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OCR for page 137
137 APPENDIX D Illustrating Regression to the Mean Consider the data in Table 42, which pertains to crash to the mean. The result is that such changes can be erro- counts at 3,699 one-mile road segments in Utah. These seg- neously attributed to a countermeasure in an observational ments averaged 0.281 crashes per year during 1995 to 1997 study that simply compares crashes before and after imple- and 0.279 crashes per year during 1998 to 2000, further evi- mentation. In particular, if the segments with high counts are dence that they were largely unaltered during the 6-year selected for treatment (as often happens) the positive effects period from 1995 to 2000, according to information in the of the treatment in such a nave study would be exaggerated Highway Safety Information System (HSIS)108 from which by the amounts shown in the last column of the earlier rows these data were extracted. In Table 42, segments are grouped in the table. This random fluctuation also suggests that a site into rows based on the count of crashes during 1995 to 1997. with a higher collision count is not necessarily a stronger can- As the last column shows, those segments in groups which didate for safety improvement than a site with a lower count. during 1995 to 1997 had more than the average number of The upshot of this phenomenon is that the crash count by crashes in this period (0.281 crashes per year or 0.843 crashes itself is not good enough for estimating the safety of a site for in 3 years) experienced a reduction in crashes during 1998 use in identifying candidate improvement locations and in to 2000. Segments with fewer crashes than the average (i.e., estimating the safety effect of potential or implemented coun- those with 0) experienced a considerable increase. termeasures. This is why more sophisticated predictive guides These changes are due to random fluctuations in short- are needed. Evidence of regression to the mean in two other term counts that result in a phenomenon known as regression states' data used for this study is presented in Tables 43 and 44. Table 42. Wildlifevehicle crash data for Utah illustrating regression to the mean. Crashes 3 yrs Number of Crashes 1995- Crashes 1998- % difference Prior Sites 1997 2000 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

OCR for page 137
138 Table 43. Data for North Carolina illustrating regression to the mean. Crashes 3 yrs Number of Crashes 1996- Crashes 1999- % difference Prior Sites 1998 2001 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 44. Data for California illustrating regression to the mean. Crashes 3 yrs Number of Crashes 1997- Crashes 2000- % difference Prior Sites 1999 2002 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