Statistical Methods for Experimental Research in Education and Psychology by Jimmie Leppink

Author:Jimmie Leppink
Language: eng
Format: epub, pdf
ISBN: 9783030212414
Publisher: Springer International Publishing

Ms and SDs of post-test performance are as follows: M = 8.170 and SD = 2.128 in the control condition, M = 9.302 and SD = 1.917 in treatment A, and M = 8.962 and SD = 1.951 in treatment B. These differences correspond with R2 = 0.054 and adjusted R2 = 0.042 (η2 = 0.054 and ω2 = 0.042). One-way ANOVA yields a statistically significant outcome: F2, 156 = 4.468, p = 0.013. Like with the two-samples t-test, the common ANOVA model assumes population SDs to be equal. In the case of a substantial departure from this assumption, there are two alternatives that do not assume equal SDs: Brown-Forsythe’s F-test (Brown & Forsythe, 1974) and Welch’s F-test (Welch, 1951). In the experiment at hand, the largest SD is 2.128 and the smallest SD is 1.917. The resulting ratio is: 2.128/1.917 ≈ 1.110. This is smaller than the ratio in Chaps. 2 and 5, where we see the two variants of the two-samples t-test yield near identical results. SPSS provides all three tests—the default ANOVA F-test and its two alternatives—and we see very similar outcomes: Brown-Forsythe’s F2, 154.645 = 4.468, p = 0.013; Welch’s F2, 103.797 = 4.240, p = 0.017. In short, we may as well proceed treating the SDs as (approximately) equal.

The −2LL of the null model (i.e., Model 0, which represents H0: no differences) is 677.615, and that of the ANOVA model is 668.759. In the null model, one M is used for all conditions; in the ANOVA model, each condition has its own M. Therefore, given three conditions, the difference between the two models in df = 2. The difference in −2LL is approximately -distributed, and the -distribution is that of the difference in df between the model, hence: . In our case, we find , p = 0.012. For Model 0, we find AIC = 681.615 and BIC = 687.752 (Mplus). For the ANOVA model, we find AIC = 676.759 and BIC = 689.034. Running a Bayesian one-way ANOVA with a default prior (Rouder, Engelhard, McCabe, & Morey, 2016; Rouder, Morey, Speckman, & Province, 2012; Rouder, Morey, Verhagen, Swagman, & Wagenmakers, 2017; Wetzels, Grasman, & Wagenmakers, 2012) in JASP, we find BF10 = 2.789 (error = 0.009%). In other words, based on AIC and p-value, we may prefer the ANOVA model, while based on BIC we may prefer the null model, and BF10 indicates some preference towards the ANOVA model but the evidence is negligible.

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