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137 Consider the data in Table 42, which pertains to crash counts at 3,699 one-mile road segments in Utah. These seg- ments averaged 0.281 crashes per year during 1995 to 1997 and 0.279 crashes per year during 1998 to 2000, further evi- dence that they were largely unaltered during the 6-year period from 1995 to 2000, according to information in the Highway Safety Information System (HSIS)108 from which these data were extracted. In Table 42, segments are grouped into rows based on the count of crashes during 1995 to 1997. As the last column shows, those segments in groups which during 1995 to 1997 had more than the average number of crashes in this period (0.281 crashes per year or 0.843 crashes in 3 years) experienced a reduction in crashes during 1998 to 2000. Segments with fewer crashes than the average (i.e., those with 0) experienced a considerable increase. These changes are due to random fluctuations in short- term counts that result in a phenomenon known as regression to the mean. The result is that such changes can be erro- neously attributed to a countermeasure in an observational study that simply compares crashes before and after imple- mentation. In particular, if the segments with high counts are selected for treatment (as often happens) the positive effects of the treatment in such a naïve study would be exaggerated by the amounts shown in the last column of the earlier rows in the table. This random fluctuation also suggests that a site with a higher collision count is not necessarily a stronger can- didate for safety improvement than a site with a lower count. The upshot of this phenomenon is that the crash count by itself is not good enough for estimating the safety of a site for use in identifying candidate improvement locations and in estimating the safety effect of potential or implemented coun- termeasures. This is why more sophisticated predictive guides are needed. Evidence of regression to the mean in two other statesâ data used for this study is presented in Tables 43 and 44. A P P E N D I X D Illustrating Regression to the Mean Crashes 3 yrs Prior Number of Sites Crashes 1995- 1997 Crashes 1998- 2000 % difference 17 17 416 340 -18.3 16 6 96 86 -10.4 15 8 120 97 -19.2 14 6 84 73 -13.1 13 5 65 45 -30.8 12 5 60 57 -5.0 11 11 121 101 -16.5 10 12 120 119 -0.8 9 17 153 112 -26.8 8 14 112 99 -11.6 7 19 133 108 -18.8 6 34 204 194 -4.9 5 34 170 160 -5.9 4 51 204 175 -14.2 3 93 279 250 -10.4 2 173 346 282 -18.5 1 431 431 377 -12.5 0 2763 0 431 infinite increase Table 42. Wildlifeâvehicle crash data for Utah illustrating regression to the mean.
138 Crashes 3 yrs Prior Number of Sites Crashes 1996- 1998 Crashes 1999- 2001 % difference 32 6 242 227 -6.2 31 3 93 65 -30.1 30 3 90 70 -22.2 29 3 87 29 -66.7 28 1 28 23 -17.9 27 2 54 50 -7.4 26 1 26 19 -26.9 25 5 125 115 -8.0 24 5 120 91 -24.2 23 3 69 43 -37.7 22 1 22 20 -9.1 21 10 210 174 -17.1 20 3 60 37 -38.3 19 7 133 103 -22.6 18 8 144 105 -27.1 17 4 68 45 -33.8 16 7 112 89 -20.5 15 19 285 213 -25.3 14 28 392 303 -22.7 13 39 507 450 -11.2 12 33 396 338 -14.6 11 44 484 386 -20.2 10 55 550 404 -26.5 9 94 846 746 -11.8 8 114 912 654 -28.3 7 144 1008 779 -22.7 6 216 1296 1145 -11.7 5 290 1450 1179 -18.7 4 429 1716 1321 -23.0 3 653 1959 1728 -11.8 2 1167 2334 2066 -11.5 1 2518 2518 2482 -1.4 0 13125 0 2586 Infinite increase Table 43. Data for North Carolina illustrating regression to the mean. Crashes 3 yr s Prior Number of Site s Crashes 1997- 1999 Crashes 2000- 2002 % difference 6 8 61 41 -32.8 5 8 40 27 -32.5 4 21 84 41 -51.2 3 55 165 84 -49.1 2 147 294 149 -49.3 1 792 792 343 -56.7 0 11941 0 951 infinite increase Table 44. Data for California illustrating regression to the mean.