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APPENDIX G
NCHRP 3-74 Appendix G Selection of Speed Reduction Treatments at High-Speed Intersections Speed Analysis Kittelson& Associates, Inc. Page G-1 Appendix G Speed Analysis by Individual Approach LLocation (Step 1 Analysis)) This appendix presents descriptive summaries and before-after speed comparisons for the individual data collection locations (A through D) at each intersection approach. The data analyzed here are all valid data collected at each location. No attempt was made to match vehicles driving through all locations within a given time period at a particular approach. Direct comparisons between locations (i.e., profile studies) are not warranted for this dataset as they would not compare the same driver populations. This is in contrast to the comparisons presented in Chapter 5 of the report where speed profiles across locations along an intersection approach were considered. There, great care was taken to consider only those data collection periods during which all traffic classifiers on an intersection approach (Locations A, B, C, and D) were collecting speed data. This permitted the general assumption that the same vehicles traversed all four data collection locations and that the population of vehicles at Location D were generally the same as the population of vehicles at the other locations. The speed reduction at an individual location was determined by comparing the speed data at an individual location before and after treatment installation. This comparison approach is perhaps less meaningful than those presented in the report because it estimates the effectiveness of the treatment only at a specific point along the intersection approach. The results do not provide information about speed reduction at any other point along that intersection approach; thus, no information is provided about the treatmentâs effect on the overall speed profile. However, the examination of individual location speed data and their before-after comparisons presents some insight into all the data as they were collected. Exhibit G-1 presents basic descriptive summaries of the speed data collected at each location by intersection approach, separately for the before and after treatment periods. Descriptive summaries are: ⢠number of measurements (clearly different between the two collection periods) ⢠speed range (i.e., minimum and maximum speeds) ⢠mean, median, and 85th percentile speeds ⢠speed standard deviation Exhibit G-2 summarizes the statistical comparisons of before and after speeds for each location. The normality of the speed data was first assessed visually to assess obvious departures from normality (e.g., severely skewed data, bimodal data). The next step was to compare speed variances using the modified Leveneâs test of homogeneity of variance. Based on the results of the normality assessment and the equality of variance test, the statistical approach used for comparing the center (e.g., mean, median) of the speed values for the before and after data collection periods is: ⢠Normally-distributed speed data and equal variances: a two-sample t-test with pooled variance
Appendix G NCHRP 3-74 Speed Analysis Selection of Speed Reduction Treatments at High-Speed Intersections Page G-2 Kittelson & Associates, Inc. ⢠Normally-distributed speed data and unequal variances: a two-sample t-test with weighted variance (with Satterthwaiteâs approximation of degrees of freedom [df]) ⢠Non normally-distributed (skewed or bimodal) speed data (no test of equal variance is needed): a Wilcoxon rank-sum test Each line in Exhibit G-2 presents the test results pertaining to the before-after speed comparison at a particular approach location. The individual columns are organized as follows: ⢠Columns 1, 2, and 3: Physical location ⢠Column 4 notes whether the speed data appear normally distributed ⢠Columns 5 through 7 address the issue of equal variance: o Column 5 shows the ratio of the after to before speed standard deviation o Column 6 shows the F-test statistic and its degrees of freedom (the omitted df is always 1) o Column 7 shows the p-value associated with the equality of variance test. A p- value of 0.05 or less indicates significance at the 5-percent significance level (row with p-value highlighted in yellow and bold). ⢠Columns 8 through 12 provide the comparison results of the after speed data to the before speed data; thus, a negative mean or median speed difference indicates a decrease from the before to the after period: o Column 8 shows the mean speed difference o Column 9 shown the median speed difference o Column 10 indicates which comparison test was used in accordance with the steps explained earlier o Column 11 shows the test statistic (either t-test or Wilcoxon rank sum test in accordance with Column 10 results) and its degrees of freedom The last column indicates the statistical significance level of the test statistic. A p-value of 0.05 or less indicates significance at the 5-percent significance level (row highlighted in yellow). Mean and median differences are provided in all cases; however, the statistical test to assess whether the treatment installation had an effect on speed pertains to comparing either the means or the medians. Therefore, median differences were grayed out when mean differences are the appropriate speed statistics, and vice versa. Some observations based on Exhibit G-2 follow:
NCHRP 3-74 Appendix G Selection of Speed Reduction Treatments at High-Speed Intersections Speed Analysis Kittelson& Associates, Inc. Page G-3 ⢠Of the 51 before-after speed comparisons made at individual intersection-approach locations, 40 were based on mean speed comparisons and 11 were based on median speed comparisons. ⢠Of the 51 comparisons, 34 were statistically significant at the 5-percent level (including a p-value of 0.051) with the following breakdown by location: o 8 at Location A (closest to intersection) o 10 at Location B o 10 at Location C o 6 at Location D ⢠The center of the speed values (mean or median) shifted from an increase of 1.8 mph to a decrease of 8.7 mph from before to after treatment installation. It should be noted that the decrease of 8.7 mph (Location A at WA1 eastbound) is an anomaly. The next largest decrease is 3.2 mph.
Appendix G NCHRP 3-74 Speed Analysis Selection of Speed Reduction Treatments at High-Speed Intersections Page G-4 Kittelson & Associates, Inc. Exhibit G-1 Descriptive Statistics Before Speed (mph) After Speed (mph) Site Approach Location Number of Measurements Speed Range Minimum- Maximum Mean Median 85th Percentile Standard Deviation Number of Measurements Speed Range Minimum- Maximum Mean Median 85th Percentile Standard Deviation OR1 NB A 426 8.3 - 41.5 29.3 29.8 34.2 5.2 235 10.4 - 40.2 27.6 28.1 32.9 5.4 B 419 9.9 - 48.8 35.0 35.2 40.4 5.6 234 4.6 - 50.0 33.5 34.4 39.4 6.3 C 419 8.2 - 64.9 44.7 45.3 52.3 8.0 230 8.6 - 68.3 43.8 44.5 52.1 9.2 D 385 16.4 - 77.8 52.4 53.1 61.2 8.6 234 12.9 - 83.4 51.4 51.9 59.5 9.7 EB A 679 10.7 - 55.0 30.6 29.9 37.6 6.6 439 7.8 - 56.5 28.3 27.4 34.6 6.4 B 675 12.7 - 57.6 37.1 37.2 42.3 5.6 443 6.1 - 58.3 35.0 35.5 40.8 6.6 C 677 12.1 - 63.3 44.7 44.9 50.3 5.9 429 7.2 - 59.0 41.7 42.4 48.1 7.1 D 159 27.5 - 72.2 49.2 49.4 55.5 6.7 432 14.1 - 72.0 47.4 48.5 54.1 8.1 OR2 NB A 1,457 4.3 - 65.2 37.6 38.8 49.6 11.4 1,023 11.4 - 67.8 38.0 39.5 49.2 10.5 C 1,399 16.7 - 66.0 47.4 47.7 53.7 6.3 971 10.8 - 72.8 47.2 47.5 53.0 6.4 D 1,278 10.4 - 65.5 46.8 47.5 52.4 6.3 850 15.3 - 65.1 47.1 47.5 52.1 5.7 SB A 493 17.2 - 70.0 42.0 43.7 51.1 9.3 572 13.4 - 60.5 40.2 41.5 48.7 8.7 B 1,432 12.3 - 69.5 42.6 43.6 50.1 7.9 770 16.1 - 60.6 42.1 42.7 49.1 7.2 C 1,322 14.1 - 73.2 48.5 48.8 54.0 6.0 769 4.7 - 66.2 47.7 48.2 53.5 6.2 D 1,308 15.5 - 75.8 49.8 50.0 55.1 5.7 770 21.3 - 70.0 49.0 49.2 54.9 5.9 OR3 EB A 1,381 7.0 - 68.4 45.3 47.7 53.1 9.1 780 8.1 - 67.5 44.9 46.9 52.3 8.5 B 1,352 8.3 - 90.2 46.9 47.9 53.0 7.2 1,183 6.6 - 68.1 46.2 47.0 52.4 6.7 C 1,356 14.5 - 71.2 48.9 49.1 54.0 5.5 1,131 8.6 - 68.1 48.2 48.5 53.3 5.5 D 1,336 18.0 - 71.4 49.6 49.8 54.6 5.6 1,097 5.4 - 74.0 49.3 49.9 54.6 6.4
NCHRP 3-74 Appendix G Selection of Speed Reduction Treatments at High-Speed Intersections Speed Analysis Kittelson& Associates, Inc. Page G-5 Before Speed (mph) After Speed (mph) Site Approach Location Number of Measurements Speed Range Minimum- Maximum Mean Median 85 th Percentile Standard Deviations Number of Measurements Speed Range Minimum- Maximum Mean Median 85 th Percentile Speed Range Minimum- Maximum OR4 WB B 1,349 9.6 - 74.3 52.6 53.3 58.2 6.5 1,072 19.6 - 73.0 51.2 51.8 56.7 6.3 C 1,352 16.0 - 77.4 52.0 52.4 57.5 6.7 1,443 3.9 - 105.0 50.6 51.4 57.0 8.2 D 1,366 5.0 - 78.5 54.8 55.4 60.5 7.0 1,480 4.6 - 78.5 53.6 54.4 59.7 7.5 OR6 EB A 822 13.5 - 66.6 51.5 54.0 58.5 9.4 1,029 15.0 - 74.4 53.1 54.7 59.0 8.2 B 852 23.2 - 66.4 52.7 54.1 58.6 6.8 1,065 5.4 - 76.7 53.6 54.8 59.3 6.9 C 918 8.9 - 71.6 55.9 56.2 60.4 4.9 1,126 14.8 - 76.7 56.3 56.4 60.6 5.0 WB A 1,139 4.7 - 69.2 51.0 52.9 58.6 8.3 668 12.6 - 68.7 51.8 53.6 59.8 8.0 B 1,079 13.5 - 74.2 53.3 54.0 59.4 6.4 759 33.6 - 66.7 52.2 53.0 58.0 5.7 C 1,212 7.2 - 73.3 55.5 55.9 60.4 5.7 762 37.7 - 71.9 55.5 55.7 60.1 4.9 D 1,232 15.3 - 76.2 54.5 56.6 61.4 9.6 821 17.6 - 76.9 53.5 55.6 60.0 9.5 TX1 SB A 1,684 19.0 - 78.8 57.5 59.2 67.6 10.6 1,670 20.1 - 80.7 57.4 58.7 67.4 10.2 B 1,329 16.5 - 79.1 59.4 60.4 68.3 8.6 1,842 33.5 - 81.4 58.9 59.6 67.9 8.5 C 1,692 20.1 - 80.0 63.3 63.7 69.8 6.5 1,828 13.2 - 89.5 62.6 62.9 70.2 7.3 D 1,721 35.6 - 85.2 65.9 66.7 71.8 6.3 1,404 22.6 - 110.0 65.9 66.9 71.9 6.5 TX2 NB A 660 10.1 - 81.4 54.8 56.2 63.4 10.3 1,588 10.4 - 104.6 56.3 57.0 63.9 9.2 B 795 12.2 - 81.8 55.8 56.9 63.4 9.0 356 18.9 - 74.8 56.5 57.0 63.6 7.9 C 1,112 14.4 - 84.5 60.1 60.7 67.2 7.6 1,806 16.7 - 93.8 60.5 61.6 67.9 8.5 D 342 22.0 - 82.1 64.9 65.7 71.4 7.3 998 20.9 - 87.4 66.3 67.0 72.1 6.3 SB A 575 10.3 - 80.9 54.9 56.0 63.3 10.0 1,077 15.2 - 76.6 54.3 55.6 63.1 10.4 B 295 13.6 - 78.5 53.8 55.2 62.3 10.3 290 24.6 - 77.9 55.6 56.4 62.1 8.3 C 741 10.8 - 87.6 58.7 58.8 65.4 7.3 1,450 15.3 - 97.1 58.8 59.0 66.2 8.1
Appendix G NCHRP 3-74 Speed Analysis Selection of Speed Reduction Treatments at High-Speed Intersections Page G-6 Kittelson & Associates, Inc. Before Speed (mph) After Speed (mph) Site Approach Location Number of Measurements Speed Range Minimum- Maximum Mean Median 85 th Percentile Standard Deviation Number of Measurements Speed Range Minimum- Maximum Mean Median 85 th Percentile Standard Deviation D 832 10.6 - 96.4 66.2 67.4 71.9 7.7 1,160 21.6 - 105.3 66.3 67.2 71.6 6.5 TX4 WB B 432 24.5 - 84.1 52.0 52.4 58.4 7.3 816 12.0 - 67.4 49.1 50.5 55.9 7.1 C 1,029 23.7 - 71.6 53.6 53.9 58.6 5.4 796 18.0 - 80.7 51.6 52.4 56.9 6.0 D 439 14.7 - 73.9 55.1 55.3 60.4 5.5 781 19.6 - 78.2 54.5 54.7 60.3 6.1 WA1 EB A 557 16.5 - 65.3 42.4 43.4 50.6 8.3 99 6.2 - 53.7 34.8 34.7 44.0 9.4 B 1,036 8.5 - 65.9 47.4 47.8 53.2 6.0 352 9.1 - 64.9 44.2 44.9 51.0 7.1 C 959 16.0 - 84.5 48.2 48.4 53.7 6.4 614 4.5 - 89.6 45.3 46.0 51.9 7.7 WB A 793 4.6 - 62.4 43.1 43.3 50.3 7.3 855 3.4 - 95.4 42.3 42.4 49.0 7.0 B 836 10.1 - 94.1 47.5 47.5 52.9 7.6 480 4.2 - 98.7 45.4 46.0 50.9 6.7 C 539 10.3 - 69.8 49.5 49.6 54.6 6.1 879 4.0 - 68.3 47.0 47.8 52.4 7.0 D 564 11.5 - 70.8 51.8 51.8 56.8 6.2 563 14.4 - 70.5 50.6 50.6 56.0 6.1
NCHRP 3-74 Appendix G Selection of Speed Reduction Treatments at High-Speed Intersections Speed Analysis Kittelson& Associates, Inc. Page G-7 Exhibit G-2 Analysis by Location Site Approach Location Distribution Normal? After/Before Std Dev F-statistic (df) P-Value Mean Difference (mph) Median Difference (mph) Selected test T-statistic (df) P-Value OR1 NB A Yes 0.96 0.77 (659) 0.382 -1.7 -1.7 Equal var. t-test 3.90 (659) <.001 B Yes 0.89 1.19 (651) 0.275 -1.4 -0.8 Equal var. t-test 2.98 (651) 0.003 C Yes 0.87 0.66 (647) 0.416 -0.9 -0.8 Equal var. t-test 1.30 (647) 0.194 D Yes 0.89 0.39 (617) 0.534 -1.0 -1.2 Equal var. t-test 1.29 (617) 0.197 EB A Yes 1.03 1.87 (1,116) 0.172 -2.3 -2.5 Equal var. t-test 5.84 (1,116) <.001 B Yes 0.84 7.44 (1,116) 0.006 -2.1 -1.7 Unequal var. t-test 5.64 (833) <.001 C Yes 0.83 6.29 (1,104) 0.012 -3.0 -2.4 Unequal var. t-test 7.18 (787) <.001 D Yes 0.83 3.20 (589) 0.074 -1.8 -1.0 Equal var. t-test 2.53 (589) 0.012 OR2 NB A No 1.09 10.96 (2,478) <.001 0.4 0.7 Wilcoxon rank sum test 0.66 (2,478) 0.509 C Yes 0.99 0.01 (2,368) 0.905 -0.2 -0.2 Equal var. t-test 0.79 (2,368) 0.427 D Yes 1.11 1.30 (2,126) 0.254 0.2 0.0 Equal var. t-test -0.89 (2,126) 0.374 SB A No 1.08 3.90 (1,063) 0.049 -1.8 -2.2 Wilcoxon rank sum test 3.42 (1,063) <.001 B No 1.10 4.02 (2,200) 0.045 -0.5 -0.9 Wilcoxon rank sum test 1.52 (2,200) 0.129 C Yes 0.97 0.02 (2,089) 0.876 -0.8 -0.6 Equal var. t-test 2.95 (2,089) 0.003 D Yes 0.97 1.77 (2,076) 0.183 -0.8 -0.8 Equal var. t-test 3.01 (2,076) 0.003 OR3 EB A No 1.06 1.17 (2,159) 0.280 -0.5 -0.8 Wilcoxon rank sum test 1.46 (2,159) 0.144
Appendix G NCHRP 3-74 Speed Analysis Selection of Speed Reduction Treatments at High-Speed Intersections Page G-8 Kittelson & Associates, Inc. Site Approach Location Distribution Normal? After/Before Std Dev F-statistic (df) P-Value Mean Difference (mph) Median Difference (mph) Selected test T-statistic (df) P-Value B Yes 1.08 0.02 (2,533) 0.880 -0.8 -0.9 Equal var. t-test 2.80 (2,533) 0.005 C Yes 1.00 0.04 (2,485) 0.834 -0.7 -0.6 Equal var. t-test 3.07 (2,485) 0.002 D Yes 0.88 0.28 (2,431) 0.595 -0.3 0.1 Equal var. t-test 1.15 (2,431) 0.249 OR4 WB B Yes 1.04 0.03 (2,419) 0.866 -1.4 -1.5 Equal var. t-test 5.35 (2,419) <.001 C No 0.82 9.64 (2,793) 0.002 -1.4 -1.0 Wilcoxon rank sum test 5.17 (2,793) <.001 D Yes 0.94 1.04 (2,844) 0.308 -1.2 -1.0 Equal var. t-test 4.33 (2,844) <.001 OR6 EB A No 1.15 6.98 (1,849) 0.008 1.6 0.7 Wilcoxon rank sum test 3.67 (1,849) <.001 B No 0.97 0.41 (1,915) 0.521 0.9 0.7 Wilcoxon rank sum test 3.34 (1,915) <.001 C Yes 0.97 0.00 (2,042) 0.992 0.4 0.2 Equal var. t-test -1.95 (2,042) 0.051 WB A Yes 1.04 0.15 (1,805) 0.702 0.8 0.7 Equal var. t-test -1.97 (1,805) 0.050 B Yes 1.13 1.96 (1,836) 0.162 -1.1 -1.0 Equal var. t-test 3.94 (1,836) <.001 C Yes 1.15 3.90 (1,972) 0.048 0.0 -0.2 Unequal var. t-test -0.16 (1,782) 0.875 D No 1.02 0.16 (2,051) 0.689 -1.0 -0.9 Wilcoxon rank sum test 3.12 (2,051) 0.002 TX1 SB A No 1.03 0.34 (3,352) 0.560 -0.1 -0.5 Wilcoxon rank sum test 0.65 (3,352) 0.518 B Yes 1.02 1.14 (3,169) 0.285 -0.5 -0.8 Equal var. t-test 1.67 (3,169) 0.095 C Yes 0.90 24.95 (3,518) <.001 -0.8 -0.8 Unequal var. t-test 3.28 (3,515) 0.001
NCHRP 3-74 Appendix G Selection of Speed Reduction Treatments at High-Speed Intersections Speed Analysis Kittelson& Associates, Inc. Page G-9 Site Approach Location Distribution Normal? After/Before Std Dev F-statistic (df) P-Value Mean Difference (mph) Median Difference (mph) Selected test T-statistic (df) P-Value D Yes 0.97 0.00 (3,123) 0.953 -0.1 0.2 Equal var. t-test 0.33 (3,123) 0.744 TX2 NB A Yes 1.11 6.67 (2,246) 0.010 1.5 0.8 Unequal var. t-test -3.27 (1,121) 0.001 B Yes 1.14 2.22 (1,149) 0.137 0.8 0.1 Equal var. t-test -1.36 (1,149) 0.175 C Yes 0.89 3.38 (2,916) 0.066 0.3 0.9 Equal var. t-test -1.01 (2,916) 0.310 D Yes 1.15 1.35 (1,338) 0.246 1.3 1.3 Equal var. t-test -3.19 (1,338) 0.001 SB A No 0.97 1.69 (1,650) 0.193 -0.6 -0.4 Wilcoxon rank sum test 1.13 (1,650) 0.257 B Yes 1.23 7.66 (583) 0.006 1.8 1.1 Unequal var. t-test -2.39 (563) 0.017 C Yes 0.91 4.75 (2,189) 0.029 0.1 0.2 Unequal var. t-test -0.28 (1,627) 0.777 D Yes 1.19 2.09 (1,990) 0.148 0.1 -0.1 Equal var. t-test -0.34 (1,990) 0.730 TX4 WB B Yes 1.02 0.00 (1,246) 0.945 -2.8 -1.9 Equal var. t-test 6.66 (1,246) <.001 C Yes 0.89 4.73 (1,823) 0.030 -2.0 -1.5 Unequal var. t-test 7.27 (1,599) <.001 D Yes 0.90 6.20 (1,218) 0.013 -0.6 -0.6 Unequal var. t-test 1.69 (989) 0.091 WA1 EB A No 0.88 0.05 (654) 0.822 -7.6 -8.7 Wilcoxon rank sum test 7.71 (654) <.001 B Yes 0.84 7.71 (1,386) 0.006 -3.2 -2.9 Unequal var. t-test 7.57 (530) <.001 C Yes 0.83 8.27 (1,571) 0.004 -2.9 -2.4 Unequal var. t-test 7.85 (1,128) <.001 WB A Yes 1.04 0.30 (1,646) 0.584 -0.9 -0.9 Equal var. t-test 2.42 (1,646) 0.016 B Yes 1.14 4.89 (1,314) 0.027 -2.1 -1.5 Unequal var. t-test 5.16 (1,106) <.001 C Yes 0.87 1.47 (1,416) 0.225 -2.5 -1.8 Equal var. t-test 6.79 (1,416) <.001 D Yes 1.03 0.31 (1,125) 0.577 -1.2 -1.2 Equal var. t-test 3.40 (1,125) <.001
