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Freeway safety management: case studies in Italy.

1. Introduction

Road safety has since become a worldwide priority and one of the major factors for a description of the state traffic system in terms of both positive and negative changes. Driver behavior is always a compromise between conditioning arising from a series of external factors (road conditions, environmental conditions, etc.) and a series of personal factors (caution, driving ability, psycho-physical state, etc. Many researchers have been dealing with the evaluation of the traffic accidents costs, other researchers have addressed driver speed behavior to identify all possible factors that may affect driving conditions during travel (Dell'Acqua, Russo 2011a, 2011b). In fact, crashes are often due to

bad decisions made by drivers in environments created by engineers (Dell'Acqua, 2011). International research has thus suggested a variety of approaches to analyze the road traffic safety level on the basis of an assessment of accident rates and frequency (Discetti et al. 2011).

Nie et al. (2007) modeled operating speeds on horizontal curves using data collected from a road experiment involving volunteer drivers and a test vehicle in Ontario, Canada. Continuous speed data were collected using instrumentation within the test vehicle. Geometric features were determined using GIS software. Driver speed trends were modeled using ordinary the least squares regression. Operating speeds along a horizontal curve were modeled, as well as speed differential values when approaching and departing the curve. Himes and Donnell (2010) investigated the effects of roadway geometric design features and traffic flow on operating speed characteristics along rural and urban four-lane highways in Pennsylvania and North Carolina. A simultaneous equations framework was used to model the speed distribution, developing equations for the mean speed and standard deviation of speed for both travel lanes using the three-stage least squares estimator. This simultaneous equation modeling framework was first introduced by Shankar and Mannering (1998) to model speeds on a freeway segment in Washington State. It was later explored in depth and compared to limited information (e.g., OLS regression) and full-information (e.g., seemingly unrelated regression) modeling methods by Porter (2007).

Dixon et al. (1999) have conducted a basic research on speed prediction for rural multi-lane highways and urban and suburban arterials. For the purposes of this research, the project should focus on passenger car operating speeds, trucks, and recreational vehicles, and be developed in a manner that complements the existing two-lane rural highway design consistency module currently available in the IHSDM (Interactive Highway Safety Design Model). The association between vehicle operating speeds and geometric design features on these facilities could assist in several design functions, particularly when used in concert with the latest enhancements to the IHSDM crash prediction module. Examples of this include: assessing the need for climbing lanes, justification of maximum grades, evaluating proposed capacity-expansion projects, and assessing speed-safety relationships on horizontal curves. The findings from this research could also be used as a framework to perform level of service analysis on uninterrupted flow facilities. In the Highway Capacity Manual, estimating free-flow speeds is an important step in freeway and multi-lane highway operational performance evaluations.

Deardoff et al. (2011) in a study conducted in Dakota proposed an important report on the free flow speed in highway. Two team members using a radar gun and manual tally sheets collected 1668 speed observations at ten sites during several weeks. Each site had a unique posted speed limit sign ranging from 20 mi/h (30 km/h) to 75 mi/h (120 km/h). Five sites were on urban streets. Three sites were on multilane highways, and two on freeways. Goodness-of-fit test results revealed that a Gaussian distribution generally fit the speed distributions at each site at a 5% level of significance. The best-fit model had a correlation coefficient of +0.99. The posted speed limit variable was significant at 5% level of significance. Examining data by highway type revealed that average free-flow speeds are strongly associated with posted speed limits with correlation coefficients of +0.99, +1.00 and +1.00 for urban streets, multilane highways, and freeways, respectively. Dell'Acqua et al. (2011a) proposed a model for estimating operative speed on motorways. The research is survey based, and takes into account various geometric conditions, making it possible to find the variables that influence operative speed in the Free Flow conditions. The research is survey-based, and takes into account various geometric conditions, making it possible to find the variables that influence [V.sub.85]. In particular, the study proposed in the next paragraphs is an update of the previous version (Dell'Acqua et al. 2011a) to estimate [V.sub.85], for non-conditioned traffic flows on freeway.

2. Data Set

The data used in the study were collected on a stretch of the A3 situated in the south of Italy. The stretch is located between the distance marker at 195.000 km (Castrovillari interchange) and another at 290.000 km (Grimaldi interchange). The geometric variables measured in each section are shown in Table 1.

3. Recording Vehicle Speed and Traffic Flow

A survey station was placed at each section, (as indicated in Table 1) to record the flow and speeds of the vehicles passing within a time interval T. The structure of the survey station is represented in Fig. 1. It consists of a digital television camera connected to a portable PC that shows the images it captures. The system is set up across a section of the road, as in Fig. 1, at a distance greater than 25 meters, allowing the vehicles that pass through the chosen section to be filmed. Knowing the distance between the three vertices, A, B and C shown in Fig. 1, it is possible to calculate 'fundamental 1' that joins points 1 and 2 and 'fundamental 2' that joins points 1' and 2'. With this information, assuming that there is uniform motion along the two 'fundamentals' (indicated as [X.sub.i]) it is possible to obtain the speed of the vehicles along 'fundamental 1' and 'fundamental 2'. In fact, the PC is fitted with a card for the acquisition and elaboration of images that make it possible to read the images one frame at a time (1 frame = 1/25 sec). It is possible to count the number of frames it takes the vehicle to cover one of the two 'fundamentals. The vehicle's speed is calculated from the relationship between the number of frames and the 'fundamentals'. To confirm the validity of the system and its calibration, checks were done at each reading, applying one of the two 'fundamentals' to three vehicles whose speeds were known. From the comparison between the speeds measured using the tachometer and those obtained by the system, it was possible to establish its reliability, which always resulted acceptable. The data acquired from the survey station were organized in the sequence shown in Table 2. Only the speeds of cars in free flow conditions ([V.sub.p] < 200 pcphpl) were counted.

[FIGURE 1 OMITTED]

4. Identifying the Distribution for the Average Speeds

In general, the distribution of the vehicles' speeds (cars in particular) is best represented by normal distribution. The [chi square] test was carried out to verify the goodness of the above distribution law, the test has provided P < 0.05 for all surveys.

Table 3 shows the values of [V.sub.85observed] and [V.sub.85normal] x [V.sub.85normal] was calculated using expression (1) for the law of normal distribution:

[V.sub.85normal] = [V.sub.average] + 1.04 x st.dev. (1)

The [V.sub.average] and the st.dev. used in (1) are shown in Table 3. The last column also shows [V.sub.85observed,] i.e., the speed that was exceeded in only 15% of the readings. The [V.sub.85observed] and the [V.sub.85calculated] using (1) are very close, which further confirms the suitability of normal distribution for the observed speeds.

5. Models for Estimating [V.sub.85]

The estimation model for [V.sub.85] was obtained by means of a multiple regression for the [V.sub.85normal] (dependent variable) and the following independent variables (predictors):

* curvature (denoted by the term 1/R) has been obtained as the inverse of radius;

* longitudinal grade (denoted by the term [absolute value of i]) has been taken at its absolute value because there is low variation in relation to 'upgrade' and 'downgrade' conditions, and is particularly weak on the tangent segments;

* tortuousness (denoted by the term [summation over (i)] [[alpha].sub.i]/2 and measured in grad/km) characterized by the form represented in Fig. 2 was introduced in order to take into account the ways drivers approach the element where their speed was measured:

In short, this term differentiates between different situations, as in the example given in Fig. 2 where the 'survey stations' share the same conditions (same length, same section width, same degree of slope etc.), but are preceded and succeeded by different degrees of tortuousness. Two attempts were made to choose the dependent variable. In the first attempt, we used [V.sub.85observed] while in the second we used [V.sub.85normal] . The best results (though only slightly) were obtained at the second attempt; for this reason, [V.sub.85normal] was used as the dependent variable. This variable is very similar to the CCR (curvature change ratio) and was calculated 1.5 km before the survey section and 0.5 km after the survey section.

[FIGURE 2 OMITTED]

The result obtained from the multiple regression is the following:

[V.sub.85] = 154.8 - 2015 x(i/R)-0.42 x [summation over (i)] [[alpha].sub.i]/2 -4.2 x [absolute value of i]. (2)

The coefficient [R.sup.2] is equal to 0.94, which confirms the strong relationship between the three independent variables and [V.sub.85]. Moreover, the 't-student' test, carried out in order to control the significance of the variables (Table 4) used in the regression, confirmed the validity of model (2). A comparison was made between the evaluation results of the proposed model's ability to simulate the observed [V.sub.85]. Table 5 shows the compared results.

With the help of model (2), some 'complex' assessments were designed and carried out (i.e. measurements on more than one element of the road alignment) on an approximately 20 km stretch of the A3 freeway. The characteristics of the stretch examined are shown in Table 6. The stretch analyzed was subdivided into 10 groups, so as to obtain sub-stretches of approximately 2 km made up of different elements of the alignment. The groups were formed in such a way that there were at least two different alignment features for each group. Then, all the variables necessary to calculate V85 were calculated for each group. In addition, the last two columns (Table 6) show for each group [V.sub.85average] and the number of crashes (Prentkovskis et al. 2010) for the interval between 31/10/2008 and 31/10/2009 respectively. Two situations are immediately clear:

* the groups with the most crashes have higher tortuousness figures (see Fig. 3);

* in the groups with a [V.sub.85average] higher than 130 km/h the number of crashes is low while in groups where [V.sub.85average] is lower than 130 km/h, the number of crashes is higher.

This second result, which seems paradoxical in some ways, highlights a very interesting aspect of freeway traffic. In fact, the user in this type of traffic wishes to maintain an average speed close to 130 km/h (Dell'Acqua et al. 2011a). This is possible only in certain particularly favorable geometric conditions. In less favorable conditions, in cases where the degree of tortuousness, slope and curvature are higher, the user must reduce the speed. In many cases, however, the user changes speed in a way which is not appropriate to the geometric conditions and so drives on the limit, thus naturally increasing the probability of crashes. This becomes even more critical when the user passes through two 'groups' characterized by a [V.sub.85average] difference greater than 10 km/h (Dell'Acqua et al. 2011b). In this regard, model (3) was constructed using linear regression (3) between [V.sub.85average] and the number of crashes in the different groups (Fig. 4):

N.Crashes = -1.516 [V.sub.85average] + 208.62; [R.sub.2] = 0.92. (3)

The significance value of model (3) is shown in Table 7. In addition, Table 8 and Fig. 5 show a correlation between the difference in velocity ([DV.sub.85average]) between subsequent groups and the difference in the number of crashes (DN) between subsequent groups.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

The higher crashes rate is found in areas with group whose [V.sub.85] average difference is greater than 10 km/h. In particular, in Fig. 5 we observe that the lines that support the curve show two different trends: low correlation with a DV less than 10 km/h (with [R.sup.2] = 0.33) and high correlation with a DV greater than 10 km/h (with [R.sup.2] = 0.71).

6. Results and Conclusions

As demonstrated, the variables that significantly affect the [V.sub.85] are 'curvature', 'longitudinal grade' and 'tortuousness'. The last term was introduced in order to take into account the ways drivers approach the element where their speed was measured. This term differentiates between different situations, as in the example given in Fig. 2, where the 'survey stations' share the same conditions (same length, the same section width, same degree of slope etc.), but are preceded and succeeded by different degrees of tortuousness. The resulting model (2) showed good reliability at a local level. In fact, the maximum residual found in the experimental tests was within 5%. Moreover, the results obtained by applying the model to a stretch of highway of about 20 km, have highlighted some particular aspects of motorway traffic. In particular, using the procedure illustrated, it has been possible to identify some particular 'black spots' due to the poor design co-ordination of the alignment, positioned between consecutive stretches (for approximately 2 km), with a difference in terms of [V.sub.85average] greater than 10 km/h.

doi:10.3846/16484142.2012.724447

Acknowledgements

The research was conducted under the Italian National Research Project 'Driver speed behavior evaluation using operating speed profile and crash predicting models'.

References

Deardoff, M. D.; Wiesner, B. N.; Fazio, J. 2011. Estimating freeflow speed from posted speed limit signs, Procedia--Social and Behavioral Sciences 16: 306-316. http://dx.doi.org/10.1016/j.sbspro.2011.04.452

Dell'Acqua, G.; De Luca, M.; Mauro, R.; Lamberti, R. 2011a. Motorway speed management in Southern Italy, Procedia Social and Behavioral Sciences 20: 49-58. http://dx.doi.org/10.1016/j.sbspro.2011.08.010

Dell'Acqua G.; De Luca, M.; Mauro, R. 2011b. Road safety knowledge-based decision support system, Procedia--Social and Behavioral Sciences 20: 973-983. http://dx.doi.org/10.1016/j.sbspro.2011.08.106

Dell'Acqua, G.; Russo, F. 2011a. Safety performance functions for low-volume roads, The Baltic Journal of Road and Bridge Engineering 6(4): 225-234. http://dx.doi.org/10.3846/bjrbe.2011.29

Dell'Acqua, G.; Russo, F. 2011b. Road performance evaluation using geometric consistency and pavement distress data, Transportation Research Record 2203: 194-202. http://dx.doi.org/10.3141/2203-24

Dell'Acqua, G. 2011. Reducing traffic injuries resulting from excess speed: low-cost gateway treatments in Italy, Transportation Research Record 2203: 94-99. http://dx.doi.org/10.3141/2203-12

Discetti, P.; Dell'Acqua, G.; Lamberti, R. 2011. Models of operating speeds for low-volume roads, Transportation Research Record 2203: 219-225. http://dx.doi.org/10.3141/2203-27

Dixon, K.; Wu, C.; Sarasua, W.; Daniel, J. 1999. Posted and free-flow speeds for rural multilane highways in Georgia, Journal of Transportation Engineering 125(6): 487-494. http://dx.doi.org/10.1061/(ASCE)0733-947X(1999)125:6(487)

Himes, S.; Donnell, E. 2010. Speed prediction models for multilane highways: simultaneous equations approach, Journal of Transportation Engineering 136(10): 855-862. http://dx.doi.org/10.1061/(ASCE)TE.1943-5436.0000149

Nie, B.; Hassan, Y. 2007. Modeling Driver Speed Behavior on Horizontal Curves of Different Road Classifications, in TRB 86th Annual Meeting Compendium of Papers CD-ROM., 21-25 January, 2007. Washington, D.C. 16 p.

Porter, R. J. 2007. Estimation of Relationships between 85th Percentile Speeds, Speed Deviations, Roadway and Roadside Geometry and Traffic Control in Freeway Work Zones. A Thesis in Civil Engineering by Richard J. Porter Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy. Pennsylvania State University. Available from Internet: http://etda.libraries.psu.edu/paper/7548

Prentkovskis, O.; Sokolovskij, E.; Bartulis, V. 2010. Investigating traffic accidents: a collision of two motor vehicles, Transport 25(2): 105-115. http://dx.doi.org/10.3846/transport.2010.14

Shankar, V.; Mannering, F. 1998. Modeling the endogeneity of lane-mean speeds and lane-speed deviations: a structural equations approach, Transportation Research Part A: Policy and Practice 32(5): 311-322. http://dx.doi.org/10.1016/S0965-8564(98)00003-2

Mario De Luca (1), Gianluca Dell'Acqua (2)

(1,2) Dept of Transportation Engineering, University of Napoli Federico II, Via Claudio 21, 80125 Napoli, Italy

E-mails: (1) mario.deluca@unina.it (corresponding author); (2) gianluca.dellacqua@unina.it

Submitted 9 December 2011; accepted 22 August 2012
Table 1. Data set organization

Survey Nr.   Date       T Duration      Distance   Dir.  Slope
(sections)              Survey [hour]   [km]             [%]

1            21/02/10   3               246.000    N     -2.0
2            14/03/10   4               236.000    S     1.0
3            30/04/10   5               236.600    S     1.5
4            05/05/10   2               207.000    N     -0.5
5            11/05/10   4               205.000    N     4.5
6            18/05/10   3               204.800    N     4.5
7            18/05/10   2               205.200    N     -4.0
8            27/05/10   4               243.200    N     -1.0
9            14/09/10   2               195.700    N     3.5
10           30/09/10   3               209.500    N     0.1
11           05/02/11   4               204.500    S     -4.5
12           11/03/11   2               204.600    N     4.5
13           18/04/11   2               289.400    N     -2.0
14           18/06/11   3               289.400    S     2.0
15           27/06/11   4               277.000    N     4.2

Survey Nr.   Width        Curvature  Tortuousness *  State
(sections)   section [m]  [1/m]      [grad/km]       of paving

1            10.7         0.0000     5.3             dry
2            10.7         0.0000     5.3             dry
3            10.7         0.0000     5.3             dry
4            8.7          0.0000     23.7            dry
5            8.7          0.0000     24.7            dry
6            8.7          0.0000     26.0            dry
7            8.7          0.0000     26.0            dry
8            10.7         0.0012     12.0            dry
9            8.7          0.0014     28.0            dry
10           8.7          0.0010     22.0            dry
11           8.7          0.0029     22.0            dry
12           8.7          0.0029     29.0            dry
13           8.7          0.0011     22.0            dry
14           8.7          0.0011     29.0            dry
15           8.7          0.0027     21.00           dry

Survey Nr.   Transverse  Distance from
(sections)   slope [%]   motorway-exit [km]

1            2.5         2.5
2            2.5         2.0
3            2.5         2.6
4            2.5         1.5
5            2.5         2.1
6            2.6         2.1
7            2.4         1.9
8            5.0         2.0
9            5.5         1.2
10           6.0         1.4
11           7.0         2.6
12           7.0         2.7
13           4.5         4.0
14           4.5         4.0
15           5.0         2.5

Note: * The meaning of this variable is explained in paragraph
'models for estimating [V.sub.85]'

Table 2. Data set processing

Num.    Veh.    DIR   T1 [sec]             T2 [sec]
veh.    type          sec        1/25 sec  sec        1/25 sec

1       Car     N     827        14        828        1
2       Car     N     55         2         55         14
3       Car     N     107        22        108        9
4       Car     S     842        1         842        12
5       Car     N     645        1         645        14
6       Car     N     410        17        411        5
7       Car     N     812        13        813        1
...     ...     ...   ...        ...       ...        ...
...     ...     ...   ...        ...       ...        ...
n-2     Car     S     335        19        336        14
n-1     Car     S     157        7         158        3
N       Car     S     644        4         645        0

Num.    [DELTA]T=(T2-T1)  Fundamental   Car Speed ([DELTA]
veh.    [sec]             Xi [m]        T-3.6)/([X.sub.i]/25)
                                        [km/h]

1       11.75             21.47         161.0
2       12.00             21.47         161.0
3       12.00             21.47         161.0
4       11.00             19.20         157.1
5       12.75             21.47         148.6
6       12.75             21.47         148.6
7       13.00             21.47         148.6
...     ...               ...
...     ...               ...
n-2     20                19.20         86.4
n-1     21                19.20         82.3
N       21                19.20         82.3

Table 3. Observed [V.sub.85] and calculated [V.sub.85] using normal
distribution.

Section    [V.sub.    St. Dev.   [V.sub.85] calculated    [V.sub.85]
location   average]   [km/h]     using Equation           observed
[km/h]     [km/h]                (1) [km/h]               [km/h]

246.000    122.7      22.20      145.8                    147.6
236.000    124.5      21.00      146.3                    145.3
236.600    125.9      21.97      148.7                    146.7
207.000    124.0      20.70      145.5                    147.3
205.000    105.6      17.28      123.6                    124.6
205.000    107.3      17.98      126.0                    124.7
205.200    109.0      18.00      127.7                    124.1
243.200    122.5      18.09      141.3                    140.9
195.700    110.0      19.20      130.0                    130.1
209.500    124.3      18.52      143.6                    143.0
204.500    107.9      18.60      127.2                    128.5
204.600    98.69      17.23      116.6                    117.9
289.400    118.5      15.85      135.0                    132.7
289.400    113.0      18.62      132.4                    132.3
277.000    104.0      14.9       119.5                    119.7

Table 4. Result of the 't-student' test

                       Coefficient  Standard  t-student  Significance
                                    deviation

Constant               154.8        2.021     76.58      0.000
1/R                    2015         789.89    -2.55      0.027
[summation over (i)]   0.42         0.107     -3.58      0.004
  [[alpha].sub.i]/2
[absolute value of i]  4.2          0.576     -7.35      0.000

Table 5. Comparison between 'observed [V.sub.85]'
and 'normal [V.sub.85]'

Section    [V.sub.85calculated]   [V.sub.85normal]
location   obtained with          obtained with
[km]      model (2) [km/h]       eq. (1) [km/h]

246.000    144.4                  145.8
236.000    148.6                  146.3
236.600    146.5                  148.7
207.000    143.5                  145.5
205.000    126.4                  123.6
205.000    125.9                  126.0
205.200    128.0                  127.7
243.200    143.6                  141.3
195.700    126.5                  130.0
209.500    143.9                  143.6
204.500    121.6                  127.2
204.600    118.9                  116.6
289.400    135.7                  135.0
289.400    133.0                  132.4
277.000    123.6                  119.5

Section    Residual between
location   [V.sub.85normal] and
[km]       [V.sub.85calculated] [%]

246.000    1.0
236.000    1.5
236.600    1.5
207.000    1.4
205.000    2.2
205.000    0.1
205.200    0.2
243.200    1.6
195.700    2.8
209.500    0.2
204.500    4.6
204.600    1.9
289.400    0.5
289.400    0.5
277.000    3.3

Table 6. 't-student' test, model (2)

Group   Initial    Final     Curvature   Slope   Length of
        distance   distance  (1/m)       [%]     the group
                                                 [m]

1       265.160    266.361   0.00000     5.0
        266.361    267.119   0.00065     5.0     1959
        267.119    267.410   0.00000     5.0
        267.410    267.860   0.00058     4.0
        267.860    268.233   0.00000     3.3
2       268.233    268.461   0.00106     3.3
        268.461    268.521   0.00000     3.3
        268.521    268.703   0.00143     3.3
        268.703    269.104   0.00000     3.3     1985
3       269.104    269.762   0.00143     4.5
        269.762    271.058   0.00000     4.4     1954
4       271.058    271.310   0.00108     2.5
        271.310    273.010   0.00000     2.5     1952
5       273.010    273.856   0.00103     3.0
        273.856    274.966   0.00000     3.0     1956
        274.966    275.710   0.00036     2.9
6       275.710    276.094   0.00000     3.8
        276.094    276.622   0.00182     3.8
        276.622    276.916   0.00000     3.8     1950
        276.916    277.187   0.00313     3.4
        277.187    277.297   0.00000     3.4
        277.297    277.636   0.00333     3.4
7       277.636    277.956   0.00000     3.4
        277.956    278.304   0.00167     3.4
        278.304    278.524   0.00000     3.4
        278.524    278.889   0.00208     3.4     1973
        278.889    279.279   0.00000     3.3
        279.279    279.384   0.00095     3.3
        279.384    279.603   0.00000     3.3
8       279.603    279.863   0.00000     3.3
        279.863    280.136   0.00000     3.3
        280.136    280.466   0.00000     3.3
        280.466    280.900   0.00000     3.3     2011
        280.900    281.240   0.00154     3.1
        281.236    281.680   0.00000     3.1
9       281.676    281.996   0.00143     3.1
        281.996    282.250   0.00143     3.1
        282.252    282.940   0.00270     3.1     2040
        282.940    283.358   0.00270     4.0
        283.358    283.408   0.00000     4.0
        283.408    283.663   0.00172     4.0
        283.663    284.153   0.00161     4.0
10      284.153    284.323   0.00000     4.0
        284.323    284.407   0.00286     4.0
        284.407    284.537   0.00000     4.0
        284.537    284.667   0.00200     4.0
        284.667    284.944   0.00000     4.0     2004

Group   Tortuousness   [V.sub.85]        Number of   Total
        of the group   calculated with   crashes     crashes
        [grad/km]      model (2)         observed    in the group

1                      128               1           10
        14.5           126               9
                       125               1
                       128               3
                       132               2
2                      130               3           10
                       132               0
                       129               0
        22.0           132               1
3                      122               10          23
        27.4           125               13
4                      139               0           6
        8.0            141               6
5                      130               2           8
        25             132               6
                       119               3
6                      116               7           32
                       112               6
        55             116               16
                       94                24
                       100               2
                       94                10
7                      100               2           71
                       97                16
                       100               10
        96             96                7
                       116               9
                       114               1
                       116               3
8                      116               1           33
                       116               16
                       116               1
        60             116               2
                       110               2
                       113               1
9                      110               2           32
                       110               7
        67             108               20
                       100               28
                       105               2
                       102               14
                       102               5
10                     105               0           51
                       99                2
                       105               0
                       101               0
        78             105               0

Group   [V.sub.85average]
        in the group
        [km/h]

1       127

2       130

3       123

4       140

5       131

6       116

7       97

8       116

9       111

10      103

Table 7. 't-student' test, model (3)

                   Coefficient Standard   t-student  Significance
                               Deviation

Constant           208.62      18.29      11.40      < 0.001
[V.sub.85average]  -1.516      0.152      -9.95      < 0.001

Table 8. Relationship between DV and DN

                                  [D.sub.V85average],   DN,
                                  speed                 crashes
                     Number       difference            difference
Group   [V.sub.      of crashes   between               between
        85average]   in the       group i and           group i and
                     group        group                 group i+1
                                  (absolute             (absolute
                                  value)                value)
1       127.6        10           ...                   ...
2       130.1        10           2.5                   0
3       123.8        23           6.3                   13
4       140.1        6            16.3                  17
5       131.3        8            8.8                   2
6       116.2        32           15.1                  24
7       97.8         71           18.4                  39
8       116.7        33           18.9                  38
9       111.9        32           4.8                   1
10      103.1        51           8.8                   19
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Author:De Luca, Mario; Dell'Acqua, Gianluca
Publication:Transport
Article Type:Case study
Geographic Code:4EUIT
Date:Sep 1, 2012
Words:4628
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