## ABSTRACT

This chapter looks at the types of data which may usefully be factor analysed. It provides the major assumption that psychologists can measure quantities using tests. The chapter explores the several ways of estimating the communality of each variable in the factor extraction. Performing and interpreting factor analyses with small samples and identifying factors on which only a few variables have large loadings is a waste of everybody's time unless the communalities of the variables are large. Most statistics packages assume that factor analyses are to be performed on interval or ratio-scaled data – numbers representing proper physical measurements. If polychoric correlations are calculated and factor analysed, it will sometimes be found that the factor analysis program fails because the matrix of polychoric correlations yields some negative eigenvalues. Like the Kaiser-Guttman criterion, the scree test is based on the eigenvalues of an initial unrotated principal-components solution.