ACCIDENT RATES AT PEDESTRIAN CROSSINGS IN HERTFORDSHIRE

Transcription

1 TRANSPORT AND ROAD RESEARCH LABORATORY Department of Transport RRL Contractor Report 154 ACCIDENT RATES AT PEDESTRIAN CROSSINGS IN HERTFORDSHIRE =,, by J G Hunt and J D Griffiths (UWIST) The authors of this report are employed by the Department of Civil Engineering and Building Technology and the Department of Mathematics, UWIST. The work reported herein was carded out under a contract placed on them by the Transport and Road Research Laboratory. The views expressed are not necessarily those of the Department of Transport. This report, like others in the series, is reproduced with the authors' own text and illustrations. No attempt has been made to prepare a standardised format or style of presentation. Traffic Management Division Traffic Group Transport and Road Research Laboratory Old Wokingham Road Crowthorne, Berkshire RG11 6AU 1989 ISSN

2 CONTENTS Page ABSTRACT i. INTRODUCTION. DATA CHARACTERISTICS 2.1 Overview 2.1 Accident records 2.3 Vehicle and pedestrian flow 2.4 Environmental and locational details MODEL SELECTION 4. VEHICLE AND PEDESTRIAN FLOW PROCESSING 4.1 Flow conversion procedures. ANALYSIS 5.1 Introduction 5.2 The effect of crossing type 5.3 The effect of pedestrian flow, vehicle flow and road width 5.4 The effect of locational and environmental parameters 5.5 Predictive equations. SENSITIVITY AND ACCURACY OF PREDICTIVE EQUATIONS 6.1 Sensitivity of the predictive equations for relevant accidents to variations in the values of the predictive variables 6.2 Accuracy of the predictive equations 7. CONCLUDING REMARKS 8. ACKNOWLEDGEMENTS 9. REFERENCES ii ii ( C ) CROWN COPYRIGHT Extracts from the text may be reproduced, except for commercial purposes, provided the source is acknowledged.

3 Ownership of the Transport Research Laboratory was transferred from the Department of Transport to a subsidiary of the Transport Research Foundation on 1 st April This report has been reproduced by permission of the Controller of HMSO. Extracts from the text may be reproduced, except for commercial purposes, provided the source is acknowledged.

4 ABSTRACT This Report describes an analysis of injury accidents at 132 Pelican crossings and iii Zebra crossings in Hertfordshire. Accident data included all accidents occurring at, or within 5m of, each crossing location and covered the period from 1981 to Pedestrian and vehicle flow were represented by 5 hour continuous counts taken on week days during the morning or afternoon in the latter part of A generalised linear modelling package was used to relate accident frequencies to functions of pedestrian counts, vehicle counts, and road width, and to examine the effects of locational and environmental features. Models for predicting the accident risk for all accidents and relevant accidents at Zebra and Pelican crossings are presented and the sensitivity and accuracy of the models is examined. - I -

5 ACCIDENT RATES AT PEDESTRIAN CROSSINGS IN HERTFORDSHIRE I. INTRODUCTION Pedestrian crossing places, both at junctions and at mid block, are installed primarily to provide increased safety for pedestrians. The design of appropriate facilities takes account of both pedestrian needs and the requirement to keep delays to vehicles to a minimum. Between junctions pedestrians may be assisted by the provision of a central refuge, an uncontrolled crossing such as the Zebra, a signal controlled crossing such as the Pelican or by a footbridge or underpass. The selection of the most appropriate type and layout of crossing depends on pedestrian and vehicle flow levels, local features, and safety considerations. Current guidance I on crossing selection is related to the degree of conflict between pedestrians and vehicles as expressed by PV 2, where V is the 2-way total hourly flow of vehicles, and P is the 2-way total hourly flow of pedestrians crossing the road within 5m either side of the site at busy times. In 1986 there were 6,875 pedestrian casualties in the United Kingdom of which 3,844 were at or within 5Om of Zebra crossings and 4,83 at or within 5Om of Pelican crossings 2 A substantial proportion of casualties were thus at facilities intended to provide a high level of pedestrian safety where pedestrian and vehicle interaction may be more concentrated. The relationship between accident rates at pedestrian crossings, pedestrian and vehicle flow, and other geometric and environmental parameters is, however, not fully understood. In 1985 the Transport and Road Research Laboratory commissioned UWIST to develop predictive equations for accident rates at a set of Pelican and Zebra crossings originally selected for a programmme of research dealing with delays at pedestrian crossings 3'4'5. The full data set in that study comprised a total of 88 sites situated in fifteen counties spread through England and Wales and included each type of Pelican crossing together with both single stage and refuged Zebras. Accident data covering a six year period, three years before and three years after the date for which flow estimates were available, were obtained from the appropriate Highway Authority. A generalised linear model package was - 2 -

6 used to develop predictive equations, relating accident rate to pedestrian and vehicle flow, but the fits achieved were generally poor. The poor fit was attributed in part to the sparseness of the data, and to possible inaccuracies in the estimates, based on short period counts, of vehicle and pedestrian flow. In order to remedy these deficiencies, both in the quantity of data and in the quality of the representation of pedestrian and vehicle flow, TRRL placed a contract with Hertfordshire County Council to assemble and provide accident data, pedestrian and vehicle flow, environmental and location data for all of the 261 crossing sites in the county. This report describes the data, and the analysis which was undertaken by UWIST. 2. DATA CHARACTERISTICS 2.1 Overview The Hertfordshire data were supplied, to a specification provided by TRRL, for 261 sites, from both urban and rural locations, spread throughout the county. The numbers of each type of crossing, which were located mainly mid-block, and in a few cases adjacent to, signalised intersections or roundabouts, were as listed below: Fixed Time Pelicans Vehicle Actuated Pelicans Single stage Zebras Refuged Zebras (5 Divided) (3 Staggered) For each crossing, Hertfordshire County Council supplied photographs showing the location of the crossing viewed from each direction of traffic flow, a sketch of the site, and data defining: accidents covering the previous five year period, vehicle and pedestrian flow, based on half day surveys, and environmental and location details. The data were collected and assembled by Hertfordshire County Council during the period June to December

7 2.2 Accident records Records of all personal injury accidents occurring at or within 5m of the crossing were made available for each site. For the purposes of this study accidents were divided into relevant and non-relevant categories. The following types of accidents were considered to be non-relevant: (a) (b) (c) (d) (e) (f) vehicle collisions due to turning manoeuvres, vehicle collisions with parked vehicles, accidents involving passengers boarding or alighting from public service vehicles, vehicle collisions due to U-turns or failing to give way at junctions, injuries to passengers on public service vehicles braking downstream of the crossing with no pedestrian involved, and accidents involving a pedestrian crossing a side road. Hertfordshire County Council prepared a s-mmary table for each site, giving the total number of accidents and the number of relevant accidents. A small number of sites were in areas where Urban Traffic Control had been introduced; in some cases, the crossing was converted from Zebra to Pelican shortly before UTC was installed. These crossings appear in the database only for the period following conversion. As the number of sites was small and accident data sparse, no attempt was made to investigate the effect, on accident rate, of linking under UTC. Data from some sites in the survey were not included in the analysis. 14 were excluded because the crossing had been installed for less than one year and 4 were excluded because the site was unusual, for example forming part of a three-arm junction. The number of data sites included in the analysis thus reduced to 243. All supplied data were carefully checked before entering into the database. Table i shows the number of sites of each category, pedestrian and vehicle counts, road widths, and the corresponding -4 -

8 number of total and relevant personal injury accidents over a five year period. On average vehicle flow was lower at the Zebra sites than at the Pelican sites, and pedestrian flow lower at the Zebra and Vehicle Actuated Pelican sites compared to the Fixed Time Pelican sites. The overall relevant accident rates were.36,.39 and.26 accidents per year per site for Zebra, Fixed Time and Vehicle Actuated Pelicans respectively. The Hertfordshire data is seen to include few examples of divided or staggered Pelican crossings so that the main deficiency in the UWIST data was repeated in the Hertfordshire data. For all crossings taken together, relevant accidents represent about 46% of the total number of accidents; comparable ratios apply for each crossing type considered separately with the exception of refuged Zebras where relevant accidents represent only about 23% of total accidents. The low proportion of relevant accidents at refuged Zebras is difficult to explain. 2.3 Vehicle and pedestrian flow Hertfordshire County Council organised and supervised flow counts at all of the crossing sites. Flow counting took place on weekdays in 1986 and avoided school holidays. Hourly counts from 8 to 13 or from 14 to 19 hours were carried out at all of the 243 sites. Hertfordshire were requested to identify the 5 busiest sites and take further counts for the period not previously covered for the other half day. These sites will be referred to as "dual count sites". Table 2 summarises the pedestrian and vehicle counts recorded over each period at the survey sites and includes the mean and range for each category. The numbers of each crossing type at which counts were taken in the morning, afternoon, or for both periods is also shown. The ratio between pedestrian counts at morning and afternoon counted sites (2.7) is much higher than the corresponding ratio at dual count sites (1.3) and may be taken as indicating a lower level of pedestrian activity at afternoon counted sites. Vehicle counts are similar for morning and afternoon counted sites and for morning and afternoon counts at dual count sites. The objective was to record counts which were typical of average conditions at each site. Any single count is unlikely to be fully -5 -

9 representative as individual counts may be influenced by transient factors such as temperature, wind, precipitation, local events, traffic incidents etc. Ideally, a count would be taken over a number of days and an average derived but cost precluded this. Every effort was made to avoid periods during which traffic flow could be abnormal (early closing day etc.), but since wet weather in particular may be expected to reduce pedestrian flow, an attempt has been made to compensate for this effect. Table 3 s-mmarises the numbers of sites at which counts were made under wet and dry conditions. There are many sites at which conditions at the time of the count were not recorded and relatively few sites at which the count was taken in wet conditions. However, the ratio between dry and wet counts (on average.9 and 1.15 for vehicle and pedestrian counts respectively) gives an indication of weather effects on the assumption that, as the sites in each sample were selected at random, the average flow would be the same if weather effects were excluded. This process is not fully satisfactory but intuitively counts recorded in wet weather scaled by the appropriate ratio are more likely to be representative than the raw data. Accordingly the vehicle and pedestrian counts recorded at the 8 sites, where data was collected in wet weather, were adjusted to give the equivalent dry weather counts. More general application of dry/wet conversion factors would require more data than is available for the current study. 2.4 Environmental and locational details Environmental and locational data for each site were also gathered. Photographs taken of each site from each side of the road, together with an Ordnance Survey map, allowed some aspects of the data to be checked. The type of land use on either side of the crossing was noted and this enabled the sites to be classified into certain categories. Data assembled for each site included the items listed below: (i) Layout Zebra sites were classified as refuged or single stage and Pelicans as single stage, divided or staggered. (ii) Road width Kerb to kerb measurements were used, excluding refuge width where applicable. -6 -

10 (iii) Number of road lanes The number of road lanes at each site was assessed from the photographs at each location. (iv) Traffic direction Data for this category in which traffic at the site was defined as one or two way were collected from the study of photographs from each site and from site survey sheets. (v) Guard rails at the crossing For the majority of sites, the guard rail length and its position in relation to the crossing was provided by Hertfordshire County Council. (vi) Site type Each site was categorized from details supplied on the site survey sheets and then checked from photographs. The categories were: (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (i) sports centres sports grounds parks town centre (offices) town centre (shops) suburban shopping residential school hospital bus station railway station industrial (vii) Proximity of public house This was determined on the basis of locations where there was a public house near to the crossing and it appeared likely that customers might make use of the crossing

11 (viii) Proximity of junction This was defined in terms of the distance of the crossing from the nearest priority intersection or roundabout. Table 4 summarises data relating to environmental and locational groupings. 3. MODEL SELECTION The purpose of the analysis was to derive a relationship between accidents and appropriate explanatory variables with the objective of providing equations which could be used to assist in preparing criteria for choice of an appropriate crossing facility. The basic model adopted in this study is given by N/Y A(P/P) B (V/V) C = e D(R-R) where N/Y is the accident frequency per year, P is a measure of pedestrian flow and P is the corresponding data mean, V is a measure of vehicle flow and V is the corresponding data mean, and R is the road width and R is the corresponding data mean. The inclusion of pedestrian flow and vehicle flow in the form indicated retains compatibility with current criteria for choice I and is consistent 6 with previous studies of this type. As the errors associated with the number of accidents in a given period are not normally distributed, standard least squares regression analysis is not appropriate and accordingly a generalised linear model package, GLIM, has been used. This allows the error distribution in the dependent variable in the regression analysis to be drawn from the Poisson distribution, and non-linear models to be fitted by means of appropriate data transformations. The principles of generalised linear models as applied to the analysis of accidents has been described by 7 Maycock and Hall

12 In the proposed model, the use of reduced variables P/P, V/V and R-R allows the accident rate at average values for flow and road width to be expressed directly in the constant A. Other parameters which it is considered may influence accident rate are not continuous and consequently their effect must be evaluated by treating them as factors and assessing both resulting variations in the constant A, and the changes in deviance, as each factor is introduced. 4. VEHICLE AND PEDESTRIAN FLOW PROCESSING 4.1 Flow conversion procedures In the previous study, the vehicle and pedestrian flows were represented by estimates of annual average hourly flow (AAHF) derived from short term counts taken at the time of the original site surveys. The methods used to expand the short term counts were not completely satisfactory, particularly in the case of pedestrian flow for which there was no established methodology and very little published information about daily and annual fluctuations. Currently, the degree of vehicle/pedestrian conflict at a potential or actual pedestrian crossing site is assessed using PV 2. The counts of P, the number of pedestrians crossing a loom stretch of road extending to 5m either side of the proposed site, and V, the number of vehicles passing the site in both directions, should be recorded for each hour on a typical working day from The four highest values of PV 2 are then selected and the average calculated for those four hours. However, in practice, the resources available to Highway Authorities make it difficult to carry out full 16 hour counts. The revised Departmental Standard allows judgement to be used to determine the actual times and methods of counting provided the count is typical and representative of local conditions. A flow count over the period 6-22h such as that used by Inwood and 6 Grayson in a similar previous study is more likely to be representative of conditions on each site than a count of shorter duration. In the current study, flow counts covering a 5 hour period on an assumed typical weekday were available for each site; for the majority of sites this count was made either in the morning -9-

13 (8-13h) or afternoon (14-19h). The use of alternative counting periods was determined by logistics and the efficient use of available resources rather than by experimental design. continuous counts taken between 7-19h. Four sites had Although the expansion of short period vehicle counts can be undertaken 8 using the method described by Phillips and that of pedestrian counts using a similar process, both techniques involve a number of assumptions, and risk the introduction of error so that the counts which are carried forward to analysis may not be typical of the site they purport to represent. This is particularly the case for pedestrian counts where the decision on site type is critical, and typical pedestrian flow profiles for each site type are not well established. Furthermore, any formulae relating accident rate to vehicle and pedestrian flow which emerged from this procedure would ideally, in application, require a count over the period 6-22h for which resources may not be easily available to the appropriate Highway Authority. In view of the form of the data provided by Hertfordshire County Council, the 5 hour counts taken during the survey periods formed the basis for the analysis. However, with the exception of the dual count sites, the data divided into two sets with morning counts available for about half the survey sites and afternoon sites available for the remainder. Separate treatment of morning counted and afternoon counted sites effectively reduced the size of each set to a point where further subdivision into crossing type, site type, etc. left very small sample sizes. An alternative was to use one set (afternoon counts) as the basis with the other set (morning counts) converted to equivalent afternoon counts. The relationship between morning counts and afternoon counts of either pedestrian or vehicle flow depends on site characteristics and will vary between sites as illustrated by Figures I and 2 which show data for the dual count sites. This data, provided it is typical may be used to determine average factors for converting morning counts to equivalent afternoon counts. Figure i shows, for the dual count sites, afternoon counts of pedestrian flow plotted against the corresponding morning counts. regression line obtained was: The - i -

14 afternoon count =.731 x morning count (4.1.1) Equation was determined by minimizing the deviation in the afternoon counts assuming the morning counts were fixed. Figure 2 shows, for the dual count sites, afternoon counts of vehicle flow plotted against the corresponding morning counts. By following a similar procedure to that described above for pedestrian counts the corresponding derived equation was: afternoon count = 1.4 x morning count (4.1.2) For both pedestrian and vehicle counts, the regression lines were forced through the origin on the basi~ that this provided the best representation of the true situation. This procedure yielded conversion factors which can be applied prior to analysis to convert morning counts for Hertfordshire to equivalent afternoon counts. 5. ANALYSIS 5.1 Introduction The analysis was based on a data set including either recorded or calculated afternoon counts over a five hour period to represent pedestrian and vehicle flow. GLIM was applied to determine the best fit relationships between accidents and possible explanatory variables. The statistical significance of the added terms or factors was assessed using the method described by Maycock and Hall 7. The Mean Deviance Ratio (MDR) which is defined as the reduction in scaled deviance produced by the addition of a term, or terms, to the model divided by the residual mean deviance was calculated as ~R = Scaled deviance difference/desrees of freedom difference Residual deviance/residual degrees of freedom The statistical significance of the added terms or factors was then assessed by comparing the MDR with the critical points of the F - statistic. - ii -

15 In view of the rapid reduction in data sample size with each subdivision in a hierarchical approach it was neither feasible nor prudent to consider all possible interactions. Accordingly, the main explanatory variables which affect the structure of the model were considered initially. The models which emerged were then carried forward into the next stage to consider the effect of other possible explanatory variables. Since the division into relevant and nonrelevant accidents may be considered subjective, the analysis was carried out for both relevant and all accidents. 5.2 The effect of crossing type The different modes of operation and layouts of Zebra and Pelican crossings suggest that they may be associated with different accident rates and so should be considered separately. Further, any criteria for choice between signal controlled crossings such as the Pelican and uncontrolled crossings such as the Zebra would require separate models to be fitted, if justified, for each crossing type. Vehicle Actuated Pelicans were introduced initially for use on roads where a speed limit of 3 mph did not apply. Their mode of operation is different from that of Fixed Time Pelicans and, except under high flow conditions, would be expected to reduce interaction between pedestrians and vehicles at the start of the pedestrian green by allowing changes to pedestrian precedence during gaps in the vehicle flow. However, this potential safety benefit may be balanced by the tendency of pedestrians to anticipate gaps in vehicle flow and cross during the pedestrian red period. This possible difference in operation of, and behaviour at, the two types of Pelican justifies an initial subdivision of the Pelican crossings in the data set into those operating on a fixed time, and vehicle actuated basis. Table 5 shows, for relevant accidents and for all accidents, the results of applying GLIM to fit the model with, (a) Zebra and Pelican (Fixed Time and Vehicle Actuated taken together) and, (b) Zebra, Fixed Time Pelican and Vehicle Actuated Pelican

16 The results for relevant accidents indicate a significant improvement in fit when the crossings are subdivided as in (a) but provide no justification for a further subdivision as in (b). For all accidents there is no significant improvement in fit when the data is subdivided into crossing type. There is not a significant difference in the accident rates for mean flows and road widths at Vehicle Actuated and Fixed Time Pelicans as expressed by the constant A (.318 and.386 respectively for relevant accidents, and.766 and.82 respectively for all accidents). Accordingly, further analysis was confined to the subdivisions represented by Zebra and Pelican crossings respectively treated as separate data sets. For consistency this was applied for both relevant accidents and all accidents although the subdivision may not be justified in the latter case. 6 Inwood and Grayson in their study of injury accidents at or near 14 pedestrian crossings found no difference in pedestrian accident rates at Pelican and Zebra crossings. Their analysis did provide evidence that Pelican crossings had a total accident frequency which was 26% lower than at Zebra crossings operated under the same conditions. the current study the subdivision into Zebra and Pelican crossings has provided a significant improvement in fit for relevant accidents (comparable with the accidents included by Inwood and Grayson). Comparison of the values of the constant A indicates that the predicted accident frequency per year at a Pelican crossing is 34% lower than that of a Zebra crossing operated under the same conditions. In 5.3 The effect of pedestrian flow~ vehicle flow and road width The suitability of the proposed model, based on afternoon recorded and and calculated counts and the chosen crossing subdivision was assessed by considering the effect of successively adding pedestrian flow, vehicle flow and road width as explanatory variables. Tables 6 and 7 show the results for relevant accidents and all accidents respectively for Pelican and Zebra crossings treated as separate data sets with appropriate means for each of the explanatory variables. As before, the data were analysed using the GLIM package to give the mean accident rate and a baseline deviance. The variables (P/P), (V/V) and (R-R)

17 were then added successlvely and the change in deviance recorded at each stage. The results for relevant accidents indicate that (P/P) and V/V) provided a significant improvement in fit for each of the groupings but that (R-R) gave no significant improvement for the Pelicans treated separately. For the Zebra case the inclusion of (R-R) as an explanatory variable had the effect of increasing the coefficient C (vehicle count) by 75% with the constant A and the B coefficient (pedestrian count) showing little change. For all accidents the inclusion of (R-R) gave no significant improvement in fit for either the Pelican or the Zebra case; the inclusion of the variable (P/P) did not improve the fit significantly in the Zebra case. This, together with the evidence of Table 5 and the need for consistency, was considered sufficient to justify the use of the two models indicated below for subsequent evaluation of the effect of introducing other possible explanatory parameters as factors. Relevant and all accidents Zebra: (N/Y) = A(P/P)B(v/v)CeD(R-R) Pelican: (N/Y) = A(P/p)B(v/v) C 5.4 The effect of locational and environmental parameters In view of the number of parameters considered as factors a full hierarchical approach was not practical; as a first stage the effect of including each of the parameters as a factor was separately assessed. Tables 8 and 9 show, for relevant accidents, the effect of introducing the environmental and locational parameters given in Table 4, as factors into the predictive equations for Zebra and Pelican crossings. Tables i and ii show an evaluation of the corresponding effect for all accidents. The number of lanes has not been included in the parameters investigated because of the small number of sites in categories other than 2 lanes. Similarly, site types 1,2,3,4,9, and I have been taken together as "grouped sites" to avoid low sample sizes

18 For the Zebra crossing none of the parameters, introduced as factors, produced a significant improvement in fit for relevant accidents. For all accidents both site type and proximity of public house considered separately produced an improvement in fit to the Zebra model at a significance level of 5% or above. The high accident rate associated with school sites is indicated by the value of the constant A for relevant accidents although other groupings have higher values of A when all accidents are considered. The effect of public house proximity is difficult to explain - for both relevant and all accidents the constant A is lower when a Zebra crossing is located close to a public house. A possible explanation is that the parameter proximity of public house has acted as a proxy for site type when a non-hierarchlcal procedure is followed. Table 12 shows the proximity to public house groupings corresponding to each site type for Zebra crossings. It is noticeable that site types, such as residential, school and industrial, which have a high accident rate (Table i) are mainly associated with locations which do not have a public house close to the crossing. In order to investigate this further the analysis for all accidents at Zebra crossings was repeated using a hierarchical approach with proximity of public house added as a factor to the model shown for site type in Table I. This had the effect of further reducing the Scaled Deviance by only 5.9 giving a Mean Deviance Ratio of 2.5 (i degrees of freedom) which does not indicate a significant improvement in fit (5% level of significance), thus supporting the hypothesis that, when considered separately, the proximity of public house parameter was acting as a proxy for site type. The inclusion of proximity of junction as a factor did not produce a significant improvement in fit for either relevant or all accidents at a Zebra crossing. However, for both accident measures the constant A was substantially higher when the Zebra was located close to either a roundabout or priority junction. For the Pelican crossing, the inclusion of junction proximity as a factor provided a significant improvement in fit for the models of both relevant and all accidents. The constant A has, as would be expected, higher values associated with sites which are close to a junction; this is similar to the effect at Zebra crossings which was described previously. In the case of relevant accidents the improvement in fit

19 and the values of the constant A for different junction proximity levels indicates that the presence of a junction may have an adverse effect on accident rates even when the accident cause is not directly associated with turning movements. The inclusion of the guard rails as a factor produced a significant improvement in fit for the Pelican model of relevant accidents; the values of the constant A associated with each level of guard rail provision are not as would be expected, with most accidents associated with guard rails on one side of the road and least accidents with no guard rails. One possible explanation for this unexpected result could be that some of the guard rails present when the sites were surveyed had not been there over the full five years for which accident data were collected. The analysed data did not include dates of guard rail installation. It is probable that only a very small proportion of sites had guard rails added after the crossing was installed. However, if guard rails had been added at some sites during the five year period they may well have been installed as accident remedial measures at sites with a high accident record. This would explain why guard rail presence tends to be associated with higher accident risk. It is not possible to verify this hypothesis without further work to attempt to determine installation dates and reasons. The values for the constant A shown in Tables 8-11 for each level of each parameter often indicate variations in accident rates which appear to be intuitively sensible, for example the relevant accident rate at a Pelican on a two way street is shown as much higher (double) than the rate on a one way street (Table 9). However, the data used in this study were insufficient to establish a significant improvement in fit for the majority of the locational and environmental parameters considered; the variation in the values of the constant A for such parameters should be considered with appropriate caution. The analysis described above justified the inclusion of the following locational and environmental parameters in the predictive equations: Relevant accidents Zebra: Pelican: (None) Proximity of junction

20 All accidents Zebra: Site type Pelican: Proximity of junction In the case of relevant accidents at Pelican crossings, guard rails have been excluded on the basis that the predicted effect may be misleading. For the all accidents case at Zebra crossings, proximity of public houses has been excluded because the effect is more accurately represented by site type. Tables 13 and 14 show the structure, constants and coefficients of the best fit models for relevant and all accidents respectively. The Zebra model for all accidents includes pedestrian flow to maintain consistency although it did not produce a significant improvement in fit (Table 7). The models shown include all those variables and parameters whose inclusion provides a significant improvement in fit (5% level of significance). As a further check the locational and environmental parameters whose inclusion did not provide a significant improvement in fit when considered separately (Tables 8-11) were added to the best fit models shown using a hierarchical procedure; no significant improvement in fit was achieved. Tables 13 and 14 indicate that the models for relevant accidents provide a better fit to observed data than the corresponding models for all accidents. 5.5 Predictive equations For relevant accidents the predictive equations for the annual accident frequency N/Y may be written as Zebra N/Y = 4.25 p"31v"77exp-"16r x 1-4 (5.5.1) Pelican N/Y = 1.14 p"46 V"87 x 1-5 (5.5.2) or based on proximity to a junction no junction: N/Y =.74 p-5 V"82 x 1-5 (5.5.3) priority junction < 2m: N/Y = 1.36 p"5 V"82 x 1-5 (5.5.4) 2m < priority N/Y = 1.83 p"5 V "82 x I -5 (5.5.5) junction < 5m:

21 roundabout <2m: N/Y = 2.28 p"5 V"82 x 1-5 (5.5.6) 2m< roundabout < 5m: N/Y =.73 p-5 V"82 x 1-5 (5.5.7) In the above equations P refers to a count of pedestrian total flow, for a section of road including the crossing location and a distance of 5m on either side, over the period 14h to 19Oh. V represents the total vehicle count in both directions (on a two way road) taken over the same time period. In both cases the counts refer to a typical week-day (Mon-Fri), and are based on dry conditions. The equations are valid only for the range of pedestrian counts, vehicle counts and road widths shown in Table i. 6. SENSITIVITY AND ACCURACY OF PREDICTIVE EQUATIONS 6.1 Sensitivity of the predictive equations for relevant accidents to variations in the values of the predictive variables In this section the effect, on the predicted accident rate, of variations in the values of the explanatory variables is considered. The values selected for each explanatory variable are based on the data range recorded at the sites in Hertfordshire with the 5 percentile and 95 percentile representing the lower and upper boundary for each explanatory variable. Table 15 shows the separate evaluation, based on each of the above values, of each term of the models for relevant accidents at Zebra and Pelican crossings. The percentage change in predicted accident rate (N/Y) relative to the value of the variable data mean is also shown; the change is based on the assumption that other terms of the predictive expression remain unchanged. For clarity the term values, which are unity by definition at the variable data means, have also been included in the Tables. For both the Zebra and Pelican models an increase in either pedestrian or vehicle count is associated with an increase in predicted accident rate. For both models the effects of variation in pedestrian and vehicle count on predicted accident rate are of the same order of magnitude, as would be expected from the corresponding coefficients B and C taken in combination with the associated data ranges. The ratio between the term values at the

22 95 percentile and 5 percentile variable values ranges from 4.52 (vehlc~e count - Zebra model) to 2.53 (vehicle count - Pelican model). With the Zebra model an increase in road width is associated with a decrease in the contribution of the corresponding term. This may indicate that the beneficial effects of increasing road width (providing more time for a driver to see and avoid pedestrians and more space to m~noeuvre) more than compensate for the additional time of exposure for pedestrians using the crossing. It was noted that the introduction of road width as an explanatory variable had the effect of increasing the coefficient C (vehicle flow) by more than 75 percent (see Table 6). If the effects of the terms representing vehicle flow and road width are considered together at the lower and upper bounds of the explanatory variables the combined terms range from.574 (5 percentile V = 116, 5 percentile R = 6.) to.68 (95 percentile V = 7871, 95 percentile R = 15.). This could be interpreted as indicating that provided any increase in vehicle flow is associated with a corresponding increase in road width the net effect on the predicted accident rate is small. It may be inferred that the predicted relevant accident rate at Zebra crossings is not influenced by vehicle flow alone but rather by the associated degree of saturation. It should not be inferred that reducing the width will necessarily increase the accident risk; other underlying causes may account for the results obtained. Figure 3 illustrates the application of the best fit equations to predict the relevant accident rates for both Pelican and Zebra crossings over a range of vehicle flow. The effect of road width on the predicted relevant accident rate at Zebra crossings is clear from the Figure. 6.2 Accuracy of the predictive equations The GLIM results provide an estimate of the mean annual accident frequency (or the mean accident frequency over a five year period) as a function of several continuous variables and a number of discrete factor levels. It is useful to provide some guidance relating to the accuracy of these predictive equations. The nature of the GLIM analysis is such that it is not possible to give explicit formulae for confidence limits at any specified level of significance; however, it is possible numerically to provide confidence limits (for the true mean accident frequency over a

23 five year period) for any given values of the variables and factor levels. The results described below for relevant accidents only, should therefore be taken as illustrative. The best fit equations, as shown in Tables 13 and 14, were used to provide estimates for the mean number of accidents over a five year period for a range of vehicle counts (5 hour total). For the Zebra crossing case, the road width was kept constant at its mean value. For both the Zebra and Pelican crossing cases, three levels of pedestrian count, P, were considered, viz P = i, P = P, p = i (5 hour total). The 95% confidence intervals for the true mean accident frequency were extracted from an extended GLIM output using a method suggested by Maher (TRRL). Basically the method consists of adding an extra set of values of the explanatory variables for which the confidence limits are required, and then undertaking the GLIM fit on the original sets of variables, excluding the dummy set of variables from the fit by giving it a weight of zero. The covariance matrix for the estimates is then displayed and from this the variance of any linear function of the estimates can be determined. Figure 4 shows the 95% confidence limits for relevant accidents at Zebra crossings, and Figure 5 illustrate the corresponding results at Pelican crossings. In each case the confidence limits are seen to be quite markedly dependent on the pedestrian and vehicle counts, the limits being wider for higher counts in each of these variables. It should be emphasised that the 95% confidence limits shown relate to the true mean accident frequency over a five year period; the application of Figures 4 and 5 to assess recorded accident frequency at individual sites should be treated with extreme caution. Maher (TRRL) has suggested an approximate method by which confidence limits may be established for the accident frequency at a particular site. Since the accident frequency is assumed to be Poisson distributed the fitted value of the mean may be used as an estimate for the variance of the accident frequency at each site. This estimated variance may then be added to the variance of the estimate of the true mean (provided by GLIM) to determine confidence limits with which to assess individual observations

24 7. CONCLUDING REMARKS This Report describes an analysis of injury accidents over a five year period at 243 pedestrian crossings in Hertfordshire. Data for 132 Pelican crossings and iii Zebra crossings were collected and assembled by Hertfordshire County Council Highways Department based on a specification agreed with the Transport and Road Research Laboratory. Accident data included all accidents occurring at, or within 5m of each crossing location and covered the period from 1981 to The overall relevant accident rates were.36,.39 and.26 accidents per year per site for Zebra, Fixed Time and Vehicle Actuated Pelicans respectively. Pedestrian and vehicle flow were represented by 5 hour continuous counts taken during the morning (8-13h) or afternoon (14-19Oh), in the period June to December In order to avoid dividing the data a method of scaling morning counts of pedestrians and vehicles was developed and applied. The purpose of the analysis, which was carried out using the generalised linear model technique, was to derive relationships between accident frequency and appropriate explanatory variables with the objective of developing equations which could be used to assist in preparing criteria for choice of an appropriate crossing facility. The basic model adopted in this study was of a similar form to that used previously, and is given by: N/Y = A(P/P)B(v/v)CeD(R-R) where N/Y is the annual accident frequency, P is a measure of pedestrian flow, V is a measure of vehicle flow, R is the road width, P, V, R are the corresponding means for the appropriate data set, A is a constant, and B, C, D are coefficients. The use of the reduced variables P/P, V/V and R-R allowed the accident rate at average values of pedestrian counts, vehicle counts and road width to be expressed directly in the constant A. Two analyses were carried out in parallel, the first using only those accidents considered relevant to the presence of a Zebra or Pelican crossing to calculate the values of the dependent variable N, and the second based on all accidents. The procedure adopted was to fit the mean value of the dependent variable to the data

25 initially with the terms (p/~)b, (V/V) C and e D(R-~) then added successively. The improvement in fit when one or more terms were added was considered significant when the reduction in scaled deviance divided by the residual mean deviance exceeded the 5% value for the F-statlstic. A similar procedure was used to assess the improvement in fit accompanying the inclusion of crossing type, locational and environmental parameters as a number of discrete factor levels. are summarised below. The main conclusions from the analysis Relevant accidents i. The inclusion of crossing type as a two level factor, Zebra and Pelican, provided a significant improvement in fit in comparison with a model based on all crossing types. The corresponding values for the constant A indicated that the overall predicted mean accident rate at a Pelican crossing was 34% lower than at a Zebra crossing operated under the same flow conditions; this is based on the assumption that the flow dependency of the two types of crossing is identical, and is similar to 6 the results obtained previously by Inwood and Grayson. There was no significant improvement in fit when Pelican crossings were divided into Fixed Time and Vehicle Actuated nor was there a significant difference in the values of the constant A. It follows that for the Hertfordshire data, which included 46 Fixed Time and 86 Vehicle Actuated Pelicans, there was no conclusive evidence that vehicle actuation reduced the accident frequency at Pelican crossings. It should be noted that the results may be influenced by the current practice of Hertfordshire County Council in installing Vehicle Actuated Pelicans at sites where vehicle speeds are high.. The inclusion of pedestrian count and vehicle count provided a significant improvement in fit for the models of both Zebra and Pelican crossings; the inclusion of road width provided a significant improvement in f%t only in the case of Zebra crossings.. The inclusion of the following environmental and locational parameters, as factors with a number of discrete levels, was considered:

26 layout (non-refuged, refuged), traffic direction, guard rails, site type, proximity of public house, and proximity of junction. None of the above produced a significant improvement in fit when included as factors in the Zebra crossing model. For the Hertfordshire data which included 25 Zebra crossings with refuges out of a total of IIi, there was thus no significant difference in the predicted accident frequency at non-refuged and refuged Zebra crossings operated under the same conditions. For the Pelican crossing model the inclusion of junction proximity as a factor provided a significant improvement in fit with the constant A having higher values associated with sites which are close to a junction. The inclusion of guard rails as a factor also produced a significant improvement in fit but the constant A was lowest for sites at which there were no guard rails. This may have been due to guard rails being added to some high accident sites during the five year period as ameliorative measures. The inclusion of guard rails as a factor in the predictive equations may be misleading for this reason. The data were insufficient to establish relative predicted accident frequencies for single stage, divided and staggered Pelican crossings.. The best fit models for predicting the annual frequency of relevant accidents at pedestrian crossings using 5 hour afternoon (14-19h) counts of pedestrians (P) and vehicles (V), and road width (R) in metres are shown below. Zebra N/Y = 4.25 p"31vo'77exp-"16r x 1-4 (Data ranges: 17 < P < < V < < R < 18.6)

27 Pelican N/Y = 1.14 p"46v"87-5 x i (Data ranges: 42 < P < < V <9584) or based on junction proximity no junction: priority junction < 2m: 2m <prlority junction <5m: NJ roundabout < 2m: 2m < roundabout <5m: 36 I! P V x 1-5 Morning counts (8-13h) for pedestrians and vehicles should be converted to corresponding afternoon counts by multiplying by.731 and 1.4 respectively before substitution in the above equations.. For both the Zebra and Pelican models an increase in either pedestrian or vehicle count is associated with an increase in the predicted annual accident frequency. The relative effects of variations in pedestrian and vehicle count over the data range are of the same order of magnitude. For the Zebra model, at constant pedestrian and vehicle counts, an increase in road width is associated with a decrease in predicted annual accident frequency. It should not be inferred that reducing the carriageway width will necessarily increase the accident risk; other underlying factors may account for the results obtained. All accidents. Overall the explanatory variables and factors provided a less satisfactory fit to the data for all accidents; this may be attributed to the inclusion of extraneous data not related to the presence of a pedestrian crossing. The improvement in fit when crossing type was included as a two level factor, Zebra and Pelican, was not significant at the 5% level. Despite this the subdivision Zebra/Pellcan was retained for consistency with the models for relevant accidents.. The inclusion of the vehicle count as an explanatory variable provided a significant improvement in fit for both the Zebra and Pelican models. The inclusion of pedestrian count provided a significant improvement in

28 fit for the Pelican model but not for the Zebra model, and the inclusion of road width did not provide a Significant improvement in fit for either the Zebra or the Pelican model.. Of the locational and environmental parameters, listed in conclusion 3 above, site type provided a significant improvement in fit for the Zebra model and proximity of junction provided a significant improvement in fit for the Pelican model.. The best fit models for predicting the annual mean frequency (N/Y) of all accidents at pedestrian crossings using 5 hour afternoon (14-19h) counts of pedestrian (P) and vehicles (V), are as shown below Zebra N/Y = 1.86 P V x I o r_r based on site type grouped sites: 3.63 town centre (shops): 6.13 suburban shopping: residential: school: N/Y = 4 [ P V x i railway: 8.ii industrial: 2,33 Pelican N/Y = 1.7 p.27 V.52 x io-3 or based on proximity of junction no junction: I i.72 priority junction< 2m:.57 2m< priority junction< 5m: N/Y =.75 roundabout < 2m: m < roundabout < 5m: i P V x i The data ranges are shown for relevant accidents. 8. ACKNOWLEDGEMENTS The work described in this report forms part of the programme of the Transport and Road Research Laboratory and the report is published by permission of the Director