Under My Umbrella: Understanding and Utilizing (Rating) Scale-Restrictions
Jens H. Fünderich
Means and standard deviations based on data on rating scale-data are not independent of each other: Means around the scale’s center can coincide with larger standard deviation than means towards either limit of the scale. Heathers et al. (2018) plot all combination of means and standard deviations for a sample of ten on a 5-point scale and observe that the results scatter in the shape of an umbrella. Based on the Bernoulli distribution, we developed a simple formalization of these umbrella restrictions that generalizes across samples sizes. We introduce that formalization and explore its implications to statistical power and meta-analytical effect heterogeneity. Further, we describe how the formalization adds to the error-detection toolbox.