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Daytime headlight operation and motorcyclist fatalities
lMO14575~84 C 1981 Pcrgamon
DAYTIME HEADLIGHT MOTORC.YCLIST
OPERATION FATALITIES
fj.00 i .30 Pros Ltd.
AND
ANDREAS MULLER Health Planning and Administration Program, College of Human Development, The Pennsylvania State University, University Park, PA 16802, U.S.A. (Received 2 Augusf 1982)
Abstract-Since 1978. all new motorcycles first registered in California are required by law to be equipped with headlights which automatically turn on when the engine is started. The purpose of this law is to increase headlight use during daytime and prevent multi-vehicle collisions due to poor conspicuity of motorcyclists. This paper examines whether the increasing operation of motorcycle headlights has been effective in reducing the number of daytime multi-vehicle fatalities in California and other states affected by the California legislation. Time series of motorcycle fatalities (1976-1981) for California and other states in the U.S.A. are analyzed by log-linear analysis. iModels representing the null-hypothesis were found to be consistent and more parsimonious descriptions of the observed data than models which incorporated additional terms indicating the effectiveness of increased headlight operation. or the effectiveness of daytime headlight use laws. Although the latter terms were not found to be statistically significant, a slight decrease in the odds ratio of multi to single vehicle collisions was predicted in states without daytime headlight use laws. This decrease suggests that daytime headlight operation may be beneficial in reducing the number of motorcycle fatalities. INTRODUCTION In
contrast to their popular image, motorcyclists are a particularly vulnerable group of traffic participants. Fatality statistics indicate that about 5000 persons died in motorcycle crashes in the U.S. in 1980 [NHTSA, FARS, 19811 and the fatality risk of motorcyclists is at least four times greater per mile than that of automobile occupants [NSC, 1977; Metropolitan Life Insurance Company, 19781. Studies of motorcycle accidents [Janoff et al., 1970; MSF 1978; Hurt et al., 19811 consistently show that the most frequent type of crash involves a collision with an automobile at an urban intersection in daylight. Automobile operators are most often at fault for the collision and frequently claim that the motorcyclist could not be seen. Headlight operation during daytime has been advocated [Thomson, 1980; Attwood, 198 I] as an effective collision countermeasure which should alert other traffic participants sooner of the approaching motorcyclist. Experimental studies and well-controlled field trials have found that daytime operation of headlights increases the contrast between the motorcyclist and his background [Janoff et al., 1970; Woltman and Austin, 1974; Williams and Hoffman, 19771 and enhances his conspicuity. Olson et al. [1981] observed that automobile drivers did not risk potential interference with the motorcyclist right-of-way quite as frequently when the headlight was on as when the headlight was turned off. In the U.S., 17 states have enacted laws which make use of motorcycle headlight mandatory during the day [Motorcycle Industry Council, 19801. The purpose of these laws is to increase headlight use over voluntary levels and reduce the number of daytime multivehicle collisions. Several studies have found varying estimates of the effectiveness of these laws ranging from no effect, or minor effects FHTSA, 1978; Muller, 1982; Janoff and Cassel, 19711to fairly large effects wailer and Griffin, 1977, 1981; Robertson, 19761. The last two studies suggest that about 20-25% of the daytime multivehicle collisions can be prevented by headlight use laws. The previous studies tend to underestimate the potential benefit of daytime headlight operation since they are only concerned with the increase in headlight use over voluntary levels resulting from the enactment of the legislation. Studies [Vaughan et al., 1977; Hurt et al., 198 l] comparing daytime headlight use between accident involved motorcyclists and randomly selected groups of non-accident involved motorcyclists suggest greater accident reduction potential. Both studies found that headlight operation was twice as frequent AAP Vol. 16. No. ,-A
I
2
A.
MULLER
among motorcyclists in the randomly selected group as among accident involved motorcyclists. The relative risk of accident involvement is about three times higher among motorcyclists not operating their headlights Vaughan, et al., 19771. Therefore, headlight operation in daylight seems to be a ‘- . . . powerful and effective way of reducing accident involvement, by making the motorcycle more conspicuous in traffic.” [Hurt et al., 1981,1982] Studies which try to detect the effectiveness of daytime headlight laws will not be likely to find effects, since in the late 1970s headlight use levels have become similar between states with and without the legislation [Muller, 19821. The convergence in headlight use levels was brought about by the introduction of motorcycles which automatically turn headlights on when the engine is started. The design change is a result of a California State law which was passed in 1972. Lack of timely compliance by several motorcycle manufacturers postponed the effective data of the legislation to 1978. Since then, the law states that “Every motorcycle manufactured and first registered shall be equipped with at least one and not more than two headlamps which automatically turn on when the engine of the motorcycle is started and which remain lighted as long as the engine is running”, ($25650.5 California Vehicle Code, West’s [ 19821). Similar legislation was enacted in Iowa (1980), Connecticut (1980) and Kansas (1982). The effect of the California passive? headlight law has been two-fold. With the replacement of old motorcycles by new hard-wired models, headlight operation during daytime will have steadily increased in California over the years. Since the California legislation affects about 15% of all motorcycles sold in the U.S.; the equipment change will have also been made on new motorcycles targeted for other states winn, 19801.This paper will investigate whether the increasing level of motorcycle headlight operation during daytime had a beneficial effect on motorcycle fatalities in California and other states. THE
INCREASE
IN DAYTIME
HEADLIGHT
OPERATION
Unfortunately, there are no regular roadside surveys which monitor daytime operation of motorcycle headlights. Therefore, the increase in daytime headlight operation must be extrapolated from a comprehensive study of motorcycle accidents in the Los Angeles area. Hurt ef al. [1981] collected data on headlight use for motorcycles involved in multivehicle collisions during 1976-77 and for a random sample of 2300 motorcyclists not involved in accidents two years later. To obtain comparable information, the motorcyclists surveyed were matched by accident location, time of day, day of week and weather conditions. In addition, the researchers collected data on 3600 accidents reported by the police. The latter sample was comparable to the in depth accident investigations. With respect to daytime headlight operation, the principal findings are shown in Table 1. Several results are noteworthy. During 1978-79 when the survey was taken, daytime headlight operation was 71%. This figure is 20% higher than that found by Robertson [ 19761who conducted a roadside survey in the Los Angeles area during September of 1975. The increase in headlight operation appears to reflect the introduction of hardwired motorcycles, since the headlight operation was only 64% in pre 1978 model years and 88% for motorcycles which had to conform with the California legislation. Apparently 12% of
Table 1. Per cent of daytime
headlight operation by type of sample and model year of motorcycle, Los Angeles area, California
Model
ore
Year
1978
1978-79 All
Note: Source:
tDoes
not require
action
Model
Accident
Exposure
Years
Excludes unknowns. Hurt -et al. (1981):
by motorcyclist.
63.5
a52
88.1
396
_
-
71.3
1248
_
-
99.
343
31.6
525
3
Daytime headlight operation and motorcyclist fatalities
model year 1978-79 motorcycles had not tutned their headlights on. Hurt et al. [1981: 3871 attribute this finding to either failing headlights or intentional change in the electrical system. About 6% of motorcyclists had installed light switches for the discretionary use of headlights. Headlight operation was only half the rate in accident involved motorcyclists when compared with the exposure sample. This finding was interpreted by Hurt et al. as evidence in support of the effectiveness of headlight operation. Some of the data in Table 1 can be used to project daytime headlight operation among accident involved motorcyclists for the period 1976-1981 (see Fig. 1). The projections are based on four assumptions. First, headlight operation among California accident involved motorcyclists was 32% in 1976. Second, hard-wired motorcycles were introduced by some manufacturers even before the effective date of the California legislation (l/1/78)?. Third, for motorcycles manufactured after 1 January 1978, headlight operation equals 88%. Fourth, the age distribution of accident involved motorcycles remains unchanged for the period 1976-1981. The calculations underlying the projections are shown in Appendix A. Figure 1 indicates that between 1976 and 1981 headlight operation is estimated to have increased between 32 and 43% points among accident involved motorcyclists. Since the timing of introduction of hard-wired motorcycles is not precisely known, the projections were calculated for two extreme situations. The “low” projection is based on the assumption that no hard-wired motorcycles were introduced before 1978, while the “high” projection assumes that hard-wired motorcycles were introduced by 1975. Apparently, the timing of the. introduction does not have a pronounced effect on the estimated increase in headlight operation. PERCENT
A m-
. 70
-
60so-
32.1
43.2
40-
30MIO
-
L
I
1976
Fig. I. Projected
I
1977
trend of headlight
I
I
1978 1979 YEAR
I
1980
I
)
1981
operation at day for accident involved motorcyclists, California.
The projected increase in daytime headlight operation may also be applicable to other states without daytime headlight use laws. Winn [I9801 mentions that since the largest number of motorcycles are sold in California, the equipment changes to conform with the California legislation will also have beets made on new motorcycles sold in other state@. tOne motorcycle manufacturer responding to an information request reported that all motorcycles quipped for legal street use have had automatic headlight on features since model year 1975. Other manufacturers followed suit as is reported by Hurt ef ~1. [1981: 3371 who observed that certain pre 1978 model year motorcycles were quipped with the automatic lights-on features. :In fact the manufacturer who responded to the information request confirmed this statement.
4
A. MULLER
A survey conducted by the Motorcycle Safety Foundation in January of 1981 suggests a high level of daytime headlight operation in states without daytime headlight use laws. About 76% of the responding motorcyclists stated that they “always” used their headlights during daytime. Although a self selection bias could account for the high use level, this explanation appears unlikely. During September of 1979 the Motorcycle Safety Foundation [ 19791conducted a roadside survey in the city of Baltimore and the surrounding state of Maryland and found headlight operations at 60%. This figure compares with 43% daytime headlight operation observed in a similar survey conducted among Baltimore motorcyclists in 1975 [Robertson, 19761. On the basis of the available evidence, it seems reasonable to conclude that the headlight operation has also increased in states other than California during the mid to late seventies and that this increase was most likely due to changes in motorcycle design. It follows then, that the level of daytime headlight operation should also have increased among accident involved motorcyclists in states without daytime headlight use laws. DATA,
HYPOTHESES
AND METHODS
The time series presented in this paper are based on motorcycle fatalities that occurred in California and other states during the six-year period 1976-198lt. The data were collected by the fatal accident reporting system [FARS; see Sebastian and Flemons, 19811 and pertain to motorcyclists excluding moped and motor-scooter fatalities. To assess the effect of increased headlight operation on motorcycle fatalities, the time series was classified by lighting condition (day and nightj and type of collision (multi vs single vehicle). Nighttime fatalities include those occurring under lighted highway conditions. Fatalities during dawn and dusk were excluded from the analysis. They comprise less than 5% of the motorcycle fatalities and will not affect the substantive conclusions of the analysis [see Muller, 19831. If daytime headlight operation is effective, then a certain number of daytime multivehicle collisions should be prevented. Since single vehicle collisions should not benefit from this collision countermeasure, it is expected that the ratio of multivehicle to single vehicle collisions will decrease corresponding with the increase in daytime headlight operation. Since several manufacturers equipped motorcycles with automatic headlights before the effective data of the California legislation (l/l/78), the effect of increased daytime headlight operation should also be present before 1978. A hypothesis which is consistent with this interpretation can be stated as follows:
Where MD = multi-vehicle collision fatalities at day; SD = single vehicle collision fatalities at day. Hypothesis (Hi) implies that the introduction of hard-wired motorcycles occurred gradually, but not necessarily at the same rate. A time series consistent with hypothesis (1) does not rule out the possibility that factors other than increased daytime headlight operation may have been responsible for the decrease in the ratios. To control such a bias, the daytime ratios are divided by their nighttime equivalents. This procedure adjusts the daytime data for trends in the nighttime data. For any given year the resultant odds ratio can be stated as follows:
MD
MN
MDxSN
(2)
@-==%=SDxMN
where o, = odds ratio for year t; MN - multi-vehicle SN = single vehicle collision fatalities at night.
collision
fatalities
&Since multivehicle collisions were diKerently determined in 1975 than in subsequent data were excluded from the analysis.
at night;
years,the 1975fatality
Daytime headlight operation and motorcyclist fatalities
5
Hypothesis H, can be restated using odds ratios. HIA: o,>o,+,*--
>o,+,
(3)
(O
(3a)
or r=ytl
and
In contrast, if increased daytime headlight operation is ineffective, then the odds ratios should remain constant for the time period 1976-1981. This null hypothesis can be written as: &:o,=k;
and
{Ock
(4)
i I =‘76,‘77...‘81;
or
Both hypotheses can be tested by log-linear analysis [Goodman, 1972; Davis, 1974; Haberman 1978 and 1979; Knoke and Burke, 19801. Log-linear analysis predicts cell frequencies in a cross-tabulation by specifying various effects by setting odds ratios at appropriate values {Davis, 1974: p. 1991.The predicted cell frequencies can then be compared with the actual data by x2 tests. In the context of this research, the log-linear model including all possible effects (saturated model) for the cross-tabulation: type of collision (C), time of day (T) and year (Y) can be stated as follows: (5) or by transfo~ation
in natural loga~thms.
where q = grand mean for the entire model: rc, T,?,T: = one variable effects, either variable C T or Y* rc’ ?cy 7TY = two variable interactions, either between variables C and T, C aid Y or ‘T”and* Ye ‘i Cry = three variable interactions among C, T and Y. The effect parameters (z) relate’to:pecific odds or odds ratios?. If the ratios are not equal to 1, effects are present which will either increase or decrease the product (F&. For instance, if the number of day and night fatalities are not identical, the parameter rf will depart from 1. Similarly, if the ratio of multi-vehicle to single vehicle collisions is different at day than at night, the parameter T:’ will not be equal to 1. That is, some association between the variables C and T exists. Moreover, if the latter association changes over the years, as is expected according to hypothesis HIA, then effects associated with parameter rr will be present. Specific hypotheses (models) can be tested by setting one or more of the tau parameters equal to 1. The following models are of interest. Model No. 1. 2. 3. 4. 5.
Effect Parameters
Fitted Marginal Notationt
qrf7j-7;
C,
q7:7;7;7;:-_
CT, Y CT, CY CT, CY, TY CTY.
tf7;7;7;+gy tfTi
c7i r 7kTiiY
c T r/7itj?,7@
Y
cr
cy TY Z& r*
CT
CY 7f& Tj&
fr fg&CTY
T,
Y
tThe relationship between T and odds, or odds ratios is discussed in Knoke and Burke [1980: pp. 1l-291. $It is more convenient to represent the models in fitted marginal notation, which does not state the lower order effects as long as they are implied by higher order effect.
A.
6
,&‘fULLER
Model I only permits single variable effects and is useful as a baseline model against which other models can be compared. Models 2 to 4 are consistent with hypothesis (H,) which stipulates that the effect parameter rF can depart from I, but will remain constant over the years. Yet models 2 to 4 vary in the number of other two variable effects whose inclusion may improve the fit of the model. Model 5 is of specific interest since it relates to hypothesis H,,. It permits departures of the relative odds ratios from 1 and is consistent with the expression r=~where{O
(7)
Yet, hypothesis H,, requires that the values of the relative odds ratios (r) are restricted to the domain (0 < r < 11. Therefore, if model 5 turns out to be the only fitting model, the relative odds ratios (r) must be inspected to determine whether they are consistent with the restriction stated by hypothesis H,,. Since model 5 will perfectly predict the data (saturated model), only the inspection of the observed data is needed. The models were estimated using the BMDP statistical software package (revised, 4182). FINDINGS
FOR CALIFORNIA
California motorcycle fatalities between 1976-1981 are presented in Table 2 and the corresponding odds ratios are displayed in Fig. 2. The ratios indicate that the odds of dying in a multi-vehicle collision rather than a single vehicle collision are roughly 2:l during daytime and somewhat more than even at night. Figure 2 shows neither a consistent decrease in the daytime odds nor in the odds ratios over the years. Table 3 presents the results of fitting specified models to the data. The models are hierarchically ordered so that specific effects can be tested for statistical significance. The association between type of collision and time of day represented by term TC is highly significant. This is not surprising, since the odds ratio is substantially greater than 1 (see Fig. 2). The association between time of day and year (TY) is marginally significant, and suggests that nighttime fatalities have increased relative to daytime fatalities. Models 2-5 fit the data well. Model 5 is of particular interest, since it relates to hypothesis H,,. The comparison with model 4 indicates that the effect of the three way Table 2. California motorcycle fatalities observed and predicted* by lighting condition, type of collision and year Observed Year
Type of Collision
1976
Multi
Predicted* Night
Oay n
MIS
203
n
1977
96
Multi
212
Single
119
Multi
249
1979
122
Multi
247
1980
119
Multi
235
1981
Single
115
flulti
237
Single
203
*Refers U/S
to flOOEL 3, TABLE
= Multi-vehicle:
1.537
TO
178
3.
single
vehicle
1.929
1.749
1.159
1.749
1.159
1.751
201.3 2.029
114.9
1.159
183.4
233.1 1.107
1.750
212.6 2.028
115.6
197
1.159
189.9
234.4 1.329
1.751
220.1 2.027
120.9
72%
1.158
168.6
245.1 2.036
1.751
195.4 2.029
122.5
1.020
1.159
145.5
248.5
207
0
168.5 2.028
1.674
WS
141.2
109.3
1.220
n
121.8
221.7
164
111
M/S
2.029
1.588
200
2.135
Night
Oay
98.7
1.122
2.043
" zoo.3
148
2.076 Single
1.774
166
2.041 Single
1.192 120
1.782
1978
0
143 2.115
Single
MIS
173.7
7
Daytime headlight operation and motorcyclist fatalities Table 3. Comparison among log-linear models and results of statistical significance tests *
Model
O.F.
1.
T. C, Y
2.
TC,
3.
TC,
4.
TC,
TY.
5.
TCY
3D.F.
IL?
L'
P
16
91.68
0
Y
15
14.10
.518
1
TY
10
5.71
.a39
5
a.39
.l
5
2.60
.761
5
3.11
.7cpc.5
0
0
-
5
2.60
.acpc .7
CY
-
P
-
77.58
m
zylo
4
I.0
I
PC.001
IlIelFMms
I 1977
I
1976
I 1979
I 1978
I
1980
I 1981
*
YEAR -
M"
mvsw
-
am
UATIO
-
*'6+u (m/a)
g
Fig. 2. The odds of multi-vehicle to single vehicle fatal collisions in California by time of day and year.
interaction (WY) is statistically insignificant and the observed data (model KY) do not show a declining trend (see Fig. 3). Therefore, a simpler model can describe the data more parsimoniously. Model 3 was selected as basis for comparison since it achieves excdlent fit relative to the degrees of freedom used for parameter estimation. Models 2 and 4 could have also been used for comparison. They imply that the odds ratio (TC) remains constant over the period 1976-l 98 1. This would be represented by a horizontal line closely parallel to the one shown in Fig. 3. The predicted data in Table 2 can be interpreted as follows. First the odds of dying in multivehicle collision rather than a single vehicle collision are 75% higher at day than at night. These odds remain constant from 1976 to 1981 and are consistent with the null hypothesis. In addition, the two-way interaction (TY) suggests that nighttime fatalities increased by 23% between 1976 and 1981 relative to daytime fatalities. The predicted data indicate that the increase occurred in single and multi-vehicle collisions. FINDINGS*OR
OTHER
STATES
The analysis of the California motorcycle fatalities suggests that the null hypothesis specifying no trend seems to fit the data best. That means, that increased daytime headlight operation may not be effective. If this inference is correct, then the null hypothesis should also be applicable to states other than California. Furthermore, it follows that daytime headlight use laws should be ineffective and the null hypothesis should apply to these states as well. The following analysis will examine these implications.
8
A.
MULLER
oom RATIO
4 3.0 -
*ooos RATIO:
!g:g
Fig. 3. Odds ratios for California, by model 1976-1981.
Table 4. Motorcycle fatalities for states with and without daytime headlight use laws by lighting condition and year States without Motorcycle Year
Type of Collision
1976
Multi
505
Single
244
Multi
617
1977
1978
1979
1980
1981
n
Single
301
Multi
708
Single
383
Multi
683
Single
336
Multi
722
Single
382
Multi
673
Single
346
Headlight Use Laws* Night Day n U/S WS 2.070
2.60
I.849
2.033
1.890
I.945
354 350 475 452 513 479 609 558 640 609 658 610
1.011
with Motorcycle Headlight Use Laws* Night Oay
States 0
2.046
1.051
1.951
1.071
1.726
1.091
1.863
1.051
1.799
1.079
1.803
n
298 165 363 186 406 200 392 228 425
H/S
1.806
1.952
2.030
1.719
1.786
238 358 227
”
M/S
0
1.215
1.487
1.103
1.770
l.lES
1.709
1.019
1.687
.943
1.894
1 .Oi?5
1.453
249
1.570
205 301 273 342 288 371 364 362 384 369 340
*See APPENDIX 6 for states included in the group. M/S = Multi-vehicle: single vehicle
Table 4 shows the aggregationi of motorcycle fatalities for states with and without daytime headlight use laws. In contrast to the California legislation these laws require motorcyclists to switch their headlight on during daytime in case the motorcycle is not equipped with the automatic lights on feature. The group of states with headlight use laws only includes states (14) which had the laws for the period, 197.5 198 1. The group of states without headlight use laws includes 32 states and the District of Columbia, and excludes California. Figures 4 and 5 present the graph of odds ratios for the two groups of states. The tThe meaningful interpretation of the aggregated fatality data assumes that the association (odds ratios) between type of collision and time of day does not greatly vary among states within each subgroup. This possibility was tested by homogeneity tests of log odds ratios [see Fleiss, 1981: l6C-681. The test results showed no statistically significant differences among states for each year.
Daytime headlight operation and motorcyclist fatalities
9
6 3.0 -
2.0 -
.
.
1.0 -
NIelT
I 1976
SOURCE:
I 1977
I 1979
I 1976
I 1960
I 1961
(lwsll)
*
lable 4
Fig. 4. Odds and odds ratios for states without daytime headlight use laws.
I 1976 SOURCE:
Table 4
I 1977
I 1976
I 1979
I 1980
I 1961
*
YEAR
Fig. 5. Odds and odds ratios for states with daytime headlight use laws.
daytime series for states without headlight use laws shows slightly lower odds for the last four years than for the first two years of the series. Since the odds for nighttime series are nearly constant for the entire period, the odds ratios parallel the daytime data series. The time series for states with daytime headlight laws (Fig. 5) shows more fluctuation. Again, the daytime odds are lower in the last part of the time series than in the first. Since the nighttime odds roughly parallel this data pattern, the odds ratios show no consistent trend for the 6yr period. Figure 6 compares the three time series of odds ratios and indicates that the time series are largely overlapping. The following analysis will determine which interpretation of the data is most supported. Table 5 presents the results of the log-linear analysis of the four variable cross tabulation: collision type (C), time of day.(T), year (I’), and states (S). To test specific effects, the models are hierarchically ordered beginning with the single variable effects model (1). Due to the introduction of a fourth variable (S) additional models need to be specified.
IO
A. .MIJLLER
CALIFORNIA
I.0
1 I
I
1976
I
1977
I
1978
I
1979
I 1980
I
*
1981
YEAR
XNNtCE:
lables
2 and 4
Fig. 6. Odds ratios for states with and without daytime headlight use laws and California. 19761981.
Models 2-7 are consistent with the null hypothesis which stipulates that the odds ratio (TC) neither changes over the years nor varies by group of state. Models 8-l 1 allow for variation in the odds ratio (TC) by year, indicated by term (KY), and relate to hypothesis H,,,. The four variable effect (K’YS) should be significant, if headlight operation is effective and motorcyclists complied with headlight use laws. A convergence of odds ratios between states with and without headlight use laws is expected according to this model. Models l-4 are inadequate representations of the observed data, although effect TC turns out highly significant and the association between state and collision type (SC) is of marginal significance. In contrast, models 5-7 fit the data, which is primarily due to the inclusion of the association between time of day and year (TY). Models 8-11 show that the incorporation of three way interactions does not substantially improve the goodness of fit. The decreasing probability estimates in column 3 indicate that small decreases in L’ are achieved at relative high costs in degrees of freedom. Therefore models 8-1 I are adequate, but less parsimonious representations of the observed data. The comparison of models I1 and 12 indicates that the four way interaction TCYS is also statistically insignificant. Model 13 is presented to show that only four associations are necessary to describe the observed data very well. The modelled data suggest the following. The odds of dying in a multivehicle rather than a single vehicle collision are 78% higher at day than at night. The corresponding odds ratios (TC) are identical for all three groups of states and all years. The odds of fatal multivehicle collision are slightly higher in states without daytime headlight use laws. The odds of a nighttime fatal collision have increased by 28% in all states over the 6 yr period. Motorcycle fatalities increased faster in states with and without headlight use laws than in California. The fastest increase occurred in states without headlight use laws. These observations are based on the predicted data shown in Table 6. Table 7 displays odds ratios, pertaining to term (TC) based on selected models which are of primary research interesf.The models are listed in Table 5. For instance model 7 predicts a constant odds ratio of 1.772 for all states and years. The model accounts for 95% of the variation in the cross-tabulation when compared with the baseline model (1). Model 8 would support hypothesis H,,, if the predicted odds ratios were to decrease over the years. This is not the case. A comparison with model 7 shows a pattern consistent with random fluctuations. The odds ratios predicted by model 11 parallel those predicted by
II
Daytime headlight operation and motorcyclist fatalities Table 5. Comparison among log-linear models and results of statistical significance tests Nodeis
D.F.
z I..
o
:D.F.
AZ
D.
-
-
I,
T, t, Y, S
62
574,54
.O
-
2.
TC. Y. 5
61
lc6.91
.OoO3
1
467.63
3.
TC, CY, 5
56
100.99
.oooz
s
5.92
fX.OOl ‘5CPC.3
4,
TC, CY, SC
54
94,30
.0006
2
6.69
;05cp<.52
5.
TC, CY, SC, TY
49
46.56
.5724
5
47.74
.45
6.
TC, 0.
47
44.24
3876
2
2.32
10
16.66
.1
5
1.22
cpc.9
SC. TY, TS
.5
7.
TC. CY, SC, TY, TS, SY
37
27.58
.a699
6.
TCY, SC, TS, SY
32
26.36
.7472
9,
TCY, SCY. TS
22
17.05
.7604
10
9.31
.7
IO
6.96
.aspc.7
2
2.91
.3
7.19
.a
TCY, S&Y, TSY
I2
lO.IO
.6075
Il. TCY, SCY. TSY, TCS
10
V-19
.7074
1%
12. TCYS 13. TC, SC. TY, SY Note:'
-la
00 44
31.85
.914
-
-
-
based on 3 gmups of states: California,states%jth and states without daytime headlight use laws.
Analysis is
Table 6. Predicted number of fatalities by model: TC, SC, TY, SY Cat ifornia
states rr'thoutMotorcycle Headfight Use Laws Night Day
States with Motorcycle Headtight tfseLaws Night Day
Year
Type of C0lIiSiW
I976
nu1t.i
195.6
145.4
492.5
366.0
306.2
227.6
Single
95.3
125.8
266.2
338.2
165.2
218.0
Multi
216.8
172.9
603.9
481.7
362.1
288.9
Single
105.6
149.6
314.2
445.1
195.3
216.7
1978
tduiti
253.2
192.2
698.9
530.4
408.5
315.1
Single
123.4
166.3
363.6
490.1
220.4
297.0
1979
Multi
243.5
221.9
667.8
608.5
407.7
37f.S
Single
113.6
192.0
347.5
562.3
zt9.9
355.9
1980
Multi
236.7
211.2
726.8
648.6
428.7
382.6
Single
115.3
182.7
378.2
599.3
231.3
366.5
380.2
362.0
205.1
346.8
1977
I983
Day
Night
Multi
221.6
211.0
682.2
649.6
Single
107.9
182.5
365.0
605.2
model 8. In addition, model 1I predicts differences in the level of the three time series (see Fig. 7). States with daytime headlight use laws have somewhat lower odds ratios than states without such laws. Model 11 also accounts for an additional 2.5% of the variation in the ~~Ss-~~~Iati~n.
The major findings of the previous analyses are as follows. The log-linear analysis of the Cafifornia motorcycle fatalities is consistent with the null hypothesis stating that the odds ratios have remained constant from 19X-1981. The extension of the analysis to other states also showed that modets consistent with the null hypothesis predict the data well and are more parsimonious than models incorporating higher order interactions. Up to
A. MULLER
12
Table 7. Predicted odds ratios (2-C) by model. state and year Model
!L$L;\)/Li . *
1976
1977
1978
1979
1980
1981
W/O Law ! 1.772
1.772
1.772
1.772
1.772
1.772
,952
1.801
1.821
1.705
1.834
1.780
1.707
,954
1.681
Cal $7
W. Law Cal #B
U/O Law W. Law
%ll
Cal
i ,780
1.799
1.689
1.811
1.760
W/O Law
1.879
1.901
1.783
1.913
1.858
1.778
W. Law
1.697
1.715
1.609
1.727
1.676
1.605
.987
Note: Model numbers refer to those used in TABLE 5. Li = Liklihood ratio x2 of baseline model, MODEL 1. LA = Liklihood ratio x2 of alternate model, see TABLE 5. Source: TABLES 1, 2, and 3 in APPENDIX D.
SOURCE: Table 3. &wendix 0
Fig. 7. Predictedodds ratios (TC) by model TCY, SCY, TSY, TCS. 95% of the variation in the observed data could be accounted for by models consistent with the null hypothesis. Moreover, three way and four way interactions were found to be statistically insignificant and the inspection of the three way interaction (KY) revealed a data pattern inconsistent with hypothesis H,,. Yet, the finding that the predicted odds ratios of states with headlight use laws are somewhat lower than those of states without such laws may be indicative of the effectiveness of headlight laws and, by implication, support for the effectiveness of headlight operation. It must be pointed out, however, that the effect (RX) is not statistically significant and mu&k interpreted with caution. On balance, the findings of this study do not provide cleZ support for the effectiveness of motorcycle daytime headlight operation. Since other studies [Thomson, 1980; Vaughan et al., 1977; Hurt et al., 19811 have concluded differently, the discrepancy in findings must be reconciled. First, the study is only based on one measure of effectiveness which may not be the most adequate for assessing the impact of increasing motorcycle daytime headlight operation. The fatality ratios used in this study include rear-end and rear-angle collisions
Daytime headlight operation and motorcyclist fatalities
13
which should not be affected by daytime headlight use. Since these types of collisions comprise less than 25% of all fatal multi-vehicle collisions, it is unlikety that the exclusion of these data changes the results of the analysis. Preliminary analysis of the head-on and side-angle fatal collisions showed no meaningful differences. Second, the exclusion of dawn and dusk fatalities might reduce the potential of detecting the effect of increasing headlight operation. Several reasons would suggest that the exclusion of these data will not alter the findings of the analysis. First, two studies [MSF, 1979; Hurt et al., 19811found that headlights are used more often at dawn and dusk than at times of plain daylight. This observation suggests that headlight operation had not increased as rapidly among dawn and dusk collisions than among daytime collisions. Consequently, it would be more di~cult to detect the effect of increasing headlight operation among dawn and dusk collisions. Since dawn and dusk fatatities comprise less than 5% of all motorcycle fatalities, the inclusion of this group of fatalities will not change the statistical results significantly. Moreover, if daytime headlight operation has the intended effect. then it should be detectable during typical daytime lighting conditions. It has been pointed out that the ratio of multi- to single vehicle collisions might be inaccurately measured. For instance, a certain number of single vehicle collisions may be the result of avoiding another motor vehicle. In fact, Hurt et al. [1981: 421 found that about one-fifth of the single vehicle collisions fit this description. Therefore, headlight operation may not only reduce multivehicle collisions, but also prevent a certain proportion of “mis-classified” single vehicle collisions. If headlight operation is as effective in reducing such near-miss collisions as it is in reducing properly classified multi-vehicle collisions, then it can be shown that the effect of daytime headlight operation is overestimated by the odds ratios used in this study. The calculations supporting this statement can be found in Appendix C. A more serious concern is the possibility that daytime headlight operation may not have sufficiently increased as to show the expected collision reductions. To evaluate this point, the effectiveness of daytime headlight operation needs to be known. Two studies [Hurt et al., 1981 and Vaughan et al., 19771determined that headlight operation was about half as frequent among motorcyclists involved in multi-vehicle collisions than among a randomly selected group of motorcyclists who were not involved in accidents. This finding was interpreted as evidence of the effectiveness of headlight operation. Assuming that this inte~retation is warrented, motorcyclists with headlights operating have about one-fourth the risk (0.266) of daytime multi-vehicle collision than motorcyclists without their headlights on [Hurt ea al., 19811.According to Vaughan et al. [I977], the risk is about 40%. If, indeed, daytime headlight operation reduces multi-vehicle collisions by 60--73x, then it follows that an increase in daytime headlight operation by 32-43x (see Fig. 1) would result in a multi-vehicle collision reduction of 19-31%. Assuming that the calculations also apply to fatal accidents, the odds ratios should be reduced by the same percentage. This means that the odds ratio should have decreased from about 2-1.5 between 1976-1981. Yet in states without daytime headlight use laws, the observed decrease is only about one-fifth of this difference; a size which does not prove to be statistically significant. The previous calculations suggest two competing explanations of the discrepant findings. Either this study has greatly overestimated the increase in daytime headlight operation, or the effectiveness of daytime headlight operation has been overestimated by Hurt et al. 119811and Vaughan et al. 119773.There is reason to suspect that the latter has occurred. Table 8 presents data on daytime motorcycle collisions in the Los Angeles area [Hurt et al., 19811 and New South Wales, Australia fVaughan, 19771. The cross-tabulations indicate that motorcyclists involved in r&mlti-vehicle collision with their headlights on were as likely or more likely to be in front-end crashes, than side angle or rear-end collisions. Only one of the tables shows results which would marginally support the effectiveness of daytime headlight operation. Vaughan’s et al. data indicate a somewhat lower involvement in multi-vehicle collision when the headlight was on. The findings in Table 8 would suggest that the comparison of headlight use levels between accident and non-accident involved motorcyclists is an inadequate measure of
A.
14
MULLER
Table 8. Type of daytime collisions and motorcycle headlight operation among accident involved motorcyclists according to two studies Hurt, et al. Type of Multi-V. Collision Head-on
37
22.3
Other
~z!?~_
Total
166
Head-on & PeripheriaI'
Total x=
Note:
100.0
57 359
15.9
f?
84.1
377.3261
100.0
22.7
75
100.0
n 137
Oil % 82.5
29 175 --_A166 100.0 4.74;
61
18.9 81.1
322
loo
.53; PC.50
3.15; &x.10
k2
Other
Vaughan, et al, Headlight Operation Oil Off n *d z n
Headlight Operation On Off n n z *,
n
Off
265
94 359
On
Off
e
"
32
42.7
131
26.2
43
__$7,3
191
59.3
100.0
75
100.0
322
1oa.o
"
x 73.8
%
40.7
-01; PC.95
PG.05
No data on single vehicle collisions reoorted by Hurt, et al. (1981)
Type of Collision
n
On
%
"
81.5
322
88.2
43
11.8
Multi-V.
75
Single
17
18.5
Total
92
100.0
x2 =
Off
%
3651oo.o
2 . 84 pc . 10
*Head-on and peripheral collisons refer to 11. I2 and i o’clock line Of sight(Hurt, et al.,1981). Vauqhan. et al (1977) define head-on and peripheralcollisions as (1) vehicle in opposite direction perfoning wrong action, and (2) faitinq to yield riqht-of-way by other vehicle,
daytime headlight effectiveness. The large differences found between the “exposure” and accident samples reflect, at least in part, self-selection biast. Although the previous studies do not provide much support for the effectiveness of daytime headlight operation, there is the possibiIity that daytime headIight operation has a rather small effect which cannot be detected as statistically significant. It was pointed out that a slight decrease in the odds ratio was predicted for the period 1976-1981, amounting to about a 5% reduction in daytime multi-vehicle fatalities (see Table 7). Assuming that the decrease is in fact due to increased headlight operation, it is estimated that in 198 1 about 50 fatal muIti-vehicle collisions were prevented in states without daytime headlight use laws. This figure represents about 1.8% of all motorcycle fatalities in those states. According to this liberal interpretation of the data, the benefit of motorcycle daytime headlight operation would be a 4.2 to 5.6% reduction in motorcycle fatalities. CONCLUSION
This study is consistent with the conclusion that motorcycle daytime headI~ght operation is either ineffective or of minor effectiveness in preventing multi-vehicle fatal collisions. The conclusion agrees with other studies on daytime headlight operation and daytime headlight legislation which found small effects [Janoff et al., 1970, 1971; Williams and Hoffman, 1977) and statistically insignificant effects PHTSA, 1978; Muller, 1982, 19831.This study does not support the claim that daytime headlight operation is a powerful collision counte~easure [Hurt et al., 1981; Zador, 19831. tFor instance,Hurt er al. [I9811 study shows that accident involved motorcycles tended to be older than those in the exposure sample even after the comparison was adjusted for the chronological difference in the samples. Age standardization would most likely ‘show reduction in the difference in headlight use between exposure and accident samples. Moreover, Hurt er al. [1981: pp. 402-31 found that accident involved motorcyclists wore less protective equipment, particularly helmet use was under-repre~nted among the accident sample. This &ding suggests that accident involved motorcyclists are less safety conscious which would also explain part of the difference in headlight use between the two types of samples.
Daytime headlight operation and motorcyclist fatalities
I5
Acknowledgements-1 would like to thank the reviewers of this paper for their helpful suggestions. Also, I am indebted to Grace Hazard (NHTSA), Gary Winn (American Morotcyclist Association) and Melvin Stahl (Motorcycle Industry Council) who provided the data and much of the pertinent literature for this paper. The careful statistical work of my assistants, Regina Imgrund and Susan Kerns. is appreciated; so is James Shocker’s assistance with the computer analysis. However, the responsibility for the content of this paper solely rests wtth the author.
REFERENCES Attwood D. A.. The Potential of Daytime Running Lights as a Vehicle Collision Countermeasure. SAE Technical Paper Series, No. 810190, Society of Automotive Engineers, Warrendale, PA U.S.A., I-19. 1981. Davis J. A., Hierarchical models for significance tests in multivariate contingency tables: an exegesis of Goodman’s recent oawrs. Sociological Methodology _. 1973-74 (Edited bv H. L. Costner).II 189-231. Jossey-Bass., San Fran&co, 1974. Fleiss J. L., Statistical Methods for Rates and Proportions. Wiley & Sons, New York, 1981. Goodman L. A., A general model for the analysis of surveys. Am. J. of Sociology 77, 1035-86, 1972. Haberman S. J., Annl,vsis of Qualitatice Data, Vol. I. Academic Press, New York, 1978. Haberman S. J., Analysis of QuolitoticeData. Vol. 2. Academic Press, New York, 1979. Hurt H. H., Ouellet J. V. and Thorn D. R., Motorcycle Accident Cause Factors and Identification of Countermeasures. Vol. I, Technical Report. DOT-HS-805-862, NTIS, Springfield, VA U.S.A., 1981. Janoff M. S. and Cassell A., Effect of daytime motorcycle headlight laws on motorcycle accidents. Highway Res. Rec. 377, 53-63, 1971. Janoff M. S., Cassell A., Fertner K. S. and Smierciak E. S., Daytime Motorcycle Headlight and Taillight Operation. Franklin Institute, Rep. No. F-C2588, Philadelphia. 1970. Knoke D. and Burke P. J., Log-Linear Models, Sage Chtiversity Papers series on Quantitative Applications in the Social Sciences, 07-020, Sage Publications, Beverly Hills, l-80, 1980. Metropolitan Life Insurance Company, Motorcycle Accident Fatalities, Stat. Bulletin 59, 5-9, 1978. Motorcycle Industry Council, 1980 Motorcycle Stotisticul Annual, Motorcycle Industry Council, Inc., Newport Beach, CA 1980. Motorcycle Safety Foundation, Motorcycle Helmet Usage, State of Maryland, Motorcycle Safety Foundation. Linthicum MD, l-15, 1979. Motorcycle Safety Foundation, An Analysis of Motorcycle Accident Statistics. Motorcycle Safety Foundation. Linthicum MD, 1978. Muller A., How effective are motorcycle daytime headlight laws? A response to Zador’s criticism. Am. J. Pub. Heulth 73, 809-10.
1983.
Muller A., An evaluation of the effectiveness of motorcycle daytime headlight laws. Am. J. Pub. Health 72, 1136-41, 1982. National Safety Council, Accident Facts, 1977. National Safety Council, Chicago, IL 1977. Olson P. L., Halstead-Nussloch R. and Sivak M., The effect of improvements in motorcycle/motorcyclist conspicuity on driver behavior. Human Factors 23, 237-48, 1981. Robertson L. S., An instance of effective legal regulation: motorcyclist helmet and daytime headlamp laws. Lcrw and Society Rat. 10. 467-77,
1976.
Sebastian A. A. and Flemons D. M., NHTSA’s Fatal Accident Reporting System. Transpn Res. News 97, 5-9, 1981.
Thomson G. A., The role frontal motorcycle conspicuity has in road accidents. Accid. Anal. & Preu. 12. 165-178, 1980. U.S. DOT, NHTSA, NCSA, Motorcycles: FARS, Special Report on Motorcycles. DOT HS-803-186: Washington. D. C., 1978. Vaughan R. G., Pettigrew K. and Lukin J., Motorcycle Crushes: A Leael Two Study. Traffic Accident Research Unit, Dept. of Motor Transport, New South Wales, 1977. Wailer P. F. and GriIIIn L. I., The impact of a motorcycle lights-on law. Proc. of the Amer. Assoc. of Automotice Medicine. Vancouver, 14-25, 1977. Wailer P. F., The Impact of a Motorcycle Lights-on Law: An Update. Paper presented to the National Safety Council Symposium on Traffic Safety Effectiveness (Impact) Evaluation Projects. Chicago, IL, l-18, 1981. West’s Annotated Vehicle Code, California Code 825650.5. Article 13. Cumulative Pocket Part. Vol. 67. West Publishing Co., St. Paul, MI, 1982. Williams M. J. and Hoffman E. R., The InpUence of Motorcycle Visibility on Trafic Accidents. Dept. of Mech. Engng, University of Melbourne, 1977. Winn G., Motorcyclist Conspicuity: A Review of Selected Literature. American Motorcyclist Association. Westerville. OH 1980. Woltman H. L. and Austin R. L., Some day and night visual aspects of motorcycle safety. Transpn Res. Rec. 502, l-8,
1974.
Zador P., How effective are motorcycle daytime headlight laws? Am. J. Pub. Health 73, 808, 1983. APPENDIX
A
Projection of daytime headlight operation trend in CaltTornia Assumptions: (I) The age distribution of accident involved motorcycles
remains constant for the period 1976-1981. The distribution is based on 3600 oolice rewrts of motorcvcle accidents in the Los Anaeles area Isee Hurt et al. 1981: p. 771. (2) The proportion of headlight operation among accident involved motorcyclists equals that found among non-accident involved motorcyclist for model years 1978 and later (after introduction of the California law). (3) Low Projection: Headlight operation is 32% for all model years prior to 1978 and 88% for model years 1978 and later.
16
A. MULLER
High Projection: Headlight operation is 88% from 1975 on. The level of headlight operation for older motorcycles is determined by the constraint that headlight operation is 32% in 1976. That is:
32 = 0.668(0,) + 0.332(oJ where o, = level of headlight operation for model years before 1975; o2 = level of headlight operation for model years 1975-1977. Since oI = 88; 0, = 4.2. Table A- I Motorcycle Uodel Year (m)
1976
1977
Year 1978 1979
1980
.153
'70
.071
.153
'71
.091
.071
.153
'72
.lll
.091
.071
.153
'73
.122
.lll
.091
.071
.153
'74
.120
.122
.lll
.091
.071
'75
.200
.120
,122
.lll
'76
.108
.200
.120
.122
'77
.024
.108
.200
.120
.122
.024
.108
.200
.120
.024
.108
.200
.024
'78
-
'79 '80
-
'81 '82
Ueights
1981
oL
OH
32
4.2
32
4.2
32
4.2
32
4.2
32
4.2
.153
32
4.2
.091
.071
32
88
,111
.091
32
88
.lll
32
88
.122
88
88
.120
88
88
.108
.200
88
88
.024
.108
88
88
.024
88
88
-
Projected Daytime Headlight Operation* (%) Low:
32
33.3
39.4
50.6
57.3
64.1
High:
32
41.6
52.3
61.6
69.2
75.2
'Daytime headlight operation is calculated by the formula:
zmioi
APPENDIX B dnytime headlight use laws for slates in&&d
EJeeorive dates of motorcycle State
in the study
Effective Date
Arkansas
71 l/67
Florida
91 l/71
Georgia
4113173
Illinois
E/26/69
Indiana
71 l/67
Maine
6/28/74
Montana
71 l/67
New York
71 l/71
North Carolina
lo/ l/73
Oregon
g/12/67
South Carolina
71 l/73
Washington:-
7/ l/74
_
Wisconsin
l/11/68
Yyoming
6/ l/73
States without motorcycle datyime headlight use laws include all states and the District of Columbia minus states mentioned above. In addition, Minnesota, Tennessee. West Vfrglnia. and Califotnla were excluded from this group.
Daytime headlight operation and motorcyclist fatalities
17
APPENDIX C DaMme headlight operation and the misclarsifcution of single cehicie colksiorfs Since daytime headlight operation affects daytime collisions, the following calculation can be restricted to the ratio of multi to single vehicle collisions occurring in daylight. This ratio is expressed as MD/SD. Let: .WD = .Y; SD =x: i = effect of daytime headlight operation, and let the domain of i be {0 s i < 1). Then. the effect of daytime headlight operation on the multi to single vehicle ratio is, assuming no misclassification of collisions: x(1 -i) -. Y
(1)
Assuming that one fifth of the single vehicle collisions are near misses and can be prevented as effectively as multi-vehicle collisions, the effect of daytime headlight operation can be restated:
-41 - i)
(2)
0.8~ + O.Zy(I - i) ’ Then. the relationship between formula (I) and (2) is: x(1 -i) - Y
x(1 -i)
1 - O.ti
’ 0.8~ + 0.2y( I - i) = I
(3)
’
Formula (3) implies that as the effect of headlight operation (i) increases, the unadjusted ratio will become progressively smaller than the adjusted ratio. It follows, that the effect of “misclassifying” single vehicle collision will result in some overestimation of the effect of daytime headlight operation. This bias is not substantial as Long as headlight operation is not very effective.
APPENDIX
D
Table DI. Predicted number of fatalities by modd: TC, CY, SC, TY, TS, SY California Year
Type of Collision
1976
Multi
States
without
Headlight Day
Night
Day
Motorcycle Use Laws Night
States with Headlight Day
Motorcycle Use Laws Night
144.7
497.8
370.1
305.7
234.1
95.3
122.3
252.4
332.6
160.1
217.2
Multi
220.3
170.7
606.7
482.9
359.1
294.3
Single
107.0
147.0
313.4
442.0
191.5
278.1
1978
nulti
258.5
191.1
706.1
536.0
407.6
318.6
Single
123.5
161.8
358.6
482.3
213.7
296.1
1979
Multi
246.0
217.2
666.3
604.1
401.1
374.4
Single
122.0
190.9
351.3
564.3
218.4
361.2
I980
Multi
238.2
205.6
722.5
640.2
420.1
383.4
Single
119.5
182.7
385.3
605.0
231.4
374.1
1981
Multi
223.7
206.3
680.1
644.1
373.5
364.2
Single
111.2
ial .a
359.5
603.3
203.9
352.3
Single 1977
AAP
Vol. 16.No. I-B
199.7
A. MULLER
18
Table DZ. Predicted number of fatalities by model: EY, California Year
Type of Collison
1976
Multi Single
Day
Night
SC, TS, SY
States without Motorcycle Headlight Use Laws Night Day
States with Headlight Day
Motorcycle Use Laws Night
zoo.3
144.1
499.2
368.8
306.5
233.2
94.0
122.8
251.0
334 .o
159.2
218.2
360.8
292.4
Multi
221.3
169.6
609.8
480.0
Single
106.0
148.0
310.3
444.9
189.7
280.0
1978
Multi
256.8
192.8
701.4
540.8
404.8
321.4
Single
125.2
160.2
363.3
477.6
216.6
293.2
1979
Multi
247.6
215.6
670.7
599.8
403.7
371.7
Single
120.5
192.4
346.9
568.6
215.6
364.0 383.0
1977
1980
1981
Multi
238.4
205.3
123.2
639.7
420.5
Single
119.3
182.9
384.6
605.5
231.0
374.5
Multi
222.0
207.9
675.2
649.1
370.8
367.0
Single
112.8
180.3
364.5
596.2
206.8
349.4
Table D3. Predicted number of fatalities by model: KY, California Year
Type of Collision
1976
Multi Single
States
without
Headlight Day
Night
Oay
Motorcycle Use Laws Night
SCY, BY,
TSC States with Headlight Day
Motorcycle Use Laws Night
203.1
142.9
497.7
361.3
305.2
241.8
95.9
liO.1
251.3
342.7
157.8
212.2
216.8
161.2
614.2
477 .a
360.9
303.1
1977
Hul ti Single
114.2
152.8
303.8
449.2
188.1
270.9
1978
Multi
249.4
199.6
712.0
509.0
401.6
346.4
Single
121.6
164.4
379.0
483.0
204.4
283.6
1979
Multi
241.7
212.3
666.4
605.6
393.9
369.1
Single
124.3
197.7
332.6
561.4
226.1
365.9
Mu1ti
240.8
220.2
726.5
635.5
414.7
372.3
Single
109.2
175.8
377.5
613.5
248.3
373.7
Multi
231.2
202.8
671.1
659.9
365.7
361.3
608.1
219.3
347.7
1980
1981
Single
116.8
172.2
347.9
DAYTIME HEADLIGHT MOTORC.YCLIST
OPERATION FATALITIES
fj.00 i .30 Pros Ltd.
AND
ANDREAS MULLER Health Planning and Administration Program, College of Human Development, The Pennsylvania State University, University Park, PA 16802, U.S.A. (Received 2 Augusf 1982)
Abstract-Since 1978. all new motorcycles first registered in California are required by law to be equipped with headlights which automatically turn on when the engine is started. The purpose of this law is to increase headlight use during daytime and prevent multi-vehicle collisions due to poor conspicuity of motorcyclists. This paper examines whether the increasing operation of motorcycle headlights has been effective in reducing the number of daytime multi-vehicle fatalities in California and other states affected by the California legislation. Time series of motorcycle fatalities (1976-1981) for California and other states in the U.S.A. are analyzed by log-linear analysis. iModels representing the null-hypothesis were found to be consistent and more parsimonious descriptions of the observed data than models which incorporated additional terms indicating the effectiveness of increased headlight operation. or the effectiveness of daytime headlight use laws. Although the latter terms were not found to be statistically significant, a slight decrease in the odds ratio of multi to single vehicle collisions was predicted in states without daytime headlight use laws. This decrease suggests that daytime headlight operation may be beneficial in reducing the number of motorcycle fatalities. INTRODUCTION In
contrast to their popular image, motorcyclists are a particularly vulnerable group of traffic participants. Fatality statistics indicate that about 5000 persons died in motorcycle crashes in the U.S. in 1980 [NHTSA, FARS, 19811 and the fatality risk of motorcyclists is at least four times greater per mile than that of automobile occupants [NSC, 1977; Metropolitan Life Insurance Company, 19781. Studies of motorcycle accidents [Janoff et al., 1970; MSF 1978; Hurt et al., 19811 consistently show that the most frequent type of crash involves a collision with an automobile at an urban intersection in daylight. Automobile operators are most often at fault for the collision and frequently claim that the motorcyclist could not be seen. Headlight operation during daytime has been advocated [Thomson, 1980; Attwood, 198 I] as an effective collision countermeasure which should alert other traffic participants sooner of the approaching motorcyclist. Experimental studies and well-controlled field trials have found that daytime operation of headlights increases the contrast between the motorcyclist and his background [Janoff et al., 1970; Woltman and Austin, 1974; Williams and Hoffman, 19771 and enhances his conspicuity. Olson et al. [1981] observed that automobile drivers did not risk potential interference with the motorcyclist right-of-way quite as frequently when the headlight was on as when the headlight was turned off. In the U.S., 17 states have enacted laws which make use of motorcycle headlight mandatory during the day [Motorcycle Industry Council, 19801. The purpose of these laws is to increase headlight use over voluntary levels and reduce the number of daytime multivehicle collisions. Several studies have found varying estimates of the effectiveness of these laws ranging from no effect, or minor effects FHTSA, 1978; Muller, 1982; Janoff and Cassel, 19711to fairly large effects wailer and Griffin, 1977, 1981; Robertson, 19761. The last two studies suggest that about 20-25% of the daytime multivehicle collisions can be prevented by headlight use laws. The previous studies tend to underestimate the potential benefit of daytime headlight operation since they are only concerned with the increase in headlight use over voluntary levels resulting from the enactment of the legislation. Studies [Vaughan et al., 1977; Hurt et al., 198 l] comparing daytime headlight use between accident involved motorcyclists and randomly selected groups of non-accident involved motorcyclists suggest greater accident reduction potential. Both studies found that headlight operation was twice as frequent AAP Vol. 16. No. ,-A
I
2
A.
MULLER
among motorcyclists in the randomly selected group as among accident involved motorcyclists. The relative risk of accident involvement is about three times higher among motorcyclists not operating their headlights Vaughan, et al., 19771. Therefore, headlight operation in daylight seems to be a ‘- . . . powerful and effective way of reducing accident involvement, by making the motorcycle more conspicuous in traffic.” [Hurt et al., 1981,1982] Studies which try to detect the effectiveness of daytime headlight laws will not be likely to find effects, since in the late 1970s headlight use levels have become similar between states with and without the legislation [Muller, 19821. The convergence in headlight use levels was brought about by the introduction of motorcycles which automatically turn headlights on when the engine is started. The design change is a result of a California State law which was passed in 1972. Lack of timely compliance by several motorcycle manufacturers postponed the effective data of the legislation to 1978. Since then, the law states that “Every motorcycle manufactured and first registered shall be equipped with at least one and not more than two headlamps which automatically turn on when the engine of the motorcycle is started and which remain lighted as long as the engine is running”, ($25650.5 California Vehicle Code, West’s [ 19821). Similar legislation was enacted in Iowa (1980), Connecticut (1980) and Kansas (1982). The effect of the California passive? headlight law has been two-fold. With the replacement of old motorcycles by new hard-wired models, headlight operation during daytime will have steadily increased in California over the years. Since the California legislation affects about 15% of all motorcycles sold in the U.S.; the equipment change will have also been made on new motorcycles targeted for other states winn, 19801.This paper will investigate whether the increasing level of motorcycle headlight operation during daytime had a beneficial effect on motorcycle fatalities in California and other states. THE
INCREASE
IN DAYTIME
HEADLIGHT
OPERATION
Unfortunately, there are no regular roadside surveys which monitor daytime operation of motorcycle headlights. Therefore, the increase in daytime headlight operation must be extrapolated from a comprehensive study of motorcycle accidents in the Los Angeles area. Hurt ef al. [1981] collected data on headlight use for motorcycles involved in multivehicle collisions during 1976-77 and for a random sample of 2300 motorcyclists not involved in accidents two years later. To obtain comparable information, the motorcyclists surveyed were matched by accident location, time of day, day of week and weather conditions. In addition, the researchers collected data on 3600 accidents reported by the police. The latter sample was comparable to the in depth accident investigations. With respect to daytime headlight operation, the principal findings are shown in Table 1. Several results are noteworthy. During 1978-79 when the survey was taken, daytime headlight operation was 71%. This figure is 20% higher than that found by Robertson [ 19761who conducted a roadside survey in the Los Angeles area during September of 1975. The increase in headlight operation appears to reflect the introduction of hardwired motorcycles, since the headlight operation was only 64% in pre 1978 model years and 88% for motorcycles which had to conform with the California legislation. Apparently 12% of
Table 1. Per cent of daytime
headlight operation by type of sample and model year of motorcycle, Los Angeles area, California
Model
ore
Year
1978
1978-79 All
Note: Source:
tDoes
not require
action
Model
Accident
Exposure
Years
Excludes unknowns. Hurt -et al. (1981):
by motorcyclist.
63.5
a52
88.1
396
_
-
71.3
1248
_
-
99.
343
31.6
525
3
Daytime headlight operation and motorcyclist fatalities
model year 1978-79 motorcycles had not tutned their headlights on. Hurt et al. [1981: 3871 attribute this finding to either failing headlights or intentional change in the electrical system. About 6% of motorcyclists had installed light switches for the discretionary use of headlights. Headlight operation was only half the rate in accident involved motorcyclists when compared with the exposure sample. This finding was interpreted by Hurt et al. as evidence in support of the effectiveness of headlight operation. Some of the data in Table 1 can be used to project daytime headlight operation among accident involved motorcyclists for the period 1976-1981 (see Fig. 1). The projections are based on four assumptions. First, headlight operation among California accident involved motorcyclists was 32% in 1976. Second, hard-wired motorcycles were introduced by some manufacturers even before the effective date of the California legislation (l/1/78)?. Third, for motorcycles manufactured after 1 January 1978, headlight operation equals 88%. Fourth, the age distribution of accident involved motorcycles remains unchanged for the period 1976-1981. The calculations underlying the projections are shown in Appendix A. Figure 1 indicates that between 1976 and 1981 headlight operation is estimated to have increased between 32 and 43% points among accident involved motorcyclists. Since the timing of introduction of hard-wired motorcycles is not precisely known, the projections were calculated for two extreme situations. The “low” projection is based on the assumption that no hard-wired motorcycles were introduced before 1978, while the “high” projection assumes that hard-wired motorcycles were introduced by 1975. Apparently, the timing of the. introduction does not have a pronounced effect on the estimated increase in headlight operation. PERCENT
A m-
. 70
-
60so-
32.1
43.2
40-
30MIO
-
L
I
1976
Fig. I. Projected
I
1977
trend of headlight
I
I
1978 1979 YEAR
I
1980
I
)
1981
operation at day for accident involved motorcyclists, California.
The projected increase in daytime headlight operation may also be applicable to other states without daytime headlight use laws. Winn [I9801 mentions that since the largest number of motorcycles are sold in California, the equipment changes to conform with the California legislation will also have beets made on new motorcycles sold in other state@. tOne motorcycle manufacturer responding to an information request reported that all motorcycles quipped for legal street use have had automatic headlight on features since model year 1975. Other manufacturers followed suit as is reported by Hurt ef ~1. [1981: 3371 who observed that certain pre 1978 model year motorcycles were quipped with the automatic lights-on features. :In fact the manufacturer who responded to the information request confirmed this statement.
4
A. MULLER
A survey conducted by the Motorcycle Safety Foundation in January of 1981 suggests a high level of daytime headlight operation in states without daytime headlight use laws. About 76% of the responding motorcyclists stated that they “always” used their headlights during daytime. Although a self selection bias could account for the high use level, this explanation appears unlikely. During September of 1979 the Motorcycle Safety Foundation [ 19791conducted a roadside survey in the city of Baltimore and the surrounding state of Maryland and found headlight operations at 60%. This figure compares with 43% daytime headlight operation observed in a similar survey conducted among Baltimore motorcyclists in 1975 [Robertson, 19761. On the basis of the available evidence, it seems reasonable to conclude that the headlight operation has also increased in states other than California during the mid to late seventies and that this increase was most likely due to changes in motorcycle design. It follows then, that the level of daytime headlight operation should also have increased among accident involved motorcyclists in states without daytime headlight use laws. DATA,
HYPOTHESES
AND METHODS
The time series presented in this paper are based on motorcycle fatalities that occurred in California and other states during the six-year period 1976-198lt. The data were collected by the fatal accident reporting system [FARS; see Sebastian and Flemons, 19811 and pertain to motorcyclists excluding moped and motor-scooter fatalities. To assess the effect of increased headlight operation on motorcycle fatalities, the time series was classified by lighting condition (day and nightj and type of collision (multi vs single vehicle). Nighttime fatalities include those occurring under lighted highway conditions. Fatalities during dawn and dusk were excluded from the analysis. They comprise less than 5% of the motorcycle fatalities and will not affect the substantive conclusions of the analysis [see Muller, 19831. If daytime headlight operation is effective, then a certain number of daytime multivehicle collisions should be prevented. Since single vehicle collisions should not benefit from this collision countermeasure, it is expected that the ratio of multivehicle to single vehicle collisions will decrease corresponding with the increase in daytime headlight operation. Since several manufacturers equipped motorcycles with automatic headlights before the effective data of the California legislation (l/l/78), the effect of increased daytime headlight operation should also be present before 1978. A hypothesis which is consistent with this interpretation can be stated as follows:
Where MD = multi-vehicle collision fatalities at day; SD = single vehicle collision fatalities at day. Hypothesis (Hi) implies that the introduction of hard-wired motorcycles occurred gradually, but not necessarily at the same rate. A time series consistent with hypothesis (1) does not rule out the possibility that factors other than increased daytime headlight operation may have been responsible for the decrease in the ratios. To control such a bias, the daytime ratios are divided by their nighttime equivalents. This procedure adjusts the daytime data for trends in the nighttime data. For any given year the resultant odds ratio can be stated as follows:
MD
MN
MDxSN
(2)
@-==%=SDxMN
where o, = odds ratio for year t; MN - multi-vehicle SN = single vehicle collision fatalities at night.
collision
fatalities
&Since multivehicle collisions were diKerently determined in 1975 than in subsequent data were excluded from the analysis.
at night;
years,the 1975fatality
Daytime headlight operation and motorcyclist fatalities
5
Hypothesis H, can be restated using odds ratios. HIA: o,>o,+,*--
>o,+,
(3)
(O
(3a)
or r=ytl
and
In contrast, if increased daytime headlight operation is ineffective, then the odds ratios should remain constant for the time period 1976-1981. This null hypothesis can be written as: &:o,=k;
and
{Ock
(4)
i I =‘76,‘77...‘81;
or
Both hypotheses can be tested by log-linear analysis [Goodman, 1972; Davis, 1974; Haberman 1978 and 1979; Knoke and Burke, 19801. Log-linear analysis predicts cell frequencies in a cross-tabulation by specifying various effects by setting odds ratios at appropriate values {Davis, 1974: p. 1991.The predicted cell frequencies can then be compared with the actual data by x2 tests. In the context of this research, the log-linear model including all possible effects (saturated model) for the cross-tabulation: type of collision (C), time of day (T) and year (Y) can be stated as follows: (5) or by transfo~ation
in natural loga~thms.
where q = grand mean for the entire model: rc, T,?,T: = one variable effects, either variable C T or Y* rc’ ?cy 7TY = two variable interactions, either between variables C and T, C aid Y or ‘T”and* Ye ‘i Cry = three variable interactions among C, T and Y. The effect parameters (z) relate’to:pecific odds or odds ratios?. If the ratios are not equal to 1, effects are present which will either increase or decrease the product (F&. For instance, if the number of day and night fatalities are not identical, the parameter rf will depart from 1. Similarly, if the ratio of multi-vehicle to single vehicle collisions is different at day than at night, the parameter T:’ will not be equal to 1. That is, some association between the variables C and T exists. Moreover, if the latter association changes over the years, as is expected according to hypothesis HIA, then effects associated with parameter rr will be present. Specific hypotheses (models) can be tested by setting one or more of the tau parameters equal to 1. The following models are of interest. Model No. 1. 2. 3. 4. 5.
Effect Parameters
Fitted Marginal Notationt
qrf7j-7;
C,
q7:7;7;7;:-_
CT, Y CT, CY CT, CY, TY CTY.
tf7;7;7;+gy tfTi
c7i r 7kTiiY
c T r/7itj?,7@
Y
cr
cy TY Z& r*
CT
CY 7f& Tj&
fr fg&CTY
T,
Y
tThe relationship between T and odds, or odds ratios is discussed in Knoke and Burke [1980: pp. 1l-291. $It is more convenient to represent the models in fitted marginal notation, which does not state the lower order effects as long as they are implied by higher order effect.
A.
6
,&‘fULLER
Model I only permits single variable effects and is useful as a baseline model against which other models can be compared. Models 2 to 4 are consistent with hypothesis (H,) which stipulates that the effect parameter rF can depart from I, but will remain constant over the years. Yet models 2 to 4 vary in the number of other two variable effects whose inclusion may improve the fit of the model. Model 5 is of specific interest since it relates to hypothesis H,,. It permits departures of the relative odds ratios from 1 and is consistent with the expression r=~where{O
(7)
Yet, hypothesis H,, requires that the values of the relative odds ratios (r) are restricted to the domain (0 < r < 11. Therefore, if model 5 turns out to be the only fitting model, the relative odds ratios (r) must be inspected to determine whether they are consistent with the restriction stated by hypothesis H,,. Since model 5 will perfectly predict the data (saturated model), only the inspection of the observed data is needed. The models were estimated using the BMDP statistical software package (revised, 4182). FINDINGS
FOR CALIFORNIA
California motorcycle fatalities between 1976-1981 are presented in Table 2 and the corresponding odds ratios are displayed in Fig. 2. The ratios indicate that the odds of dying in a multi-vehicle collision rather than a single vehicle collision are roughly 2:l during daytime and somewhat more than even at night. Figure 2 shows neither a consistent decrease in the daytime odds nor in the odds ratios over the years. Table 3 presents the results of fitting specified models to the data. The models are hierarchically ordered so that specific effects can be tested for statistical significance. The association between type of collision and time of day represented by term TC is highly significant. This is not surprising, since the odds ratio is substantially greater than 1 (see Fig. 2). The association between time of day and year (TY) is marginally significant, and suggests that nighttime fatalities have increased relative to daytime fatalities. Models 2-5 fit the data well. Model 5 is of particular interest, since it relates to hypothesis H,,. The comparison with model 4 indicates that the effect of the three way Table 2. California motorcycle fatalities observed and predicted* by lighting condition, type of collision and year Observed Year
Type of Collision
1976
Multi
Predicted* Night
Oay n
MIS
203
n
1977
96
Multi
212
Single
119
Multi
249
1979
122
Multi
247
1980
119
Multi
235
1981
Single
115
flulti
237
Single
203
*Refers U/S
to flOOEL 3, TABLE
= Multi-vehicle:
1.537
TO
178
3.
single
vehicle
1.929
1.749
1.159
1.749
1.159
1.751
201.3 2.029
114.9
1.159
183.4
233.1 1.107
1.750
212.6 2.028
115.6
197
1.159
189.9
234.4 1.329
1.751
220.1 2.027
120.9
72%
1.158
168.6
245.1 2.036
1.751
195.4 2.029
122.5
1.020
1.159
145.5
248.5
207
0
168.5 2.028
1.674
WS
141.2
109.3
1.220
n
121.8
221.7
164
111
M/S
2.029
1.588
200
2.135
Night
Oay
98.7
1.122
2.043
" zoo.3
148
2.076 Single
1.774
166
2.041 Single
1.192 120
1.782
1978
0
143 2.115
Single
MIS
173.7
7
Daytime headlight operation and motorcyclist fatalities Table 3. Comparison among log-linear models and results of statistical significance tests *
Model
O.F.
1.
T. C, Y
2.
TC,
3.
TC,
4.
TC,
TY.
5.
TCY
3D.F.
IL?
L'
P
16
91.68
0
Y
15
14.10
.518
1
TY
10
5.71
.a39
5
a.39
.l
5
2.60
.761
5
3.11
.7cpc.5
0
0
-
5
2.60
.acpc .7
CY
-
P
-
77.58
m
zylo
4
I.0
I
PC.001
IlIelFMms
I 1977
I
1976
I 1979
I 1978
I
1980
I 1981
*
YEAR -
M"
mvsw
-
am
UATIO
-
*'6+u (m/a)
g
Fig. 2. The odds of multi-vehicle to single vehicle fatal collisions in California by time of day and year.
interaction (WY) is statistically insignificant and the observed data (model KY) do not show a declining trend (see Fig. 3). Therefore, a simpler model can describe the data more parsimoniously. Model 3 was selected as basis for comparison since it achieves excdlent fit relative to the degrees of freedom used for parameter estimation. Models 2 and 4 could have also been used for comparison. They imply that the odds ratio (TC) remains constant over the period 1976-l 98 1. This would be represented by a horizontal line closely parallel to the one shown in Fig. 3. The predicted data in Table 2 can be interpreted as follows. First the odds of dying in multivehicle collision rather than a single vehicle collision are 75% higher at day than at night. These odds remain constant from 1976 to 1981 and are consistent with the null hypothesis. In addition, the two-way interaction (TY) suggests that nighttime fatalities increased by 23% between 1976 and 1981 relative to daytime fatalities. The predicted data indicate that the increase occurred in single and multi-vehicle collisions. FINDINGS*OR
OTHER
STATES
The analysis of the California motorcycle fatalities suggests that the null hypothesis specifying no trend seems to fit the data best. That means, that increased daytime headlight operation may not be effective. If this inference is correct, then the null hypothesis should also be applicable to states other than California. Furthermore, it follows that daytime headlight use laws should be ineffective and the null hypothesis should apply to these states as well. The following analysis will examine these implications.
8
A.
MULLER
oom RATIO
4 3.0 -
*ooos RATIO:
!g:g
Fig. 3. Odds ratios for California, by model 1976-1981.
Table 4. Motorcycle fatalities for states with and without daytime headlight use laws by lighting condition and year States without Motorcycle Year
Type of Collision
1976
Multi
505
Single
244
Multi
617
1977
1978
1979
1980
1981
n
Single
301
Multi
708
Single
383
Multi
683
Single
336
Multi
722
Single
382
Multi
673
Single
346
Headlight Use Laws* Night Day n U/S WS 2.070
2.60
I.849
2.033
1.890
I.945
354 350 475 452 513 479 609 558 640 609 658 610
1.011
with Motorcycle Headlight Use Laws* Night Oay
States 0
2.046
1.051
1.951
1.071
1.726
1.091
1.863
1.051
1.799
1.079
1.803
n
298 165 363 186 406 200 392 228 425
H/S
1.806
1.952
2.030
1.719
1.786
238 358 227
”
M/S
0
1.215
1.487
1.103
1.770
l.lES
1.709
1.019
1.687
.943
1.894
1 .Oi?5
1.453
249
1.570
205 301 273 342 288 371 364 362 384 369 340
*See APPENDIX 6 for states included in the group. M/S = Multi-vehicle: single vehicle
Table 4 shows the aggregationi of motorcycle fatalities for states with and without daytime headlight use laws. In contrast to the California legislation these laws require motorcyclists to switch their headlight on during daytime in case the motorcycle is not equipped with the automatic lights on feature. The group of states with headlight use laws only includes states (14) which had the laws for the period, 197.5 198 1. The group of states without headlight use laws includes 32 states and the District of Columbia, and excludes California. Figures 4 and 5 present the graph of odds ratios for the two groups of states. The tThe meaningful interpretation of the aggregated fatality data assumes that the association (odds ratios) between type of collision and time of day does not greatly vary among states within each subgroup. This possibility was tested by homogeneity tests of log odds ratios [see Fleiss, 1981: l6C-681. The test results showed no statistically significant differences among states for each year.
Daytime headlight operation and motorcyclist fatalities
9
6 3.0 -
2.0 -
.
.
1.0 -
NIelT
I 1976
SOURCE:
I 1977
I 1979
I 1976
I 1960
I 1961
(lwsll)
*
lable 4
Fig. 4. Odds and odds ratios for states without daytime headlight use laws.
I 1976 SOURCE:
Table 4
I 1977
I 1976
I 1979
I 1980
I 1961
*
YEAR
Fig. 5. Odds and odds ratios for states with daytime headlight use laws.
daytime series for states without headlight use laws shows slightly lower odds for the last four years than for the first two years of the series. Since the odds for nighttime series are nearly constant for the entire period, the odds ratios parallel the daytime data series. The time series for states with daytime headlight laws (Fig. 5) shows more fluctuation. Again, the daytime odds are lower in the last part of the time series than in the first. Since the nighttime odds roughly parallel this data pattern, the odds ratios show no consistent trend for the 6yr period. Figure 6 compares the three time series of odds ratios and indicates that the time series are largely overlapping. The following analysis will determine which interpretation of the data is most supported. Table 5 presents the results of the log-linear analysis of the four variable cross tabulation: collision type (C), time of day.(T), year (I’), and states (S). To test specific effects, the models are hierarchically ordered beginning with the single variable effects model (1). Due to the introduction of a fourth variable (S) additional models need to be specified.
IO
A. .MIJLLER
CALIFORNIA
I.0
1 I
I
1976
I
1977
I
1978
I
1979
I 1980
I
*
1981
YEAR
XNNtCE:
lables
2 and 4
Fig. 6. Odds ratios for states with and without daytime headlight use laws and California. 19761981.
Models 2-7 are consistent with the null hypothesis which stipulates that the odds ratio (TC) neither changes over the years nor varies by group of state. Models 8-l 1 allow for variation in the odds ratio (TC) by year, indicated by term (KY), and relate to hypothesis H,,,. The four variable effect (K’YS) should be significant, if headlight operation is effective and motorcyclists complied with headlight use laws. A convergence of odds ratios between states with and without headlight use laws is expected according to this model. Models l-4 are inadequate representations of the observed data, although effect TC turns out highly significant and the association between state and collision type (SC) is of marginal significance. In contrast, models 5-7 fit the data, which is primarily due to the inclusion of the association between time of day and year (TY). Models 8-11 show that the incorporation of three way interactions does not substantially improve the goodness of fit. The decreasing probability estimates in column 3 indicate that small decreases in L’ are achieved at relative high costs in degrees of freedom. Therefore models 8-1 I are adequate, but less parsimonious representations of the observed data. The comparison of models I1 and 12 indicates that the four way interaction TCYS is also statistically insignificant. Model 13 is presented to show that only four associations are necessary to describe the observed data very well. The modelled data suggest the following. The odds of dying in a multivehicle rather than a single vehicle collision are 78% higher at day than at night. The corresponding odds ratios (TC) are identical for all three groups of states and all years. The odds of fatal multivehicle collision are slightly higher in states without daytime headlight use laws. The odds of a nighttime fatal collision have increased by 28% in all states over the 6 yr period. Motorcycle fatalities increased faster in states with and without headlight use laws than in California. The fastest increase occurred in states without headlight use laws. These observations are based on the predicted data shown in Table 6. Table 7 displays odds ratios, pertaining to term (TC) based on selected models which are of primary research interesf.The models are listed in Table 5. For instance model 7 predicts a constant odds ratio of 1.772 for all states and years. The model accounts for 95% of the variation in the cross-tabulation when compared with the baseline model (1). Model 8 would support hypothesis H,,, if the predicted odds ratios were to decrease over the years. This is not the case. A comparison with model 7 shows a pattern consistent with random fluctuations. The odds ratios predicted by model 11 parallel those predicted by
II
Daytime headlight operation and motorcyclist fatalities Table 5. Comparison among log-linear models and results of statistical significance tests Nodeis
D.F.
z I..
o
:D.F.
AZ
D.
-
-
I,
T, t, Y, S
62
574,54
.O
-
2.
TC. Y. 5
61
lc6.91
.OoO3
1
467.63
3.
TC, CY, 5
56
100.99
.oooz
s
5.92
fX.OOl ‘5CPC.3
4,
TC, CY, SC
54
94,30
.0006
2
6.69
;05cp<.52
5.
TC, CY, SC, TY
49
46.56
.5724
5
47.74
.45
6.
TC, 0.
47
44.24
3876
2
2.32
10
16.66
.1
5
1.22
cpc.9
SC. TY, TS
.5
7.
TC. CY, SC, TY, TS, SY
37
27.58
.a699
6.
TCY, SC, TS, SY
32
26.36
.7472
9,
TCY, SCY. TS
22
17.05
.7604
10
9.31
.7
IO
6.96
.aspc.7
2
2.91
.3
7.19
.a
TCY, S&Y, TSY
I2
lO.IO
.6075
Il. TCY, SCY. TSY, TCS
10
V-19
.7074
1%
12. TCYS 13. TC, SC. TY, SY Note:'
-la
00 44
31.85
.914
-
-
-
based on 3 gmups of states: California,states%jth and states without daytime headlight use laws.
Analysis is
Table 6. Predicted number of fatalities by model: TC, SC, TY, SY Cat ifornia
states rr'thoutMotorcycle Headfight Use Laws Night Day
States with Motorcycle Headtight tfseLaws Night Day
Year
Type of C0lIiSiW
I976
nu1t.i
195.6
145.4
492.5
366.0
306.2
227.6
Single
95.3
125.8
266.2
338.2
165.2
218.0
Multi
216.8
172.9
603.9
481.7
362.1
288.9
Single
105.6
149.6
314.2
445.1
195.3
216.7
1978
tduiti
253.2
192.2
698.9
530.4
408.5
315.1
Single
123.4
166.3
363.6
490.1
220.4
297.0
1979
Multi
243.5
221.9
667.8
608.5
407.7
37f.S
Single
113.6
192.0
347.5
562.3
zt9.9
355.9
1980
Multi
236.7
211.2
726.8
648.6
428.7
382.6
Single
115.3
182.7
378.2
599.3
231.3
366.5
380.2
362.0
205.1
346.8
1977
I983
Day
Night
Multi
221.6
211.0
682.2
649.6
Single
107.9
182.5
365.0
605.2
model 8. In addition, model 1I predicts differences in the level of the three time series (see Fig. 7). States with daytime headlight use laws have somewhat lower odds ratios than states without such laws. Model 11 also accounts for an additional 2.5% of the variation in the ~~Ss-~~~Iati~n.
The major findings of the previous analyses are as follows. The log-linear analysis of the Cafifornia motorcycle fatalities is consistent with the null hypothesis stating that the odds ratios have remained constant from 19X-1981. The extension of the analysis to other states also showed that modets consistent with the null hypothesis predict the data well and are more parsimonious than models incorporating higher order interactions. Up to
A. MULLER
12
Table 7. Predicted odds ratios (2-C) by model. state and year Model
!L$L;\)/Li . *
1976
1977
1978
1979
1980
1981
W/O Law ! 1.772
1.772
1.772
1.772
1.772
1.772
,952
1.801
1.821
1.705
1.834
1.780
1.707
,954
1.681
Cal $7
W. Law Cal #B
U/O Law W. Law
%ll
Cal
i ,780
1.799
1.689
1.811
1.760
W/O Law
1.879
1.901
1.783
1.913
1.858
1.778
W. Law
1.697
1.715
1.609
1.727
1.676
1.605
.987
Note: Model numbers refer to those used in TABLE 5. Li = Liklihood ratio x2 of baseline model, MODEL 1. LA = Liklihood ratio x2 of alternate model, see TABLE 5. Source: TABLES 1, 2, and 3 in APPENDIX D.
SOURCE: Table 3. &wendix 0
Fig. 7. Predictedodds ratios (TC) by model TCY, SCY, TSY, TCS. 95% of the variation in the observed data could be accounted for by models consistent with the null hypothesis. Moreover, three way and four way interactions were found to be statistically insignificant and the inspection of the three way interaction (KY) revealed a data pattern inconsistent with hypothesis H,,. Yet, the finding that the predicted odds ratios of states with headlight use laws are somewhat lower than those of states without such laws may be indicative of the effectiveness of headlight laws and, by implication, support for the effectiveness of headlight operation. It must be pointed out, however, that the effect (RX) is not statistically significant and mu&k interpreted with caution. On balance, the findings of this study do not provide cleZ support for the effectiveness of motorcycle daytime headlight operation. Since other studies [Thomson, 1980; Vaughan et al., 1977; Hurt et al., 19811 have concluded differently, the discrepancy in findings must be reconciled. First, the study is only based on one measure of effectiveness which may not be the most adequate for assessing the impact of increasing motorcycle daytime headlight operation. The fatality ratios used in this study include rear-end and rear-angle collisions
Daytime headlight operation and motorcyclist fatalities
13
which should not be affected by daytime headlight use. Since these types of collisions comprise less than 25% of all fatal multi-vehicle collisions, it is unlikety that the exclusion of these data changes the results of the analysis. Preliminary analysis of the head-on and side-angle fatal collisions showed no meaningful differences. Second, the exclusion of dawn and dusk fatalities might reduce the potential of detecting the effect of increasing headlight operation. Several reasons would suggest that the exclusion of these data will not alter the findings of the analysis. First, two studies [MSF, 1979; Hurt et al., 19811found that headlights are used more often at dawn and dusk than at times of plain daylight. This observation suggests that headlight operation had not increased as rapidly among dawn and dusk collisions than among daytime collisions. Consequently, it would be more di~cult to detect the effect of increasing headlight operation among dawn and dusk collisions. Since dawn and dusk fatatities comprise less than 5% of all motorcycle fatalities, the inclusion of this group of fatalities will not change the statistical results significantly. Moreover, if daytime headlight operation has the intended effect. then it should be detectable during typical daytime lighting conditions. It has been pointed out that the ratio of multi- to single vehicle collisions might be inaccurately measured. For instance, a certain number of single vehicle collisions may be the result of avoiding another motor vehicle. In fact, Hurt et al. [1981: 421 found that about one-fifth of the single vehicle collisions fit this description. Therefore, headlight operation may not only reduce multivehicle collisions, but also prevent a certain proportion of “mis-classified” single vehicle collisions. If headlight operation is as effective in reducing such near-miss collisions as it is in reducing properly classified multi-vehicle collisions, then it can be shown that the effect of daytime headlight operation is overestimated by the odds ratios used in this study. The calculations supporting this statement can be found in Appendix C. A more serious concern is the possibility that daytime headlight operation may not have sufficiently increased as to show the expected collision reductions. To evaluate this point, the effectiveness of daytime headlight operation needs to be known. Two studies [Hurt et al., 1981 and Vaughan et al., 19771determined that headlight operation was about half as frequent among motorcyclists involved in multi-vehicle collisions than among a randomly selected group of motorcyclists who were not involved in accidents. This finding was interpreted as evidence of the effectiveness of headlight operation. Assuming that this inte~retation is warrented, motorcyclists with headlights operating have about one-fourth the risk (0.266) of daytime multi-vehicle collision than motorcyclists without their headlights on [Hurt ea al., 19811.According to Vaughan et al. [I977], the risk is about 40%. If, indeed, daytime headlight operation reduces multi-vehicle collisions by 60--73x, then it follows that an increase in daytime headlight operation by 32-43x (see Fig. 1) would result in a multi-vehicle collision reduction of 19-31%. Assuming that the calculations also apply to fatal accidents, the odds ratios should be reduced by the same percentage. This means that the odds ratio should have decreased from about 2-1.5 between 1976-1981. Yet in states without daytime headlight use laws, the observed decrease is only about one-fifth of this difference; a size which does not prove to be statistically significant. The previous calculations suggest two competing explanations of the discrepant findings. Either this study has greatly overestimated the increase in daytime headlight operation, or the effectiveness of daytime headlight operation has been overestimated by Hurt et al. 119811and Vaughan et al. 119773.There is reason to suspect that the latter has occurred. Table 8 presents data on daytime motorcycle collisions in the Los Angeles area [Hurt et al., 19811 and New South Wales, Australia fVaughan, 19771. The cross-tabulations indicate that motorcyclists involved in r&mlti-vehicle collision with their headlights on were as likely or more likely to be in front-end crashes, than side angle or rear-end collisions. Only one of the tables shows results which would marginally support the effectiveness of daytime headlight operation. Vaughan’s et al. data indicate a somewhat lower involvement in multi-vehicle collision when the headlight was on. The findings in Table 8 would suggest that the comparison of headlight use levels between accident and non-accident involved motorcyclists is an inadequate measure of
A.
14
MULLER
Table 8. Type of daytime collisions and motorcycle headlight operation among accident involved motorcyclists according to two studies Hurt, et al. Type of Multi-V. Collision Head-on
37
22.3
Other
~z!?~_
Total
166
Head-on & PeripheriaI'
Total x=
Note:
100.0
57 359
15.9
f?
84.1
377.3261
100.0
22.7
75
100.0
n 137
Oil % 82.5
29 175 --_A166 100.0 4.74;
61
18.9 81.1
322
loo
.53; PC.50
3.15; &x.10
k2
Other
Vaughan, et al, Headlight Operation Oil Off n *d z n
Headlight Operation On Off n n z *,
n
Off
265
94 359
On
Off
e
"
32
42.7
131
26.2
43
__$7,3
191
59.3
100.0
75
100.0
322
1oa.o
"
x 73.8
%
40.7
-01; PC.95
PG.05
No data on single vehicle collisions reoorted by Hurt, et al. (1981)
Type of Collision
n
On
%
"
81.5
322
88.2
43
11.8
Multi-V.
75
Single
17
18.5
Total
92
100.0
x2 =
Off
%
3651oo.o
2 . 84 pc . 10
*Head-on and peripheral collisons refer to 11. I2 and i o’clock line Of sight(Hurt, et al.,1981). Vauqhan. et al (1977) define head-on and peripheralcollisions as (1) vehicle in opposite direction perfoning wrong action, and (2) faitinq to yield riqht-of-way by other vehicle,
daytime headlight effectiveness. The large differences found between the “exposure” and accident samples reflect, at least in part, self-selection biast. Although the previous studies do not provide much support for the effectiveness of daytime headlight operation, there is the possibiIity that daytime headIight operation has a rather small effect which cannot be detected as statistically significant. It was pointed out that a slight decrease in the odds ratio was predicted for the period 1976-1981, amounting to about a 5% reduction in daytime multi-vehicle fatalities (see Table 7). Assuming that the decrease is in fact due to increased headlight operation, it is estimated that in 198 1 about 50 fatal muIti-vehicle collisions were prevented in states without daytime headlight use laws. This figure represents about 1.8% of all motorcycle fatalities in those states. According to this liberal interpretation of the data, the benefit of motorcycle daytime headlight operation would be a 4.2 to 5.6% reduction in motorcycle fatalities. CONCLUSION
This study is consistent with the conclusion that motorcycle daytime headI~ght operation is either ineffective or of minor effectiveness in preventing multi-vehicle fatal collisions. The conclusion agrees with other studies on daytime headlight operation and daytime headlight legislation which found small effects [Janoff et al., 1970, 1971; Williams and Hoffman, 1977) and statistically insignificant effects PHTSA, 1978; Muller, 1982, 19831.This study does not support the claim that daytime headlight operation is a powerful collision counte~easure [Hurt et al., 1981; Zador, 19831. tFor instance,Hurt er al. [I9811 study shows that accident involved motorcycles tended to be older than those in the exposure sample even after the comparison was adjusted for the chronological difference in the samples. Age standardization would most likely ‘show reduction in the difference in headlight use between exposure and accident samples. Moreover, Hurt er al. [1981: pp. 402-31 found that accident involved motorcyclists wore less protective equipment, particularly helmet use was under-repre~nted among the accident sample. This &ding suggests that accident involved motorcyclists are less safety conscious which would also explain part of the difference in headlight use between the two types of samples.
Daytime headlight operation and motorcyclist fatalities
I5
Acknowledgements-1 would like to thank the reviewers of this paper for their helpful suggestions. Also, I am indebted to Grace Hazard (NHTSA), Gary Winn (American Morotcyclist Association) and Melvin Stahl (Motorcycle Industry Council) who provided the data and much of the pertinent literature for this paper. The careful statistical work of my assistants, Regina Imgrund and Susan Kerns. is appreciated; so is James Shocker’s assistance with the computer analysis. However, the responsibility for the content of this paper solely rests wtth the author.
REFERENCES Attwood D. A.. The Potential of Daytime Running Lights as a Vehicle Collision Countermeasure. SAE Technical Paper Series, No. 810190, Society of Automotive Engineers, Warrendale, PA U.S.A., I-19. 1981. Davis J. A., Hierarchical models for significance tests in multivariate contingency tables: an exegesis of Goodman’s recent oawrs. Sociological Methodology _. 1973-74 (Edited bv H. L. Costner).II 189-231. Jossey-Bass., San Fran&co, 1974. Fleiss J. L., Statistical Methods for Rates and Proportions. Wiley & Sons, New York, 1981. Goodman L. A., A general model for the analysis of surveys. Am. J. of Sociology 77, 1035-86, 1972. Haberman S. J., Annl,vsis of Qualitatice Data, Vol. I. Academic Press, New York, 1978. Haberman S. J., Analysis of QuolitoticeData. Vol. 2. Academic Press, New York, 1979. Hurt H. H., Ouellet J. V. and Thorn D. R., Motorcycle Accident Cause Factors and Identification of Countermeasures. Vol. I, Technical Report. DOT-HS-805-862, NTIS, Springfield, VA U.S.A., 1981. Janoff M. S. and Cassell A., Effect of daytime motorcycle headlight laws on motorcycle accidents. Highway Res. Rec. 377, 53-63, 1971. Janoff M. S., Cassell A., Fertner K. S. and Smierciak E. S., Daytime Motorcycle Headlight and Taillight Operation. Franklin Institute, Rep. No. F-C2588, Philadelphia. 1970. Knoke D. and Burke P. J., Log-Linear Models, Sage Chtiversity Papers series on Quantitative Applications in the Social Sciences, 07-020, Sage Publications, Beverly Hills, l-80, 1980. Metropolitan Life Insurance Company, Motorcycle Accident Fatalities, Stat. Bulletin 59, 5-9, 1978. Motorcycle Industry Council, 1980 Motorcycle Stotisticul Annual, Motorcycle Industry Council, Inc., Newport Beach, CA 1980. Motorcycle Safety Foundation, Motorcycle Helmet Usage, State of Maryland, Motorcycle Safety Foundation. Linthicum MD, l-15, 1979. Motorcycle Safety Foundation, An Analysis of Motorcycle Accident Statistics. Motorcycle Safety Foundation. Linthicum MD, 1978. Muller A., How effective are motorcycle daytime headlight laws? A response to Zador’s criticism. Am. J. Pub. Heulth 73, 809-10.
1983.
Muller A., An evaluation of the effectiveness of motorcycle daytime headlight laws. Am. J. Pub. Health 72, 1136-41, 1982. National Safety Council, Accident Facts, 1977. National Safety Council, Chicago, IL 1977. Olson P. L., Halstead-Nussloch R. and Sivak M., The effect of improvements in motorcycle/motorcyclist conspicuity on driver behavior. Human Factors 23, 237-48, 1981. Robertson L. S., An instance of effective legal regulation: motorcyclist helmet and daytime headlamp laws. Lcrw and Society Rat. 10. 467-77,
1976.
Sebastian A. A. and Flemons D. M., NHTSA’s Fatal Accident Reporting System. Transpn Res. News 97, 5-9, 1981.
Thomson G. A., The role frontal motorcycle conspicuity has in road accidents. Accid. Anal. & Preu. 12. 165-178, 1980. U.S. DOT, NHTSA, NCSA, Motorcycles: FARS, Special Report on Motorcycles. DOT HS-803-186: Washington. D. C., 1978. Vaughan R. G., Pettigrew K. and Lukin J., Motorcycle Crushes: A Leael Two Study. Traffic Accident Research Unit, Dept. of Motor Transport, New South Wales, 1977. Wailer P. F. and GriIIIn L. I., The impact of a motorcycle lights-on law. Proc. of the Amer. Assoc. of Automotice Medicine. Vancouver, 14-25, 1977. Wailer P. F., The Impact of a Motorcycle Lights-on Law: An Update. Paper presented to the National Safety Council Symposium on Traffic Safety Effectiveness (Impact) Evaluation Projects. Chicago, IL, l-18, 1981. West’s Annotated Vehicle Code, California Code 825650.5. Article 13. Cumulative Pocket Part. Vol. 67. West Publishing Co., St. Paul, MI, 1982. Williams M. J. and Hoffman E. R., The InpUence of Motorcycle Visibility on Trafic Accidents. Dept. of Mech. Engng, University of Melbourne, 1977. Winn G., Motorcyclist Conspicuity: A Review of Selected Literature. American Motorcyclist Association. Westerville. OH 1980. Woltman H. L. and Austin R. L., Some day and night visual aspects of motorcycle safety. Transpn Res. Rec. 502, l-8,
1974.
Zador P., How effective are motorcycle daytime headlight laws? Am. J. Pub. Health 73, 808, 1983. APPENDIX
A
Projection of daytime headlight operation trend in CaltTornia Assumptions: (I) The age distribution of accident involved motorcycles
remains constant for the period 1976-1981. The distribution is based on 3600 oolice rewrts of motorcvcle accidents in the Los Anaeles area Isee Hurt et al. 1981: p. 771. (2) The proportion of headlight operation among accident involved motorcyclists equals that found among non-accident involved motorcyclist for model years 1978 and later (after introduction of the California law). (3) Low Projection: Headlight operation is 32% for all model years prior to 1978 and 88% for model years 1978 and later.
16
A. MULLER
High Projection: Headlight operation is 88% from 1975 on. The level of headlight operation for older motorcycles is determined by the constraint that headlight operation is 32% in 1976. That is:
32 = 0.668(0,) + 0.332(oJ where o, = level of headlight operation for model years before 1975; o2 = level of headlight operation for model years 1975-1977. Since oI = 88; 0, = 4.2. Table A- I Motorcycle Uodel Year (m)
1976
1977
Year 1978 1979
1980
.153
'70
.071
.153
'71
.091
.071
.153
'72
.lll
.091
.071
.153
'73
.122
.lll
.091
.071
.153
'74
.120
.122
.lll
.091
.071
'75
.200
.120
,122
.lll
'76
.108
.200
.120
.122
'77
.024
.108
.200
.120
.122
.024
.108
.200
.120
.024
.108
.200
.024
'78
-
'79 '80
-
'81 '82
Ueights
1981
oL
OH
32
4.2
32
4.2
32
4.2
32
4.2
32
4.2
.153
32
4.2
.091
.071
32
88
,111
.091
32
88
.lll
32
88
.122
88
88
.120
88
88
.108
.200
88
88
.024
.108
88
88
.024
88
88
-
Projected Daytime Headlight Operation* (%) Low:
32
33.3
39.4
50.6
57.3
64.1
High:
32
41.6
52.3
61.6
69.2
75.2
'Daytime headlight operation is calculated by the formula:
zmioi
APPENDIX B dnytime headlight use laws for slates in&&d
EJeeorive dates of motorcycle State
in the study
Effective Date
Arkansas
71 l/67
Florida
91 l/71
Georgia
4113173
Illinois
E/26/69
Indiana
71 l/67
Maine
6/28/74
Montana
71 l/67
New York
71 l/71
North Carolina
lo/ l/73
Oregon
g/12/67
South Carolina
71 l/73
Washington:-
7/ l/74
_
Wisconsin
l/11/68
Yyoming
6/ l/73
States without motorcycle datyime headlight use laws include all states and the District of Columbia minus states mentioned above. In addition, Minnesota, Tennessee. West Vfrglnia. and Califotnla were excluded from this group.
Daytime headlight operation and motorcyclist fatalities
17
APPENDIX C DaMme headlight operation and the misclarsifcution of single cehicie colksiorfs Since daytime headlight operation affects daytime collisions, the following calculation can be restricted to the ratio of multi to single vehicle collisions occurring in daylight. This ratio is expressed as MD/SD. Let: .WD = .Y; SD =x: i = effect of daytime headlight operation, and let the domain of i be {0 s i < 1). Then. the effect of daytime headlight operation on the multi to single vehicle ratio is, assuming no misclassification of collisions: x(1 -i) -. Y
(1)
Assuming that one fifth of the single vehicle collisions are near misses and can be prevented as effectively as multi-vehicle collisions, the effect of daytime headlight operation can be restated:
-41 - i)
(2)
0.8~ + O.Zy(I - i) ’ Then. the relationship between formula (I) and (2) is: x(1 -i) - Y
x(1 -i)
1 - O.ti
’ 0.8~ + 0.2y( I - i) = I
(3)
’
Formula (3) implies that as the effect of headlight operation (i) increases, the unadjusted ratio will become progressively smaller than the adjusted ratio. It follows, that the effect of “misclassifying” single vehicle collision will result in some overestimation of the effect of daytime headlight operation. This bias is not substantial as Long as headlight operation is not very effective.
APPENDIX
D
Table DI. Predicted number of fatalities by modd: TC, CY, SC, TY, TS, SY California Year
Type of Collision
1976
Multi
States
without
Headlight Day
Night
Day
Motorcycle Use Laws Night
States with Headlight Day
Motorcycle Use Laws Night
144.7
497.8
370.1
305.7
234.1
95.3
122.3
252.4
332.6
160.1
217.2
Multi
220.3
170.7
606.7
482.9
359.1
294.3
Single
107.0
147.0
313.4
442.0
191.5
278.1
1978
nulti
258.5
191.1
706.1
536.0
407.6
318.6
Single
123.5
161.8
358.6
482.3
213.7
296.1
1979
Multi
246.0
217.2
666.3
604.1
401.1
374.4
Single
122.0
190.9
351.3
564.3
218.4
361.2
I980
Multi
238.2
205.6
722.5
640.2
420.1
383.4
Single
119.5
182.7
385.3
605.0
231.4
374.1
1981
Multi
223.7
206.3
680.1
644.1
373.5
364.2
Single
111.2
ial .a
359.5
603.3
203.9
352.3
Single 1977
AAP
Vol. 16.No. I-B
199.7
A. MULLER
18
Table DZ. Predicted number of fatalities by model: EY, California Year
Type of Collison
1976
Multi Single
Day
Night
SC, TS, SY
States without Motorcycle Headlight Use Laws Night Day
States with Headlight Day
Motorcycle Use Laws Night
zoo.3
144.1
499.2
368.8
306.5
233.2
94.0
122.8
251.0
334 .o
159.2
218.2
360.8
292.4
Multi
221.3
169.6
609.8
480.0
Single
106.0
148.0
310.3
444.9
189.7
280.0
1978
Multi
256.8
192.8
701.4
540.8
404.8
321.4
Single
125.2
160.2
363.3
477.6
216.6
293.2
1979
Multi
247.6
215.6
670.7
599.8
403.7
371.7
Single
120.5
192.4
346.9
568.6
215.6
364.0 383.0
1977
1980
1981
Multi
238.4
205.3
123.2
639.7
420.5
Single
119.3
182.9
384.6
605.5
231.0
374.5
Multi
222.0
207.9
675.2
649.1
370.8
367.0
Single
112.8
180.3
364.5
596.2
206.8
349.4
Table D3. Predicted number of fatalities by model: KY, California Year
Type of Collision
1976
Multi Single
States
without
Headlight Day
Night
Oay
Motorcycle Use Laws Night
SCY, BY,
TSC States with Headlight Day
Motorcycle Use Laws Night
203.1
142.9
497.7
361.3
305.2
241.8
95.9
liO.1
251.3
342.7
157.8
212.2
216.8
161.2
614.2
477 .a
360.9
303.1
1977
Hul ti Single
114.2
152.8
303.8
449.2
188.1
270.9
1978
Multi
249.4
199.6
712.0
509.0
401.6
346.4
Single
121.6
164.4
379.0
483.0
204.4
283.6
1979
Multi
241.7
212.3
666.4
605.6
393.9
369.1
Single
124.3
197.7
332.6
561.4
226.1
365.9
Mu1ti
240.8
220.2
726.5
635.5
414.7
372.3
Single
109.2
175.8
377.5
613.5
248.3
373.7
Multi
231.2
202.8
671.1
659.9
365.7
361.3
608.1
219.3
347.7
1980
1981
Single
116.8
172.2
347.9