Mathematics & Statistics Dictionaries

The eigenvalues for successive factors can be displayed in a simple line plot. Cattell (1966) proposed that this scree plot can be used to graphically determine the optimal number of factors to retain.

The scree test involves finding the place where the smooth decrease of eigenvalues appears to level off to the right of the plot. To the right of this point, presumably, one finds only "factorial scree" -- "scree" is the geological term referring to the debris which collects on the lower part of a rocky slope. Thus, no more than the number of factors to the left of this point should be retained.
For more information on procedures for determining the optimal number of factors to retain, see the section on Reviewing the Results of a Principal Components Analsysis in the Factor Analysis chapter and How Many Dimensions to Specify in the Multi-dimensional Scaling chapter.