AN EMPIRICAL EXAMINATION OF THE RELATIONSHIP BETWEEN SPEED .
APPENDIX FAN EMPIRICAL EXAMINATION OF THE RELATIONSHIPBETWEEN SPEED AND ROAD ACCIDENTSINTRODUCTIONAt the expert panel meeting to develop AMFs for urban/suburban arterials (conducted atthe UNC Highway Safety Research Center in July 2005), the findings of Elvik et al. about therelationship between speed and accidents were discussed. (1) The following questions wereraised:1. Does the power model hold for North American data?2. Does the power model appropriately account for a variety of ‘before’ speedconditions?3. Are there no conditions (variables) about which we have information other thanbefore and after mean speed that significantly affect the speed-accidents relationship?To answer these questions, consultants Dr. Ezra Hauer and Dr. James Bonneson,conducted a study:1. To examine whether it is possible to provide a logical justification to the power modelor whether a different model from is indicated and could be derived from ‘firstprinciples.’2. To use Elvik’s data in an attempt to answer questions 1, 2 and 3 above.Both researchers used the same common data base to conduct their own analyses.Preliminary results and insights were frequently exchanged. This mode of research co-operationproved very fruitful by ensuring a certain amount of commonality and the ability to correctmissteps and errors while still enabling each author to pursue directions they thought promising.The two approaches are described in separate sections and compared in the last section.DATAThe data used for the examination were provided by Elvik et al. A sample of these datais provided in the table below. It shows the headings and the data for three studies, as reported inthe literature by the original authors. Column headings 1-30 and 41-51 identify the original data.Column headings 31 to 40 identify additional variables estimated for this examination.Columns 31 to 40 (in italics) contain the variables that were added to the original data.The notations (rc, rf, etc.) and the formulae are based on Hauer (1997). (2) Using the authorsestimated number of accidents expected in the after period, had there been no change in speed (πin column 34). This quantity is later referred to as N. The expected change in accidents (Delta incolumn 36, later referred to as dN) and its standard error (se(Delta) in column 37) were alsoestimated. Similarly, the ratio Theta of expected with speed change/expected without speedchange (column 38) and its standard error (column 39) were estimated.NCHRP 17-25 Final Report AppendixesF-1
1Studyrec noF12Resultrec SPOLIS11Veh/usersInvolvedF1112Types ofaccidentF1213Acc/injseverityF1314Accs orvictimsF1415Speedlimit – bF1516SpeedLimit - anspeed - bF17mph31.531.530.018Meanspeed - nF10URBANURBANURBAN19Veh kmbefore (case)F19O120Veh kmafter (case)F20P1.021222324252627282930Veh kmVeh icbefore (contr)after 290.36031323334353637383940rc rt VAR(rt)/rt 2 c*P/O1/M ncEst erbiasbiasbiasbiasweightlimit - blimit - aspeed – bspeed - 35.667YESNONONO2.8948.249.6In some instances, the values of Theta (i.e., the computed AMF in column 38) for variousstudies did not agree with the equivalent value computed by Elvik (shown in column 30).Through correspondence with Elvik et al., many of these discrepancies were eliminated.NCHRP 17-25 Final Report AppendixesF-2
Elvik et al. (p.29) categorized each published study they identified in the literature interms of its study design (see column 7). The seven study design designations they used arelisted in Table F-1.Table F-1. Study Design Designations.1234567DesignationStudy DesignEXPRandomized Controlled TrialBAMBefore-After with Matched Comparison GroupBACBefore-After with Non-Equivalent Comparison GroupBASBefore-After, NO Comparison GroupCSTCross-SectionCACOCase-ControlTI-SETime Series AnalysisA subsequent comparison of study design with the data provided for comparison sitesrevealed a few discrepancies. In some instances, comparison site data were provided yet thestudy was classified as a simple before-after study. In some other instances, no comparison sitedata were provided yet the study was classified as a before-after with comparison group. Thedesign designation of the following studies (as identified in column 1) was modified to reflectthe provision of comparison group data.Study Designation Changed from BAC to BAS:Study 12 Kemper, Byington, andStudy 48 Andersson (PDO records only).Study Designation Changed from BAS to BAC:Study 18 Christensen,Study 72 Lamm, Psarianos, Mailaender, andStudy 77 Kronberg, Nilsson.The standard errors se(Delta) and se(Theta) reflect mainly the number of accidents in thestudy. They are ‘ideal’ in the sense that they rely on the assumption that all confounding factorswere appropriately accounted for and all functional forms used are the correct ones. Since this isnever true, a multiplicative Method Correction Factor (MCF in column 40) was used to adjustthe standard errors. The magnitude of the MCF depends on the study design. Judgement wasused to establish the set of MCFs listed in Table F-2. These MCFs are an elaboration of thevalues used in the forthcoming Highway Safety Manual.NCHRP 17-25 Final Report AppendixesF-3
Table F-2. Method Correction Factors.B-A traffic correction for both treatment and comparison groupEXP B-A traffic correction only for treatment groupNo traffic correctionB-A traffic correction for both treatment and comparison groupBAM B-A traffic correction only for treatment groupNo traffic correctionB-A traffic correction for both treatment and comparison groupBAC B-A traffic correction only for treatment groupNo traffic correctionWith traffic correctionBASWithout traffic correctionCST With traffic correctionMCF1.21.51.82.02.42.82.22.634.555The database thus developed was used by both authors in their modeling efforts. Thefindings from these efforts are described in sections 3 and 4. The potential for regression-to-themean bias was identified by Elvik et al. in the database on a study-by-study basis. The effect ofthis bias was examined in the context of the regression modeling, as described in subsequentsections of this report.MODELING APPROACH 1Model ExaminationThis section examines two models that relate speed to crash frequency. The first modelexamined is that described by Elvik et al. (2004) as the "power" model. This model relates crashfrequency to speed, where the speed variable has an exponent of two or more. The second modelis developed by the authors of this paper. It relates crash frequency to the probability of a crash,where crash probability is based on the travel time required for the crash avoidance maneuver.Power ModelThe power model developed by Elvik et Al.(2004) is defined as:N Ec0 v α. 1where:N E v α c0 crash frequency of specified severity (i.e., PDO, injury, fatal);exposure;mean speed, mph;power term; andempirical constant.Values of c0 and α vary, depending on whether the model is used to estimate PDO, injury, orfatal crash frequency.NCHRP 17-25 Final Report AppendixesF-4
Equation 1 could also be restated as:N E P(crash) P( severe crash crash). 2The rationale for this model is that crash occurrence is related to the distance required tostop, which is a function of the square of speed. If a vehicle is unable to stop prior to reaching aroadway hazard, then a collision will likely occur. From this relationship, it is postulated thatcrash frequency is proportional to the square of speed (i.e., P(crash) v2 ). Hence, whenEquation 1 is calibrated to property-damage-only (PDO) crash data, the power term istheoretically equal to about 2.0.Elvik et al. (2004) also rationalize that the kinetic energy involved in a collision is relatedto the square of speed and that the likelihood of a severe (i.e., injury or fatal) crash is related tothe amount of kinetic energy in the collision (i.e., P(severe crash crash) v2 ). Hence, whenEquation 1 is calibrated to severe crash data, the power term α is theoretically equal to 4.0 ( 2.0 2.0).The first derivative of the power model is:dN a Ndv v. 3In the context of a before-after study, the change in crash frequency dN equals the crashfrequency with (i.e., after) treatment Nw minus the crash frequency without (i.e., before)treatment Nw/o. Similarly, the change in speed dv represents the difference between the meanspeed with, and without, treatment. Thus, the derivative in Equation 3 is used in its discrete (asopposed to "continuous") form when applied to before-after data. In recognition of this discretenature, the value of N on the right side of Equation 3 can be set to equal Nw/o and v can be set toequal vw/o. Substitution of these two variables yields the following variation of Equation 3:dNa Nw/odv v w / o. 4where:Nw/o vw/o crash frequency without treatment to effect a change in speed; andmean speed without treatment, mph.Equation 4 indicates that the change in crash frequency associated with a change in speedis proportional to the number of crashes before the change and inversely proportional to thespeed before the change. The magnitude of the change in crash frequency is also proportional tothe power term.The "percent change ratio" can be defined as the ratio of the percent change in crashes tothe percent change in speed. It is computed as:NCHRP 17-25 Final Report AppendixesF-5
Rc dN v w / o dv N w / o . 5 αwhere:Rc percent change ratio.Equation 5 indicates that the percent change ratio is a constant. The percent change incrash frequency does not depend on the percent change in speed (i.e., that the percent change incrashes is the same irrespective of whether the speed changes from 30 to 31 mph or from 60 to62 mph).Exponential ModelThe exponential model is defined as:()1 N E c 3 e MT / MT ( c1 v ) / c 2 1 e . 6where:c3 MT MT m ci Dc constant of proportionality;maneuver time needed to avoid a crash ( Dc/v), s;average maneuver time ( Dc/m), s;average maneuver speed based on facility design, mph;empirical constants, i 1, 2, 3; andmaneuver distance needed to avoid a crash, miles.The first term in parentheses represents the probability of a crash P(crash). It is based onmaneuver time which, in turn, is based on speed and the "critical maneuver distance" Dc. Thisdistance could be stopping distance or lane-change distance. It would include the distancetraveled during perception-reaction time plus the distance traveled during the avoidancemaneuver. With some cancellation, this term can be reduced to e(m/v) , where m is the averagemaneuver speed. This speed is related to the design speed of the road and represents the speed atwhich the roadway design can accommodate the critical maneuver with reasonable safety.The probability of a crash predicted from the power model and the exponential model isshown in Figure F-1. The P(crash) term for the exponential model is equal to c3 e(m/v). It isshown using a dashed line. The P(crash) term for the power model is equal to c4 v2 . The dashedtrend line has a slight concave shape while the solid line has a convex shape. It should be notedthat a concave relationship between speed and crash frequency was developed by Kockelman(2006, Table 4-20) using HSIS data for 3370 miles of interstate and highway in WashingtonState.NCHRP 17-25 Final Report AppendixesF-6
0.010scaled for illustrative purposesPower modela 2.0P(crash)0.0080.006Exp. modelm 62 mph0.0040.0020.0003040506070Mean Speed in Before Period, mphFigure F-1. Comparison of P(crash) for two models.The second term in the parentheses in Equation 6 represents the probability of a severecrash, given that a crash has occurred P(severe crash crash). This term would not be includedif Equation 6 were used to estimate the expected PDO crash frequency. For mathematicalconvenience, this probability is specified using the logistic function. This probability is shown inFigure 2 using a dashed line. It is compared to the P(severe crash crash) term from the powermodel (i.e., P(severe crash crash) c5 v2 ).P(severe crash crash)0.40scaled for illustrative purposesPower modela 2.0c 5 7.8 10-50.300.20Exp. modelc 1 80 mph0.10c 2 200.003040506070Mean Speed in Before Period, mphFigure F-2. Comparison of P(severe crash crash) for two models.NCHRP 17-25 Final Report AppendixesF-7
The logistic formulation has the logical bounds of 0.0 and 1.0 at very low and highspeeds, respectively. The formulation from the power model can yield values greater than 1.0 atexceptionally high speeds. However, over the range of typically encountered speeds, the twoprobability functions yield effectively equivalent values for any given speed. Therefore, therelationship P(severe crash crash) c5 v2 appears sufficiently accurate for the prediction of theprobability of a severe crash, given that a crash occurred.Based on the preceding discussion, the exponential model is revised to the followingform:()N E c 3 e m / v v c6 I. 7where:I indicator variable (0.0 when predicting PDO crash frequency, 1.0 when predictingsevere crash frequency).The revised exponential and power models are compared in Figure 3. The exponentialmodel is shown using a dashed line. The upper pair of trend lines illustrates the use of eachmodel to predict PDO crashes. The lower pair of trend lines illustrate the use of each model topredict severe crashes (i.e., injury fatal). To predict PDO crashes, the P(severe crash crash)term was excluded from each model.The two models are shown in Figure 3 to have generally similar trends for the range ofspeeds shown. However, the PDO versions of each model are less similar than the severe crashversions. The PDO crash trend line for the exponential model has a concave shape and thepower model has a convex shape. In contrast, the severe crash versions of each model have afairly similar convex shape. The severe crash trend lines are similar for both models at speeds upto 60 mph. Above 60 mph, the two models diverge slightly with the exponential model having asmaller rate of increase in slope.Expected Crash Frequency,crashes/yr30scaled for illustrative purposes25Exp. modelPower modelm 62 mpha 2.0c 5 7.8 10-520PDO1510Injury Fatal503040506070Mean Speed in Before Period, mphFigure F-3. Comparison of expected crash frequency from two models.NCHRP 17-25 Final Report AppendixesF-8
The first derivative of the exponential model is:dN m c6 I Ndv v 2v 8In recognition of the discrete nature of before-after crash data, the value of N on the rightside of Equation 8 can be set to equal Nw/o and v can be set to equal vw/o. Substitution of thesetwo variables yields the following variation of Equation 8:c IdN m 2 6dv v w / o v w / o N w / o . 9Equation 9 indicates that the change in crash frequency associated with a change in speedis proportional to the number of crashes before the change and inversely proportional to thespeed before the change. The magnitude of the change in crash frequency is also directlyproportional to the value of m and c6.The "percent change ratio" can be computed as: m c 6 I vw / o Rc dN v w / o dv N w / o. 10Examination of Equation 10 indicates that the percent change ratio is a function of speedfor the exponential model. This relationship suggests that the percent change in crash frequencyfor a given percent change in speed is larger at lower speeds than it is at higher speeds. Thistrend holds when the exponential model is applied to the PDO, injury, or fatal crash frequency.It should be noted that if m 0.0, I 1.0, and c6 α, then Equation 10 yields the percent changeratio for the power model.Accident Modification FunctionsThe following equation was used to estimate the AMF for both models:AMF NwNw/o. 11where:Nw/o crash frequency without treatment; andNw crash frequency with treatment to produce a change in speed.The crash frequency without treatment Nw/o was estimated using the following equation:N w / o K rd rtf rcNCHRP 17-25 Final Report Appendixes. 12F-9
where:K rd rtf rc count of crashes in the before period;ratio of the after period duration to the before period duration;ratio of the after period traffic volume to the before period traffic volume; andratio of the after period crash frequency at the comparison sites to the beforeperiod crash frequency at the comparison sites.It should be noted that some of the studies included in the database did not include data tocompute the traffic volume ratio, in which case this ratio was assumed to equal 1.0. Also, somestudies were simple before-after studies that did not include comparison sites, in which case thecomparison site ratio was assumed to equal 1.0.Combining Equation 1 with Equation 11 yields the following AMF for the power model: vAMF w vw / o α. 13where:vw vw/o mean speed without treatment, mph; andmean speed with treatment applied to change speed, mph.Similarly, combining Equation 7 with Equation 11 yields the following AMF for theexponential model: vAMF w vw / oc6 I e m (1 / vw 1 / vv / o ) . 14Model EvaluationThe power and exponential models were evaluated using before-after data assembled byElvik et al. (2004) from 98 studies conducted in 20 countries. One objective of this evaluationwas to determine whether the supports the power or exponential model forms (or perhaps a thirdmodel form). A second objective was to determine if the trends in the data from U.S. studieswere different from those in the data from other countries.Initially, a qualitative evaluation was undertaken that focused on the percent change incrashes relative to the percent change in speed. Then, a quantitative evaluation was undertakenthat focused on the change in crashes associated with a specified change in speed. For thisevaluation, the AMF for speed change was related to the data using regression analysis. Finally,some alternative data subsets and model forms are discussed.Qualitative EvaluationThe qualitative evaluation focused on graphically exploring the relationship betweenpercent change in crash frequency and percent change in speed. An examination of Equation 5suggested that the two percentages are related by a constant. In contrast, an examination ofEquation 10 suggests that the relationship between the two percentages is a function of speed.NCHRP 17-25 Final Report AppendixesF-10
To facilitate the graphical examination, the data were sorted to include only those studiesthat satisfied the following criteria:1. Crash count in the "before" period of 50 crashes or more.2. A change in mean speed from before to after period of 1.0 mph or more.3. Mean speed in the "before" period of 40 mph or more.Criterion 1 was intended to provide some stability to the "percent change in crashes"variable used in the graphical examination. Similarly, Criterion 2 was established to providesome stability to the "percent change in speed" variable. The mathematics of one of thestatistics being examined (i.e., percent change ratio) caused it to have a high variability when thespeed change was small. Hence, to facilitate the graphical examination of trend, data associatedwith a very small speed change were excluded for conven
AN EMPIRICAL EXAMINATION OF THE RELATIONSHIP BETWEEN SPEED AND ROAD ACCIDENTS INTRODUCTION At the expert panel meeting to develop AMFs for urban/suburban arterials (conducted at the UNC Highway Safety Research Center in July 2005), the findings of Elvik et al. about the relationship between speed and accidents were discussed.
May 02, 2018 · D. Program Evaluation ͟The organization has provided a description of the framework for how each program will be evaluated. The framework should include all the elements below: ͟The evaluation methods are cost-effective for the organization ͟Quantitative and qualitative data is being collected (at Basics tier, data collection must have begun)
Silat is a combative art of self-defense and survival rooted from Matay archipelago. It was traced at thé early of Langkasuka Kingdom (2nd century CE) till thé reign of Melaka (Malaysia) Sultanate era (13th century). Silat has now evolved to become part of social culture and tradition with thé appearance of a fine physical and spiritual .
On an exceptional basis, Member States may request UNESCO to provide thé candidates with access to thé platform so they can complète thé form by themselves. Thèse requests must be addressed to esd rize unesco. or by 15 A ril 2021 UNESCO will provide thé nomineewith accessto thé platform via their émail address.
̶The leading indicator of employee engagement is based on the quality of the relationship between employee and supervisor Empower your managers! ̶Help them understand the impact on the organization ̶Share important changes, plan options, tasks, and deadlines ̶Provide key messages and talking points ̶Prepare them to answer employee questions
Dr. Sunita Bharatwal** Dr. Pawan Garga*** Abstract Customer satisfaction is derived from thè functionalities and values, a product or Service can provide. The current study aims to segregate thè dimensions of ordine Service quality and gather insights on its impact on web shopping. The trends of purchases have
Chính Văn.- Còn đức Thế tôn thì tuệ giác cực kỳ trong sạch 8: hiện hành bất nhị 9, đạt đến vô tướng 10, đứng vào chỗ đứng của các đức Thế tôn 11, thể hiện tính bình đẳng của các Ngài, đến chỗ không còn chướng ngại 12, giáo pháp không thể khuynh đảo, tâm thức không bị cản trở, cái được
Le genou de Lucy. Odile Jacob. 1999. Coppens Y. Pré-textes. L’homme préhistorique en morceaux. Eds Odile Jacob. 2011. Costentin J., Delaveau P. Café, thé, chocolat, les bons effets sur le cerveau et pour le corps. Editions Odile Jacob. 2010. Crawford M., Marsh D. The driving force : food in human evolution and the future.
Le genou de Lucy. Odile Jacob. 1999. Coppens Y. Pré-textes. L’homme préhistorique en morceaux. Eds Odile Jacob. 2011. Costentin J., Delaveau P. Café, thé, chocolat, les bons effets sur le cerveau et pour le corps. Editions Odile Jacob. 2010. 3 Crawford M., Marsh D. The driving force : food in human evolution and the future.
