Accident Models for Two-Lane Rural Roads: Segment and Intersections
4. Analysis
Univariate Statistics
Tables 2 through 7 indicate the behavior of the chief variables on the six data sets: segments, three-legged intersections, and four-legged intersections in both Minnesota and Washington. It is instructive to make comparisons among these tables and in the case of Minnesota to compare the sample data with the population data in Appendix 1.
Minnesota versus Washington
Accidents tend to be more serious in Washington State than in Minnesota for segments and intersections, and the accident rate (accidents per MVM) on segments is much higher in Washington than in Minnesota. The accident rates appear to be comparable in the two States on intersections, but this may be somewhat misleading since the conflict index is lower for Washington than Minnesota. There also appears to be a higher percentage of run-off-road accidents in Washington. (This may be due to the indirect method employed to count Washington run-off-road
accidents.)
There is more traffic in Washington on segments and major intersection approaches, and a higher density of driveways. Both of these suggest that the Washington data sets are less rural than those of Minnesota. Annual exposure (MVM per year) is about the same on average in both States, and this is accounted for by the fact that segment lengths are shorter on average in Washington.
Roadside Hazard Rating tends to be higher in Washington, with steeper grades. Washington averages for horizontal and vertical alignment are the same as or higher than Minnesota's, but Washington tends to have fewer curves than Minnesota both on segments and in the vicinity of intersections. This may reflect historical differences in highway design practice and/or in the principles used to label roadway segments as segments. Likewise, Minnesota appears to have more angular variation at intersections than Washington (perhaps due in part to data shortcomings),
and more turning lanes on the major road. Minnesota has wider shoulders than Washington, but Washington has more that are paved. These differences may also reflect design considerations and history.
Segments versus Intersections
Accidents at intersections tend to be more serious than those on segments, and accidents at intersections are more frequent (if an intersection is regarded as a segment 500 feet long), other things being equal. ADT rises as one goes from segments to major roads of three-legged intersections to major roads of four-legged intersections. The tables also show that three-leggeds tend to have more horizontal curvature than four-leggeds, but that vertical alignment tends to be about the same in three-leggeds and four-leggeds.
Minnesota Sample versus Population
The Minnesota samples are quite comparable in the distribution of severities and the percentage of run-off-road accidents to their counterparts in the Minnesota populations represented in Appendix 1. With respect to segments, we can also compare ADT, commercial vehicle percentage, and lane width and find that they are quite similar between the sample and the population. Shoulder width and shoulder type between sample and population are also similar although there seems to be a slight tendency for the population of segments to have less shoulder
width (albeit more of it paved) than the sample does.
Table 2. Summary Statistics: 619 Segments, Minnesota State
Two-Lane Rural Roads, 1985 -1989
Variable and Abbreviation
|
Min.
|
Max.
|
Median
|
Mean
|
Freq
|
%Zero
|
Total Number of Accidents (TOTACC)
|
0
|
58
|
1
|
2.74
|
1694
|
36.3
|
Total Number of Injury Accidents (INJACC)
|
0
|
23
|
0
|
0.99
|
614 (36.25%)
|
58.3
|
Total Number of Run-Off-Road Accidents (RORACC)
|
0
|
15
|
0
|
0.88
|
547 (32.29%)
|
61.6
|
Severity: Fatal = K
Injury = A
Non-incap= B
Poss-inj = C
Prop-dam = P
|
|
|
|
|
32 (1.9%)
89 (5.2%)
256 (15.1%)
237 (14.0%)
1080 (63.7%)
|
|
Accident Rate (0.6656 TOTACC/MVM)
|
0
|
9.32
|
0.44
|
0.70
|
|
36.3
|
Injury Accident Rate (0.2413 INJACC/MVM)
|
0
|
4.66
|
0
|
0.25
|
|
58.3
|
Average Daily Traffic = ADT
|
208
|
15,162
|
1,866
|
2,402
|
|
|
Segment Length = seg_lng (miles)
|
0.1
|
8.237
|
0.659
|
1.14
|
|
|
Exposure over five years = EXPO (MVM)
|
0.13
|
68.32
|
2.25
|
4.11
|
|
|
Commercial Vehicle Percentage = T (%)
|
1.90
|
26.86
|
9.87
|
10.45
|
|
|
Lane Width = LW (feet)
|
10
|
12
|
12
|
11.54
|
|
|
Shoulder Width = SHW (feet)
|
0
|
12
|
8
|
7.08
|
|
0.3
|
Shoulder Type None
Gravel or Stone
Composite
Paved
|
|
|
|
|
2 (0.3%)
341 (55.1%)
35 (5.7%)
241 (38.9%)
|
|
1 mi = 1.61 km, 1 ft = 0.3048 m
Table 2. Summary Statistics: 619 Segments, Minnesota State
(continued)
Two-Lane Rural Roads, 1985 -1989
Variable and Abbreviation
|
Min.
|
Max.
|
Median
|
Mean
|
Freq
|
%Zero
|
Roadside Hazard Rating = RHR = 1
2
3
4
5
6, 7
|
1
|
6
|
2
|
2.14
|
174 (28.1%)
248 (40.1%)
141 (22.8%)
48 (7.8%)
6 (1%)
2 (0.3%), 0
|
|
Driveway Density = DD
|
0
|
100
|
3.73
|
6.58
|
|
22.5
|
Intersection Density = INTD
|
0
|
22.7
|
1.14
|
2.60
|
|
31.7
|
Light Yes
No
|
|
|
|
|
5 (0.8%)
614 (99.2%)
|
|
Terrain Flat
Rolling
Mountainous
Missing (not noted)
|
|
|
|
|
249 (46.2%)
28 (4.5%)
1 (0.2%)
341 (55.5%)
|
|
Degree of Curve = H = 3WH{i}DEG{i}
|
0
|
7.50
|
0.078
|
0.51
|
|
33.4
|
Crest Curve Grade rate = VC = 3WV{i}(|Dg{i}|/l{i})
(crests only)
|
0
|
0.89
|
0.037
|
0.067
|
|
16.5
|
Absolute Grade = GR = 3WG{i}GR{i} (%)
|
0
|
4.46
|
0.24
|
0.38
|
|
1.9
|
Speed = SPD (mph)
|
20
|
55
|
55
|
48.7
|
|
|
Snow Percentage = SNP
|
22.9
|
36.9
|
32.5
|
29.4
|
|
|
Non-dry Percentage = NONDRYP
|
41.0
|
56.6
|
45.5
|
47.4
|
|
|
1 mi = 1.61 km, 1 ft = 0.3048 m
Table 3. Summary Statistics: 712 Segments, Washington State
Two-Lane Rural Roads, 1993 -1995
Variable and Abbreviation
|
Min.
|
Max.
|
Median
|
Mean
|
Freq
|
%Zero
|
Total Number of Accidents (TOTACC)
|
0
|
29
|
1
|
2.40
|
1706
|
37.6
|
Total Number of Injury Accidents (INJACC)
|
0
|
13
|
0
|
1.11
|
790 (46.31%)
|
53.8
|
Total Number of Run-Off-Road Accidents (RORACC)
|
0
|
19
|
1
|
1.39
|
993 (58.21%)
|
48.6
|
Severity: Fatal = K
Injury = A
Non-incap = B
Poss-inj = C
Prop-dam = P
|
|
|
|
|
39 (2.3%)
130 (7.6%)
381 (22.3%)
240 (14.1%)
916 (53.7%)
|
|
Accident Rate (1.0228 TOTACC/MVM)
|
0
|
33.60
|
0.649
|
1.096
|
|
37.6
|
Injury Accident Rate (0.4736 INJACC/MVM)
|
0
|
9.65
|
0
|
0.495
|
|
53.8
|
Average Daily Traffic = ADT
|
159
|
17,766
|
2,239
|
3,352
|
|
|
Segment Length = seg_lng (miles)
|
0.1
|
13.233
|
0.554
|
0.75
|
|
|
Exposure over three years = EXPO (MVM)
|
0.04
|
22.4
|
1.31
|
2.34
|
|
|
Commercial Vehicle Percentage = T (%)
|
1.55
|
52.22
|
11.73
|
13.04
|
|
|
Lane Width = LW (feet)
|
9
|
12
|
11
|
11.37
|
|
|
Shoulder Width = SHW (feet)
|
0
|
10
|
5
|
5.01
|
|
0.8
|
Shoulder Type Missing or other
Gravel or Stone
Composite
Paved
|
|
|
|
|
8 (1.1%)
72 (10.1%)
230 (32.3%)
402 (56.5%)
|
|
1 mi = 1.61 km, 1 ft = 0.3048 m
Table 3. Summary Statistics: 712 Segments, Washington State
(continued)
Two-Lane Rural Roads, 1993 -1995
Variable and Abbreviation
|
Min.
|
Max.
|
Median
|
Mean
|
Freq
|
%Zero
|
Roadside Hazard Rating = RHR = 1
2
3
4
5
6
7
|
1
|
7
|
3
|
3.67
|
38 (5.3%)
152 (21.4%)
181 (25.4%)
109 (15.3%)
128 (18.0%)
73 (10.3%)
31 (4.4%)
|
|
Driveway Density = DD
|
0
|
85.07
|
6.12
|
10.12
|
|
18.1
|
Intersection Density = INTD
|
0
|
17.3
|
0
|
0.12
|
|
97.5
|
Light Yes
No
|
|
|
|
|
21 (2.9%)
691 (97.1%)
|
|
Terrain Flat
Rolling
Mountainous
|
|
|
|
|
157 (22.1%)
485 (68.1%)
70 (9.8%)
|
|
Degree of Curve = H = 3WH{i}DEG{i}
|
0
|
30.55
|
0.319
|
1.028
|
|
36.7
|
Crest Curve Grade rate = VC = 3WV{i}(|Dg{i}|/l{i})
(crests only)
|
0
|
1.997
|
0.026
|
0.068
|
|
36.8
|
Absolute Grade = GR = 3WG{i}GR{i} (%)
|
0
|
6.92
|
0.494
|
0.92
|
|
13.1
|
Speed = SPD (mph)
|
21.9
|
55
|
55
|
50.5
|
|
|
1 mi = 1.61 km, 1 ft = 0.3048 m
Table 4. Summary Statistics: 389 Three-Legged Intersections,
Minnesota State
Two-Lane Rural Roads, 1985 - 1989
Variable and Abbreviation
|
Min.
|
Max.
|
Median
|
Mean
|
Freq
|
%Zero
|
Total Number of Accidents (TOTACC)
|
0
|
39
|
0
|
1.35
|
524
|
51.9
|
Total Number of Injury Accidents (INJACC)
|
0
|
17
|
0
|
0.59
|
229 (43.70%)
|
69.9
|
Total Number of Run-Off-Road Accidents (RORACC)
|
0
|
4
|
0
|
0.12
|
45 (8.59%)
|
90.7
|
Severity: Fatal = K
Injury = A
Non-incap = B
Poss-inj = C
Prop-dam = P
|
|
|
|
|
8 (1.5%)
26 (5.0%)
84 (16.0%)
111 (21.2%)
295 (56.3%)
|
|
Accident Rate (TOTACC per million entering vehicles)
|
0
|
3.08
|
0
|
0.16
|
|
51.9
|
Accident Rate (0.269 TOTACC /YEAR)
|
0
|
7.8
|
0
|
0.269
|
|
51.9
|
Injury Accident Rate (0.118 INJACC/YEAR)
|
0
|
0.8
|
0
|
0.118
|
|
69.9
|
Average Daily Traffic on Major Road = ADT1
|
201
|
19,413
|
2,313
|
3,687
|
|
|
Average Daily Traffic on Minor Road = ADT2
|
4.5
|
4,206
|
240
|
413
|
|
|
Conflict Index = CINDEX
|
0.002
|
0.442
|
0.049
|
0.077
|
|
|
Angular Deviation from 90° = DEV (degrees)
|
0
|
90
|
0
|
13.4
|
|
50.6
|
Roadside Hazard Rating = RHRI = 1
2
3
4
5
6,7
|
1
|
5
|
2
|
2.11
|
98 (25.2%)
184 (47.3%)
74 (19.0%)
32 (8.2 %)
1 (0.3%)
0 (0.0%)
|
|
Number of Driveways = ND
|
0
|
9
|
1
|
1.26
|
|
37.5
|
1 mi = 1.61 km, 1 ft = 0.3048 m
Table 4. Summary Statistics: 389 Three-Legged Intersections,
Minnesota State (continued)
Two-Lane Rural Roads, 1985 - 1989
Variable and Abbreviation
|
Min.
|
Max.
|
Median
|
Mean
|
Freq
|
%Zero
|
Light Yes
No
|
|
|
|
|
1 (0.3%)
388 (99.7%)
|
|
Terrain Flat
Rolling
Missing (not noted)
|
|
|
|
|
115 (29.6%)
28 (7.2%)
246 (63.2%)
|
|
Degree of Curve = HI = (1/n)3DEG{i}
|
0
|
29
|
0
|
1.21
|
|
54.0
|
Crest Curve Grade Rate = VCI = (1/m)3(|Dg{i}|/l{i})
(crests only)
|
0
|
4.39
|
0
|
0.14
|
|
52.7
|
Speed = SPDI (mph)
|
22.5
|
55
|
55
|
52.7
|
|
|
Turning Lanes on Main Road None
Right Turn
Bypass Lane
Both
|
|
|
|
|
216 (55.5%)
119 (30.6%)
8 (2.1%)
46 (11.8%)
|
|
Right Turn/Acceleration Lane on Minor Leg Yes
No
|
|
|
|
|
8 (2.1%)
381 (97.9%)
|
|
Snow Percentage = SNP
|
22.9
|
36.9
|
28.4
|
29.1
|
|
|
Non-dry Percentage = NONDRYP
|
41.0
|
55.6
|
46.7
|
47.5
|
|
|
1 mi = 1.61 km, 1 ft = 0.3048 m
Table 5. Summary Statistics: 181 Three-Legged Intersections,
Washington State
Two-Lane Rural Roads, 1993 - 1995
Variable and Abbreviation
|
Min.
|
Max.
|
Median
|
Mean
|
Freq
|
%Zero
|
Total Number of Accidents (TOTACC)
|
0
|
9
|
0
|
1.02
|
184
|
58.6
|
Total Number of Injury Accidents (INJACC)
|
0
|
7
|
0
|
0.470
|
85 (46.20%)
|
72.4
|
Total Number of Run-Off-Road Accidents (RORACC)
|
0
|
5
|
0
|
0.204
|
37 (20.11%)
|
85.1
|
Severity: Fatal = K
Injury = A
Non-incap = B
Poss-inj = C
Prop-dam = P
|
|
|
|
|
2 (1.1%)
12 (6.5%)
37 (20.1%)
34 (18.5%)
99 (53.8%)
|
|
Accident Rate (TOTACC per million entering vehicles)
|
0 |
1.00 |
0 |
0.135 |
|
58.6 |
Accident Rate (0.339 TOTACC/YEAR) |
0 |
3 |
0 |
0.339 |
|
58.6 |
Injury Accident Rate (0.157 INJACC/YEAR) |
0 |
2.333 |
0 |
0.157 |
|
72.4 |
Average Daily Traffic on Major Road = ADT1 |
897 |
15,995 |
4,838 |
5,780 |
|
|
Average Daily Traffic on Minor Road = ADT2 |
4 |
7,529 |
196 |
573 |
|
|
Conflict Index = CINDEX |
0.0003 |
0.366 |
0.020 |
0.052 |
|
|
Angular Deviation from 90° = DEV (degrees) |
0 |
55 |
0 |
8.93 |
|
95.6 |
Roadside Hazard Rating = RHRI = 1
2
3
4
5
6, 7
|
1 |
6 |
3 |
3.3 |
7 (3.9%)
39 (21.5%)
51 (28.2%)
61 (33.7%)
21 (11.6%)
2 (1.1%), 0 (0.0%) |
|
Number of Driveways = ND |
0 |
12 |
1 |
1.486 |
|
37.0 |
1 mi = 1.61 km, 1 ft = 0.3048 m
Table 5. Summary Statistics: 181 Three-Legged Intersections,
Washington State (continued)
Two-Lane Rural Roads, 1993 - 1995
Variable and Abbreviation
|
Min.
|
Max.
|
Median
|
Mean
|
Freq
|
%Zero
|
Light Yes
No
|
|
|
|
|
35 (19.3%)
146 (80.7%)
|
|
Terrain Flat
Rolling
Mountainous
|
|
|
|
|
42 (23.2%)
124 (68.5%)
15 (8.3%)
|
|
Degree of Curve = HI = (1/n)3DEG{i}
|
0
|
22.2
|
0
|
1.22
|
|
68.0
|
Crest Curve Grade Rate = VCI = (1/m)3(|Dg{i}|/l{i})
(crests only)
|
0
|
4.32
|
0
|
0.16
|
|
68.0
|
Speed = SPDI (mph)
|
23.75
|
55
|
55
|
52.1
|
|
|
Turning Lanes on Main Road None
Right Turn
Bypass Lane
Both
|
|
|
|
|
143 (79.0%)
12 (6.6%)
12 (6.6%)
14 (7.7%)
|
|
Right Turn/Acceleration Lane on Minor Leg Yes No
|
|
|
|
|
4 (2.2%)
177 (97.8%)
|
|
1 mi = 1.61 km, 1 ft = 0.3048 m
Table 6. Summary Statistics: 327 Four-Legged Intersections,
Minnesota State
Two-Lane Rural Roads, 1985 - 1989
Variable and Abbreviation |
Min.
|
Max.
|
Median
|
Mean
|
Freq
|
%Zero
|
Total Number of Accidents (TOTACC) |
0 |
16 |
1 |
1.51 |
494 |
39.8 |
Total Number of Injury Accidents (INJACC) |
0 |
9 |
0 |
0.77 |
253 (51.2%) |
59.9 |
Total Number of Run-Off-Road Accidents (RORACC) |
0 |
2 |
0 |
0.092 |
30 (6.1%) |
92.4 |
Severity: Fatal = K
Injury = A
Non-incap = B
Poss-inj = C
Prop-dam = P |
|
|
|
|
18 (3.6%)
40 (8.1%)
96 (19.4%)
99 (20.0%)
241 (48.8%) |
|
Accident Rate (TOTACC per million entering
vehicles) |
0 |
2.87 |
0.201 |
0.323 |
|
39.8 |
Accident Rate (0.302 TOTACC/YEAR) |
0 |
3.2 |
0.2 |
0.302 |
|
39.8 |
Injury Accident Rate (0.155 INJACC/YEAR) |
0 |
1.8 |
0 |
0.155 |
|
59.9 |
Average Daily Traffic on Major Road = ADT1 |
174 |
14,611 |
2,620 |
2,238 |
|
|
Average Daily Traffic on Minor Road = ADT2 |
6.9 |
3,414 |
192 |
308 |
|
|
Conflict Index = CINDEX |
0.003 |
0.637 |
0.103 |
0.142 |
|
|
Angular Deviation from 90° = DEV(degrees)
|
0
|
75
|
0.6
|
9.9
|
|
37.6
|
Roadside Hazard Rating = RHRI = 1
2
3
4
5
6, 7
|
1
|
6
|
2
|
2.02
|
97 (29.7%)
157 (48.0%)
51 (15.6%)
16 (4.9%)
5 (1.5%)
1 (0.3%), 0 (0.0%)
|
|
Number of Driveways = ND
|
0
|
6
|
0
|
0.62
|
|
67.6
|
1 mi = 1.61 km, 1 ft = 0.3048 m
Table 6. Summary Statistics: 327 Four-Legged Intersections,
Minnesota State (continued)
Two-Lane Rural Roads, 1985 - 1989
Variable and Abbreviation
|
Min.
|
Max.
|
Median
|
Mean
|
Freq
|
%Zero
|
Light Yes
No
|
|
|
|
|
1 (0.3%)
326 (99.7%)
|
|
Terrain Flat
Rolling
Missing (not noted)
|
|
|
|
|
166 (50.8%)
20 (6.1%)
141 (43.1%)
|
|
Degree of Curve = HI = (1/n)3DEG{i}
|
0
|
9
|
0
|
0.49
|
|
59.9
|
Crest Curve Grade Rate = VCI = (1/m)3(|Dg{i}|/l{i})
(crests only)
|
0
|
2.94
|
0.025
|
0.152
|
|
48.0
|
Speed = SPDI (mph)
|
30
|
55
|
55
|
54.0
|
|
|
Right Turn Lanes on Main Road
None
One Right Turn
Two Right Turns
|
|
|
|
|
155 (47.4%)
30 (9.2%)
142 (43.4%)
|
|
Right Turn/Acceleration Lanes on Minor Legs None
Both
|
|
|
|
|
326 (99.7%)
1 (0.3%)
|
|
1 mi = 1.61 km, 1 ft = 0.3048 m
Table 7. Summary Statistics: 90 Four-Legged Intersections,
Washington State
Two-Lane Rural Roads, 1993 - 1995
Variable and Abbreviation
|
Min.
|
Max.
|
Median
|
Mean
|
Freq
|
%Zero
|
Total Number of Accidents (TOTACC)
|
0
|
18
|
1
|
2.83
|
255
|
42.2
|
Total Number of Injury Accidents (INJACC)
|
0
|
13
|
0
|
1.77
|
159 (62.35%)
|
53.3
|
Total Number of Run-Off-Road Accidents (RORACC)
|
0
|
2
|
0
|
0.24
|
22 (8.63%)
|
78.9
|
Severity: Fatal = K
Injury = A
Non-incap = B
Poss-inj = C
Prop-dam = P
|
|
|
|
|
5 (2.0%)
20 (7.8%)
72 (28.2%)
62 (24.3%)
96 (37.6%)
|
|
Accident Rate (TOTACC per million entering vehicles)
|
0 |
1.73 |
0.131 |
0.328 |
|
42.2 |
Accident Rate (0.944 TOTACC/YEAR) |
0 |
6 |
0.333 |
0.944 |
|
42.2 |
Injury Accident Rate (0.589 INJACC/YEAR) |
0 |
4.33 |
0 |
0.589 |
|
78.9 |
Average Daily Traffic on Major Road = ADT1
|
1,143 |
17,205 |
6,540 |
7,381 |
|
|
Average Daily Traffic on Minor Road = ADT2
|
6 |
3,165 |
416 |
718 |
|
|
Conflict Index = CINDEX |
0.001 |
0.480 |
0.0646 |
0.0934 |
|
|
Angular Deviation from 90° = DEV(degrees)
|
0
|
45
|
0
|
2.47
|
|
88.9
|
Roadside Hazard Rating = RHRI = 1
2
3
4
5
6, 7
|
1
|
5
|
3
|
2.82
|
9 (10.0%)
23 (25.6%)
38 (42.2%)
15 (16.7%)
5 (5.6%)
0 (0.0%), 0 (0.0%)
|
|
Number of Driveways = ND
|
0
|
7
|
0
|
1.11
|
|
53.3
|
1 mi = 1.61 km, 1 ft = 0.3048 m
Table 7. Summary Statistics: 90 Four-Legged Intersections,
Washington State (continued)
Two-Lane Rural Roads, 1993 - 1995
Variable and Abbreviation
|
Min.
|
Max.
|
Median
|
Mean
|
Freq
|
%Zero
|
Light Yes
No
|
|
|
|
|
33 (36.7%)
57 (63.3%)
|
|
Terrain Flat
Rolling
Mountainous
|
|
|
|
|
28 (31.1%)
60 (66.7%)
2 (2.2%)
|
|
Degree of Curve = HI = (1/n)3DEG{i}
|
0
|
6.50
|
0
|
0.497
|
|
78.9
|
Crest Curve Grade Rate = VCI = (1/m)3(|Dg{i}|/l{i})
(crests only)
|
0
|
3.585
|
0
|
0.185
|
|
66.7
|
Speed = SPDI (mph)
|
22.5
|
55
|
55
|
51.0
|
|
|
Right Turn Lanes on Major Road None
One Right Turn
Two Right Turns
|
|
|
|
|
53 (58.9%)
8 (8.9%)
29 (32.2%)
|
|
Right Turn/Acceleration Lanes on Minor Legs None
Both
|
|
|
|
|
89 (98.9%)
1 (1.1%)
|
|
1 mi = 1.61 km, 1 ft = 0.3048 m
|