slate, J. R.,&Viglietti, G. C. (2009). Children’s weight and academic performance in elementary school: Cause for concern? Analyses of Social Issues and Public Policy (ASAP), 9 (1), 185-204. doi: 10.1111/j.1530-2415.2009.01186.x Available online at (External Link)
  • In this study, Clark, Slate, and Viglietti (2009) report the results of several nonparametric independent samples t-tests. After documenting that their data were not normally distributed, they conducted Mann-Whitney U statistical procedures. In accordance with APA 6th edition, they provided effect size estimates for their statistically significant results.

Nonparametric dependent samples t-test:

For writeups of nonparametric wilcoxon’s dependent samples t -test (i.e., wilcoxon signed-ranks test), please see:

  • 1. Moore, G. W.,&Slate, J. R. (2008). Who’s in the Advanced Placement courses and how are they doing? A two-year statewide study. The High School Journal, 92 (1), 55-67. doi:10.1353/hsj.0.0013
  • In this study, the second and third research questions involved determining the extent to which statistically significant differences were present between groups. After calculating measures of normality (i.e., skewness and kurtosis), Moore and Slate (2008) determined that their data were not normally distributed and, as a result, used nonparametric independent samples t -tests to address their second and third research questions.
  • 2. Bustamante, R., Slate, J. R., Edmonson, S., Combs, J., Moore, G.,&Onwuegbuzie, A. J. (2010). College-Readiness considerations for English Language Learners and students with special learning needs. International Journal of Educational Leadership Preparation, 5 (4). Available online at (External Link)
  • Bustamante and colleagues (2010) had one research question that involved differences between paired or dependent groups. After determining that their data were not normally distributed, they conducted several nonparametric dependent t -tests.

Parametric analysis of variance:

For writeups of parametric anova, please see:

  • 1. Schulte, D. P.,&Slate, J. R. (2011). Charter schools: Instructional expenditures and college-readiness. International Journal of Educational Leadership Preparation, 5 (2). Available online at (External Link)&issueID=74
  • In this study, Schulte and Slate (2011) had three research questions in which ANOVAs, of measures of differences, were calculated. They indicated that they had checked for normality of their data. Statistical significant results were described in adherence with APA 6th edition. Moreover, effect sizes were present.
  • 2. Garcia, C., Slate, J. R.,&Delgado, C. (2009). Salary and ranking and teacher turnover: A statewide study. International Journal of Education Policy and Leadership, 4(7). Retrieved from (External Link)
  • In this study, Garcia, Slate, and Delgado (2009) report the results of three ANOVAs they calculated to determine whether statistically significant differences in teacher turnover were present as a function of school accountability rating. Effect sizes and tables in which descriptive statistics for the groups were present.

Nonparametric analysis of variance:

For writeups of nonparametric anova (i.e., kruskal-wallis), please see:

  • 1. Clark, D., Slate, J. R.,&Viglietti, G. C. (2009). Children’s weight and academic performance in elementary school: Cause for concern? Analyses of Social Issues and Public Policy (ASAP), 9 (1), 185-204. doi: 10.1111/j.1530-2415.2009.01186.x Available online at (External Link)
  • In this study, Clark, Slate, and Viglietti (2009) report the results of nine nonparametric ANOVAs. After demonstrating that their data were not normally distributed, they conducted Kruskal-Wallis statistical procedures. In accordance with APA 6th edition, they provided effect size estimates for their statistically significant results.

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Source:  OpenStax, Presenting and communicating your statistical findings: model writeups. OpenStax CNX. Apr 27, 2011 Download for free at http://cnx.org/content/col11299/1.3
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