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Experimental Research Methods in Language Learning

Experimental Research Methods in Language Learning. Chapter 15 Non-parametric Versions of T-tests and ANOVAs. Leading Questions. What is a non-normal data distribution? What does it look like? How do we know whether a data set is normally distributed?

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Experimental Research Methods in Language Learning

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  1. Experimental Research Methods in Language Learning Chapter 15 Non-parametric Versions of T-tests and ANOVAs

  2. Leading Questions • What is a non-normal data distribution? What does it look like? • How do we know whether a data set is normally distributed? • Do you any know of a nonparametric test that can analyze non-normally distributed data? If so, what is it?

  3. Non-parametric Tests This chapter presents four non-parametric tests: • Wilcoxon Signed Ranks Test (the nonparametric version of the paired-samples t-test) • Mann-Whitney U Test (the nonparametric version of the independent-samples t-test); • Kruskal-Wallis H Test (the nonparametric version of the one-way ANOVA); • Friedman Test (the nonparametric version of the repeated-measures ANOVA).

  4. Wilcoxon Signed Ranks Test • This test is the non-parametric version of the paired-samples t-test. • The Z score is used for statistical testing. • Table 15.1.1 reports the descriptive statistics of a pretest and a posttest to be compared.

  5. Wilcoxon Signed Ranks Test • Table 15.1.2 presents the score ranks using the posttest and pretest scores.

  6. Wilcoxon Signed Ranks Test • Negative ranks refer to the observation that an individual scored lower in the posttest than in the pretest. • Positive ranks refer to the observation that an individual scored higher in the posttest than the pretes.

  7. Wilcoxon Signed Ranks Test • Table 15.1.3 reports the Wilcoxon signed ranks test statistic. • Examine the Z score and the Assymp. Sig (2-tailed) value.

  8. Wilcoxon Signed Ranks Test Effect size: r = Z ÷ √N (Larson-Hall (2010, p. 378) presents a formula to compute the r effect size for both the Mann-Whitney and Wilcoxon signed ranks tests. The formula is simple to calculate: It is important. We can use the following statistical website practical to compute effect sizes: <http://www.ai-therapy.com/psychology-statistics/effect-size-calculator>

  9. Examples of Studies • Gass, Svetics, & Lemelin 2003; • Kim & McDonough 2008; • Marsden & Chen 2011; • Yilmaz 2011; • Yilmaz & Yuksel 2011

  10. Mann-Whitney U Test • Has a similar function to that of the independent-samples t-test for comparing two groups of participants • Table 15.2.1 reports the descriptive statistics of each test.

  11. Mann-Whitney U Test • Table 15.2.2 presents the mean ranks using the speaking pretest and posttest scores.

  12. Mann-Whitney U Test • Table 15.2.3 reports the Mann-Whitney U test statistic. • We examine the Z score and the Assymp. Sig (2-tailed) value.

  13. Examples of Studies • Henry et al. (2009); • Macaro & Masterman (2006); • Marsden & Chen (2011); • Yilmaz and Yuksel (2011)

  14. Kruskal-Wallis H Test • Can help us determine differences between two or more groups. • Used when our data are not normally distributed. • Table 15.3.1reports the descriptive statistics of each test.

  15. Kruskal-Wallis H Test • Table 15.3.2 presents the mean ranks using the speaking posttest scores.

  16. Kruskal-Wallis H Test • Table 15.2.3 reports the Kruskal-Wallis H test statistic. • Examine the chi-square (χ2) statistic, df and the Assymp. Sig value.

  17. Kruskal-Wallis H Test • post hoc test for Kruskal-Wallis H test is typically a Mann-Whitney U test in SPSS • Alternatively use the following website to compute a post hoc test: <http://www.ai-therapy.com/psychology-statistics/hypothesis-testing/two-samples?groups=0&parametric=1>; accessed 01/03/2014.

  18. Examples of Studies • Chen & Truscott 2010; • Li 2011; • Marsden & Chen 2011

  19. Friedman Test • Can do more than two levels of repeated measures • Note that the Friedman test cannot test a group difference like the repeated-measures ANOVA. • Therefore, the Friedman test is not a full parametric version of the repeated-measures ANOVA.

  20. Friedman Test • Table 15.4.1reports the descriptive statistics of each test.

  21. Friedman Test • Table 15.4.2 presents the mean ranks of the three test scores. In this table, we can see the delayed reading posttest had the highest rank (i.e., 2.87).

  22. Friedman Test • Table 15.4.3 reports the Friedman test statistic. • Examine the chi-square (χ2) statistic, df and the Assymp. Sig value.

  23. Examples of Studies • Li (2011) • Marsden and Chen (2011)

  24. Discussion • What do you think are analytical limitations when raw scores are ranked before being analyzed? • Do you find it useful to know the logic of these nonparametric tests? Does it help you understand experimental studies using these statistical tests? • What are benefits of knowing an alternative statistics when our data are not normally distributed?

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