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Publication Number: FHWA-RD-98-133
Date: October 1998

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

 

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