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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

Bivariate Statistics

In this section tables are exhibited that indicate the correlation coefficient between accident count and one other highway variable. A positive coefficient indicates that as the highway variable increases accident counts do also; a negative coefficient indicates that as one variable increases the other tends to decrease. When a relationship is pronounced significant in this discussion, it means that the P-value is small (say, under 15%, and usually under 5%). The P-value is the probability that the sample correlation would have the given magnitude or greater when the true correlation in the population is zero. Thus significant relationships are ones that provide strong evidence that the two variables are correlated on the population from which the sample comes.

A major limitation of bivariate statistics is that the relationship between one variable and another may be masked or appear in a misleading light when a few especially influential variables such as ADT are present and their effect is ignored. The effect of a geometric variable, for example, on accidents when ADT is held constant is best revealed by the modeling to be discussed later since the modeling attempts to assess the combined contributions of all variables. With this caveat, bivariate statistics for accidents versus other variables are presented in Tables 8, 9, and 10. In Tables 11, 12, and 13 some of the significant correlations of highway variables with one another are also shown (in qualitative form rather than quantitative).

Segment Accidents

The most pronounced correlations with accidents, applicable in both Minnesota and Washington, are as follows:

Horizontal and vertical alignment also correlate positively with accidents but are not consistently significant. Some variables yield opposite signs from one State to the other, notably, lane and shoulder width, each of which is negatively correlated with accidents in Minnesota and positively in Washington. The consistent negative correlation of truck percentage suggests that trucks avoid the most dangerous roads. The weather variables in Minnesota are not significant.

If the accidents are restricted to serious accidents or run-off-road accidents, the same relationships persist with slight changes. The negative correlation of truck percentage is less significant. On the other hand, for run-off-road accidents both horizontal alignment H and grade GR are more significant.

Three-legged Intersection Accidents

Accidents at three-legged intersections show the following relationships:

positive correlation

ADT1

ADT2

RT

Horizontal and vertical alignment or driveways nearby generally contribute positively to accident counts but not in a consistently significant manner. Turning lanes are often installed at intersections with high turning volumes and high accident counts, but it is not clear why a right turn lane on the mainline would correlate positively with accidents while the conflict index would show much less significance (in Minnesota). Bad weather is marginally significant at Minnesota three-leggeds.

Serious accidents and run-off-road accidents show the same pattern although major road ADT is not significant for run-off-road accidents.

Four-legged Intersection Accidents

The significant correlations in this case are:

Positive correlation

ADT1

ADT2

CINDEX

The Minnesota data, but not the Washington data, show expected dependencies on channelization, alignment, Roadside Hazard Rating, number of driveways, as well as (weak) positive dependence on bad weather.

Serious and run-off-road accidents behave likewise, but major road ADT is not significant for run-off-road accidents.

 

Table 9. Bivariate Statistics: 3-Legged Intersection Accidents versus Other Variables

 

Table 10: Bivariate Statistics: 4-Legged Intersection Accidents versus Other Variables

 

Table 11. Correlations between Segment Variables in

MN and WA Samples

 

VARIABLE

POSITIVE CORRELATES

NEGATIVE CORRELATES

ADT

SHW, TOTWIDTH

T, SEG_LGN

T

Truck %

SEG_LGN, SHW, TOTWIDTH, SPD

ADT, SNP, NONDRYP

SEG_LGN

T, RHR, SPD, SNP, NONDRYP

ADT, DD, INTD, SHW

LW Lane width

SPD

 

 

SHW Shoulder width

ADT, T, SPD

RHR, H, VC, GR

TOTWIDTH

ADT, T, SPD

RHR, H, VC, GR

RHR

Roadside Hazard Rating

SEG_LGN, H, VC, GR, SNP, NONDRYP

SHW, TOTWIDTH, SPD

DD Drwyrate

INTD

T, SEG_LGN, SPD

INTD Intrate

DD

SEG_LGN

H Hor

RHR, VC, GR

SEG_LGN, SHW, TOTWIDTH, SPD

VC Crests

RHR, H, GR

T, TOTWIDTH, SPD

GR Absolute grade

RHR, H, VC

SHW, TOTWIDTH, SPD

SPD Speed

T, SEG_LGN, LW, SHW, TOTWIDTH

RHR, DD, H, VC, GR

SNP, NONDRYP (MN only)

SEG_LGN, RHR, H

T

NOTE: Segment length (SEG_LGN), Roadside Hazard Rating (RHR), Speed (SPD), and Truck Percentage (T) show strong correlation with a large number of variables. Segment lengths tend to be longer in rural areas and this accounts for the negative correlation with ADT, driveway density, and intersection density. The Roadside Hazard Rating and Speed variables also show expected correlates. The behavior of the Truck Percentage variable suggests that teamsters favor routes with certain characteristics and/or that such routes are more likely to have commercial development nearby.

 

Table 12. Correlations between 3-Legged Intersection Variables in

MN and WA Samples

 

VARIABLE

POSITIVE CORRELATES

NEGATIVE CORRELATES

ADT1

ADT2, ND, SNP, NONDRYP

CINDEX, SPDI

ADT2

ADT1, CINDEX, ND, HI, RT

SPDI

CINDEX

ADT2, HI

ADT1, SPDI, SNP, NONDRYP

DEV from 90°

RHRI

 

 

RHRI Roadside Hazard Rating

DEV, HI, VI

 

 

ND No. of Drwys " 250 ft

ADT1, ADT2, HEI, SNP, NONDRYP

SPDI

HI Hor. to ± 250 ft

ADT2, CINDEX, RHRI, VCI, VI, VEI

SPDI

HEI Hor. to ± 764 ft

ADT2, CINDEX, RHRI, ND, VI, VEI

SPDI

VCI Crests to ± 250 ft

HI, VI, VEI

SPDI

VI Vert. to ± 250 ft

RHRI, HI, HEI, VCI, VEI

SPDI

VEI Vert. to ± 764 ft

RHRI, HI, HEI, VCI, VI

SPDI

SPDI Speed

 

 

ADT1, ADT2, CINDEX, ND, HI, HEI, VCI, VI, VEI

RT Right Turn Lane on Major Road

ADT2

 

 

SNP, NONDRYP (MN only)

ADT1, ND

CINDEX

1 mile = 1.61 km, 1 ft = .3048 m

NOTE: Perhaps the fact of chief interest in Table 12 (the 3-legged intersections) is the negative correlation between posted speed and the other variables of interest. In Table 13 (the 4-legged intersections) speed plays a similar role but not quite so marked.

 

Table 13. Correlations between 4-Legged Intersection Variables in
MN and WA Samples

 

VARIABLE

POSITIVE CORRELATES

NEGATIVE CORRELATES

ADT1

ADT2, DEV, HI, SNP, NONDRYP

CINDEX

ADT2

ADT1, CINDEX, RT

 

 

CINDEX

ADT2, RT

ADT1

DEV from 90E

ADT1

SPDI

RHRI Roadside Hazard Rating

VI, VEI

 

 

ND No. of Drwys ± 250 ft

SNP, NONDRYP

SPDI

HI Hor. to ± 250 ft

HEI, SNP, NONDRYP

 

 

HEI Hor. to ± 764 ft

HI, RT, SNP, NONDRYP

SPDI

VCI Crests to ± 250 ft

VI, VEI

SPDI

VI Vert. to ± 250 ft

RHRI, VCI, VEI

 

 

VEI Vert. to ± 764 ft

RHRI, VCI, VI

SNP, NONDRYP

SPDI Speed

 

 

DEV, ND

RT Right Turn Lanes on Major Road

ADT2, CINDEX, HEI

 

 

SNP, NONDRYP (MN only)

ADT1, DEV, ND, HI. HEI

VEI, SPDI

1 mile = 1.61 km, 1 ft = .3048 m

Other Bivariate Relationships

Bivariate relationships between highway variables are also in evidence as might be expected. In Tables 11, 12, and 13 above we indicate relationships in which the correlation coefficient has the same sign in both Minnesota and Washington and the correlation is strongly significant in both States (P-value typically less than 5%) or strongly significant in one State and moderately significant in the other (P-value typically less than 15%). We omit obvious correlations (e.g., between different vertical measures).

In the case of weather variables (SNP and NONDRYP) the correlation is for Minnesota data, the only State where weather data were collected. The weather variables show some surprising correlations in the intersection samples. See Table 14 below. These correlations have no counteparts in the segment data. The direct implication, however frivolous it may be, is that rural intersections.

 

Table 14. Correlations between Weather and Minnesota Highway Variables

 

Correlation coefficient and P-value

Minnesota 3-legged intersection sample

Minnesota 4-legged intersection sample

ADT1

ND

ADT1

ND

NONDRYP

.21201, .0001

.12608, .0128

.12202, .0274

.21916, .0001

SNP

.19164, .0001

.13523, .0076

.09611, .0827

.21555, .0001

with high major road ADT or with nearby driveways tend to have more rain and snow than other rural intersections. The correlation of weather with minor road ADT is not significant.

 

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