ABSTRACT
In its basic form, a correlation matrix is square, that is, there are as many rows as there are columns. The diagonal of cells running from top left to bottom right is known as the principal diagonal of the matrix. The correlations in the off-diagonal cells are the same above and below the principal diagonal (e.g. the correlation of French with German is the same as that of German with French). Each row (or column) of the R-matrix contains all the correlations involving one particular test in the battery. Since the variables are labelled in the same order
in the rows and columns of the R-matrix, each of the cells along the principal diagonal contains the correlation of one of the variables with itself (i.e. 7). The R-matrix can be the starting point for a variety of multivariate statistical procedures, but in this chapter we shall consider just one technique: factor analysis. The presence in the R-matrix of clusters of sizeable correlations among subsets of the tests in the battery (e.g. Music and Maths; French and German) would suggest that these subset tests may be tapping the same underlying intellectual dimension or ability. If the traditional British theories of the psychology of intelligence are correct, there should be fewer (indeed, far fewer) dimensions than there are tests in the battery. The purpose of factor analysis is to identify and to quantify the dimensions supposed to underlie performance on a variety of tasks.
