# Composite scores

## Overview An example of a simple, first-order factor structure; which would justify the calculation of three composite scores

In statistics, and particularly psychometrics, composite scores are calculated from data in multiple variables in order to form reliable and valid measures of latent, theoretical constructs.

The variables which are combined to form a composite score should be related to one another. This can be tested through factor analysis and reliability analysis.

Higher-order composite scores (such as global or total scores) may also be appropriate when factors themselves are correlated and theoretically related.

## Methods

Two common methods for calculating composite scores are:

• Unit weighted - each item is equally weighted, e.g., X = mean (A, B, C, D)
• Regression-weighted - each item is weighted according to its factor loading, e.g., X = .5*A + 0.4*B + 0.4*C + 0.3*D

In most situations, you can use either unit-weighted or regression-weighted composite scores. Regression-weighted scores are, technically, more valid. However regression-weighted scores are standardised (to a mean of 0 and SD of 1), so in some situations e.g., comparisons between means of two or more composite scores (e.g., for an RM ANOVA or Mixed ANOVA), unit-weighted scores should be used. But regression-weighted are appropriate for MLR and some ANOVAs, as well as many other types of statistical analysis.