The Square-Root Scree Plot: A Simple Improvement to a Classic Display

Abstract

<div class="page" title="Page 2"> <div class="layoutArea"> <div class="column"> <span style="font-size: 12.000000pt; font-family: 'TimesNewRomanPSMT'">Scree plots are ubiquitous in applications of exploratory factor analysis (EFA) and principal component analysis (PCA); they are used to visualize the relative importance of different factors/components and display the results of selection procedures (e.g., parallel analysis). Because the eigenvalues shown in the scree plot indicate the amounts of variance accounted for by the corresponding factors/components, they tend to give a distorted picture of the relative importance of the factors/components with respect to the original units of the variables. Specifically, variances inflate the apparent importance of large effects and deflate that of small effects; as a result, traditional scree plots exaggerate the differences between larger and smaller factors/components, and flatten the visual representation of the smaller ones. In this brief note, I propose a simple solution in the form of </span><span style="font-size: 12.000000pt; font-family: 'TimesNewRomanPS'; font-style: italic">square-root scree plots</span><span style="font-size: 12.000000pt; font-family: 'TimesNewRomanPSMT'">, i.e., scree plots based on the square root of the eigenvalues. Square-root scree plots provide a balanced display of the relative importance of the factors/components, and a more legible representation of the smaller ones. They are a useful addition to the toolkit of EFA and PCA, and may be preferable as a default option in most common applications. </span> </div> </div> </div>