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Results

Some results of our application of the graphic svf method to the WAIS data are presented in the figures 5, 6 and 7.

 

Figure 5. svf plot of WAIS Block Design scores as a function of age at testing.

In Figure 5 the majority of the data comes from 70 to 85 year--olds; one can observe this in the svf plot by noting that the arrows are larger in this age range. Looking vertically along the cells representing 80 year--olds we can see a unimodal, approximately normal distribution of scores. However for 25 year--olds this normal distribution is not apparent. Of course, the 25 year--olds in this study were mostly college students so the majority of scores are higher than expected by chance alone. Block Design shows a striking downward trend if we treat the sample as simply cross-sectional and fit a regression line to all of the data points (). But if you look at the vector field cells, the downward slope is not nearly so great. It is likely that a simple cross--sectional regression is in error due to skew in the sampling.

  Figure 6. svf plot of WAIS Vocabulary scores as a function of age at testing.

In Figure 6 once again the majority of the sample is in the 70 to 90 age range, but now there is a bimodal distribution of verbal abilities. This is striking since these are the same individuals as in the previous graph. Note also that the group of lower scoring 70 to 90 year--olds has a much smaller standard deviation in angle than does the higher scoring 70 to 90 year--olds.

There is very little declining trend apparent in the slopes of the vector field cells, even in the over 85 age group. However, once again a simple cross-sectional regression line would show a minor decline with age; this effect may be due to sampling skew. It is important to note that even though an assumption of normal distribution of verbal abilities with respect to age is somewhat inconsistent with these data in the 70 to 90 age group, the vector field method remains robust.

Another point worth noting is that in the 30 to 40 year age group there appears to be some evidence of a bifurcation or splitting, such that individuals with scores above 75 appear to have increasing verbal abilities, whereas individuals with scores below 75 appear to have decreasing verbal abilities (see Figure 7). This intriguing hint might help explain the bimodal distribution within the older population. A focussed experiment on the 30 to 50 age group is needed to be able to test this hypothesis, since there is currently insufficient data from the 30 to 50 age group to be able view a clear pattern of growth or decline.

  Figure 7. Detail of the 20 to 40 age group from the svf plot of WAIS Vocabulary scores as a function of age at testing.



next up previous
Next: Discussion Up: Statistical Vector Field Analysis Previous: The svf Algorithm



Steven M. Boker
Sun Feb 12 18:20:50 EST 1995