The kinds of problems that we are interested in dealing with are described in Figures 2 and 3 below. Here we have taken data from the archives developed by McArdle. These data represent a subset of the collection of psychometric information from all the available studies of adult development using the Weschler Adult Intelligence Scale (WAIS). In Figure 2 we plot the scores for N=1693 longitudinal pairs of measurements from 10 separate longitudinal WAIS studies. Figure 2 gives scores for the Block Design subtest variable which is thought to indicate General Visualization or Fluid ability [Gv or Gf; after Horn 1988, Horn & Cattell 1966].
Figure 3. WAIS Block Design scores as a function of age from multiple study samples (N = 1693). [McArdle & Horn 1991]
Figure 2 presents the longitudinal data pairs as line segments only. The X axis is chronological age and Y axis is the score obtained at that age. The scores for each individual are represented by a single polyline. A polyline is created by simply ``connecting the dots'' with straight lines between the score values for one individual at successive ages. The resulting graph is so complex that it is difficult to gain a great deal of insight into the statistical properties of these data by only plotting polylines.
We find that often when we have enough data to make statistically significant calculations, any trend that might be apparent to the researcher's eye is lost in a black mass of over-struck line segments. The same large sample size that is helpful to our multivariate analyses becomes an obstacle to our being able to visually discern a trend, much less a field.
Figure 3. WAIS Vocabulary scores as a fuction of age from multiple study samples (N=1693). [McArdle & Horn 1991]
Figure 3 presents the longitudinal data pairs for vocabulary abilities as line segments. Once again, it is difficult to make much more than gross interpretation of these data. This is the same set of subjects that we used to plot the Block Design abilities in Figure 2.