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34 error structure is assumed, with k being the dis- of . Thus, if equals 0.7 and the standard error is 0.12, then persion parameter of this distribution. the confidence interval ranges from 0.46 to 0.94. This confi- dence interval indicates a significant positive effect. Step 6: Calculate the total expected number of noninter- To summarize, if the confidence interval contains the value section crashes (B) and its variance [VAR(B)] during 1, then no significant effect has been observed. If is less the after period that would have occurred if PRPMs than the value 1 and the upper value of the confidence inter- were not implemented: val is less than the value 1, then the treatment has had a sig- nificant positive effect on safety (i.e., a reduction in crashes). ^ 1 Ca B=K (4-5) Conversely, if is greater than 1 and the lower value of the confidence interval is greater than 1, then the treatment had B + Ca a significant negative effect on safety (i.e., an increase in VAR( B) = (4-6) Cb + k E( K1 ) crashes). Step 7: Determine for each site its index of effectiveness (site) and it variance VAR(site): 4.2 DISAGGREGATE ANALYSIS METHODOLOGY A site = ( B)(1 + VAR( B) B2 ) (4-7) Disaggregate analysis performed on nighttime crashes included both univariate exploratory analysis and formal VAR( site ) = site 2 (1 A + VAR( B) B2 ) multivariate modeling. The univariate exploratory analysis (4-8) was used to identify and isolate factors that might be asso- (1 + VAR( B) B2 ) 2 ciated with the variation in the safety impact of PRPM installations. The results of the exploratory analysis were Where used to guide the multivariate modeling in an attempt to A = Total crash count during the after period. relate the safety impact of PRPMs to variables found in the initial univariate analysis. These two analyses are Step 8: Determine the composite index of effectiveness described below. () and it variance VAR() for all sites combined: = A (4-9) 4.2.1 Univariate Exploratory Analysis ( B)(1 + ( VAR( B)) B2 ) Using two-dimensional plots and spreadsheets sorted on variables of interest, the relationship between various factors VAR() = 2 1( ( A) + ( VAR( B)) ( B)2 ) (4-10) and the calculated index of effectiveness () for each site was (1 + ( VAR( B)) ( B)2 ) explored by visual inspection for differences in effects that 2 might relate to different levels of a variable in the statistical analysis. For the purpose of this study, a site is a homoge- Where neous segment of road represented by a set of attributes (shoul- A = Sum of all crashes over the after period der width, type, lane width, AADT, terrain, guide rails, hor- for all PRPM locations, izontal alignment, etc.). B = Sum of the expected number of crashes (B) for all PRPM locations, and 4.2.2 Multivariate Modeling of the Index VAR(B) = Sum of the variances of the expected of Effectiveness () number of crashes, VAR(B). The results of the nighttime crash composite analysis The standard error (s.e.) of is given by for all states were combined to develop a model to estimate the index of effectiveness (i.e., the safety effect of PRPMs) s.e.() = VAR() (4-11) using traffic volumes, site characteristics (e.g., surface width, shoulder widths, illumination, and other delin- The percent change in the number of crashes is equal to eators), and PRPM characteristics (e.g., spacing) as 100(1 - ); thus, = 0.7 denotes a 30-percent reduction in explanatory variables. The model form is a linear model crashes. The standard error (s.e.) indicates the accuracy of with a gamma error distribution for (39). The model was the index of effectiveness. An approximate 95-percent con- of the general form: fidence interval can be determined by adding and subtracting twice the value of the standard error (2 s.e.) from the value site = + b1 x1 + b2 x2 + b3 x3 + ... bn xn (4-12)