## ABSTRACT

Looking at the overall grid In the 1960s Patrick Slater (Slater, 1964) introduced a technique (that he called ‘principal components’) we now know as singular-value-decomposition which enables both elements and constructs to be represented together. There have been a number of different ways of representing the constructs and elements in these maps. Elements always appear as points in the map. Constructs however, are shown in different ways. The construct data are like a principal component solution with two columns of coordinates which define a point in the space. However representations differ. Often the point is reflected back through the origin to make a line symmetric about the origin, the two ends of which represent the construct poles. Other representations (such

as that originally used by Slater) show the construct poles as points on a circle encompassing the elements. Figure 25.5 shows a spatial representation of our sample grid using the program Idiogrid with elements shown as points and constructs shown as vectors (lines) symmetric about the origin. The longer the line, the more important the construct. The horizontal dimension separates better and poorer teachers, with constructs similarly aligned, while the vertical axis is aligned with the isolated construct aloof – sociable distinguishing principally between teacher I didn’t learn well with and me as a teacher now. Another way of representing the whole grid is by a technique known in the repertory grid world as ‘focusing’. This means the rows (constructs) and columns

(elements) are reordered and the grid data and labels shown in this reordering. This approach was originally devised by Shaw and Thomas (1978) and employs single-linkage hierarchical clustering to align constructs and elements. Other clustering such as k­ means can be used and Table 25.3 shows such a rearrangement of the sample grid from the GRIDSTAT program referred to earlier. The focused grid is shown in two forms. On the left is shown the grid with two misaligned constructs, ‘sociable – aloof ’ and ‘rejects ideas – accepts’ realigned as ‘aloof – sociable’ and ‘accepts – rejects ideas’ while on the right, the grid as elicited is shown. The original grid has four groups of constructs but in the aligned form there are only two.