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Necessary parts of conducting statistics
As I have been adding statistical assumptions to the website, it is safe to say that the "levee" has broke and I have A LOT more work to do to make this the best statistical and empirical website. With this being said, check out the new assumptions pages:
Analyze three or more measures of an ordinal outcome
Wilcoxon is used as a post hoc test for significant main effects
The Greenhouse-Geisser correction is often employed when analyzing data with repeated-measures ANOVA. The statistical assumption of sphericity, as assessed by Mauchly's test in SPSS, is more often times than not violated. The Greenhouse-Geisser correction is robust to the violation of this statistical assumption with repeated-measures ANOVA. The means and standard deviations from a repeated-measures ANOVA can then be interpreted.
Friedman's ANOVA, in my experience, does not make many appearances in the empirical literature. Few people take three or more within-subjects or repeated measures of an ordinal outcome in order to answer their primary research question, I guess. It is a non-parametric statistical test since the data is measured at more of an ordinal level. When a significant main effect is found with a Friedman's ANOVA, then post hoc comparisons must be made within-subjects or amongst observations using Wilcoxon tests.
Friedman's ANOVA, while being a non-parametric statistic, may have the most statistical power when employed with cross-sectional data yielded from a survey instrument that has limited reliability and validity evidence. Likert scales and composite scores from such tests may be naturally skewed due to systematic and unsystematic error. Friedman's ANOVA is robust to these types of distributions that come from cross-sectional studies in the social sciences.
If the assumption of normality among the difference scores between observations of a continuous outcome cannot be met, then Friedman's ANOVA can be used to yield inferential evidence. But it is always a better idea to first check for outliers in a distribution (individual observations that are more than 3.29 standard deviations away from the mean) and make a decision as to whether 1) delete the observation in a listwise fashion, or 2) run a logarithmic transformation on the distribution.
You will have transform the other observations of the outcome if you choose #2 above. The means and standard deviations of transformed variables cannot be interpreted but the p-values can be interpreted. Report the median and interquartile range for transformed variables.
Deleting observations can introduce bias into the statistical analysis. This should only be done if the number of outliers constitutes less than 10% of the overall distribution. One can also run between-subjects comparisons between participants with all observations of the outcome versus participants without all observations. If there are no differences on predictor, confounding, and outcome variables between these two groups, then lessened observation bias can be assumed.
Eric Heidel, Ph.D. is Owner and Operator of Scalë, LLC.
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