scree test

An alternative method of deciding how many factors should be retained in any particular factor analysis . The principal method of deciding how many of the smaller factors to exclude, after retaining those which explain most of the common variance in a set of variables, utilizes Kaiser's criterion to select out those factors which have an eigenvalue of less than one. In effect, this excludes those factors which explain less variance than a single variable, a procedure that is done automatically by most statistical computer packages. However, as an alternative or complement to this technique, a graph can be generated which shows the descending variance accounted for by the factors extracted in the analysis. The term ‘scree’ derives from the geological analogy of debris found at the bottom of a rocky slope. For example, in the hypothetical instance shown in the illustration, the scree test suggests that there is a clear break between the steep slope of the initial factors and the gentler slope of those extracted later. Unfortunately, interpretation of the plot is rarely as clear-cut as this, and in practice tends to involve a fairly subjective assessment of which factors fall below an imaginary straight line extrapolated from the plots of the smaller factors.

FIGURE 10. An example of a scree test