First and foremost it is essential to emphasize the term “generally” in the statement that “the repeated-measures ANOVA is generally more powerful than the one-way ANOVA.” It means that this analysis will target to prove the advantage of the repeated-measures ANOVA in a general context, without considering potential exceptions where the one-way ANOVA is more efficient. Also, it essential to exclude the multivariate design from this analysis as the repeated –measures ANOVA cannot be applied to those measurements that imply the variables of different qualities (D’Amico, Neilands, & Zambarano, 2001).
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To begin with, it is necessary to define the factors that determine the measure’s power. Let us assume that the power of a test is determined by its power to reject the null hypothesis. Now, it is essential to consider the factors that affect this power: the sample size and the p-value. A larger sample size, as well as a lower p-value, increases the chances of rejecting the null hypothesis (Razali & Wah, 2011).
It is suggested that in order to compare the repeated-measures ANOVA and the one-way ANOVA, it is essential to compare the power of paired samples t-tests and independent samples t-tests. Therefore, it is necessary to examine any data sets retrieved from two types of tests to examine the tests’ power. Let us refer to the paper that provides an explicit description of the tests’ outputs. Upon the consideration of these data sets, two critical observations need to be made. On the face of it, the observed independent sample t-tests might appear more powerful as they have larger sample sizes. In the meantime, closer consideration reveals that the paired samples t-tests tend to show lower p-value than the independent samples t-tests.
A lower p-value increases the chances of rejecting the null hypothesis – as a result, it is rational to assume that paired-samples tests have an advantage over independent samples t-tests in terms of power. The next stage implies finding evidence for the parallels between the repeated-measures ANOVA and paired samples t-tests and between the one-way ANOVA and independent sample t-tests. The analyzed paper demonstrates the sets of data retrieved from the four types of measurements. The presented tables show that the results retrieved through the paired samples t-test are equal to those retrieved through repeated-measures ANOVA, while the independent sample t-test shows the same results as the one-way ANOVA. Therefore, it might be concluded that the repeated-measures ANOVA is generally more powerful than the one-way ANOVA (Dr. RSM700 lecture notes, April 15, 2016).
The proposed explanation relies on the assumption that the power of measures is determined by the low p-value that increases the chances of rejecting the null hypothesis. Meanwhile, the power of the repeated-measures ANOVA might be likewise evidenced from a different perspective. Hence, let us assume that the power of measures is determined by the low error variance. Therefore, another advantage of the repeated-measures ANOVA regarding power resides in the fact that it allows distinguishing between within-subject and between-subject variability ensuring additional degrees of freedom. The variation among sample members allows reducing the error variance (Dimitrov & Rumrill, 2003).
As a result, it might be concluded that there are at least two factors proving that the repeated-measures ANOVA is generally more powerful than the one-way ANOVA. First, it shows a lower p-value (as it is evidenced by the example of ANOVA and paired samples t-tests comparison). Second, it offers reduced error variance in comparison with the one-way ANOVA.
D’Amico, E. J., Neilands, T. B., & Zambarano, R., (2001). Power analysis for multivariate and repeated measures designs A flexible approach using the SPSS MANOVA procedure. Behavior Research Methods, Instruments, & Computers, 33(4), 479-484.
Dimitrov, D. M., & Rumrill, P. D., (2001). Pretest-posttest designs and measurement of change. Work, 20(2), 159-165.
Razali, N. M., & Wah, Y. B., (2011). Power comparisons of Shapiro-Wilk, Kolmogorov-Smirnov, Lilliefors and Anderson-Darling tests. Journal of Statistical Modeling and Analytics, 2(1), 21-33.