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Graphic Display III

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   Fig. 5 is a graphic display of the relations between the residuals of the percent pass/rank across rank. While it stands as an odd set of things to compare statistically, I did it to improve visualization of the behavior of the very top and very bottom most groups. No correlation (r = 0.0) is what we might expect with this particular analysis. However, the regression was run to better view the curving at the ends of the percent passing. . . something it clearly shows. Note that the behavior of those school districts ranking lowest (upper left-hand area) and those school districts ranked highest (lower, right-hand area) show very definite skewing in the extent to which they over/under performed in terms of the data. The next graph, my personal favorite because of its wild shape, shows the same phenomena in a slightly different view.

   This wild looking curve shows the residuals from the data analysis shown in Figure 6 as a function of the percent passing. Simply interpreted, the data show the districts with the very highest and very lowest rates of passing as having exaggerated tendency in the direction of their overall performance. I am not certain if there is a statistical significance in this. I am currently attempting to get expert advice on whether there are enough cases in the very highest and lowest groups to merit further analysis (logistical). Stay tuned. . .