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Publication Number:  FHWA-HRT-17-077    Date:  November 2017
Publication Number: FHWA-HRT-17-077
Date: November 2017

 

Safety Evaluation of Red-Light Indicator Lights (RLILs) At Intersections

Chapter 3. Study Design

The study design involved a sample size analysis and prescription of needed data elements. The sample size analysis assessed the size of sample required to statistically detect an expected change in safety and also determined what changes in safety could be detected with likely available sample sizes.

Sample Size Estimation Overview

When planning a before–after safety evaluation study, it is vital to ensure that enough data are included such that it is statistically possible to detect the expected change in safety. While the expected change in safety is unknown in the planning stages, it is still possible to estimate the number of required sites (i.e., intersections) based on the best available information about the expected change in safety. Alternatively, one could estimate the change in safety that one could statistically detect for the number of available sites. Chapter 9 of Hauer provides a detailed explanation of sample size considerations and estimation methods.(5) The sample size analysis presented in this section addresses two cases: (1) how large a sample would be required to statistically detect an expected change in safety and (2) what changes in safety could be detected with available sample sizes.

For case 1, the research team assumed that a conventional before–after study with comparison group design would be used because available sample size estimation methods were based on this assumption. The sample size estimates from this method would be conservative in that the EB methodology would likely require fewer sites. To facilitate the analysis, it was also assumed that the number of comparison intersections was equal to the number of treatment intersections and the durations of the before and after periods were equal, which was again a conservative assumption.

Table 1 provides the crash rate assumptions. Initially, the research team assumed that the locations of interest for this treatment would be four-legged and three-legged signalized intersections. However, very few three-legged intersections were treated, and therefore, these intersections were dropped from the dataset. The research team used a central Florida study as the basis for assumptions on intersection crash rates.(6) Intersection crash rates differ substantially depending on a number of factors (e.g., traffic volume, geometric configuration, and area type). Therefore, the intersection crash rates assumed represent the general lower and upper end of the crash frequency spectrum in Florida. Rate C represents the intersection crash rate for before-period data for all intersections in Florida.

Table 1 . Before-period crash rate assumptions for signalized intersections in Florida.

Crash Type

Rate A: Orange County (2x2 Lane Signalized Intersections)1

Rate B: Seminole County(6x4 Lane or 6x6 Lane Signalized Intersections)1

Rate C: Before-Period

(All Treatment Sites)2

All

2.47

28.45

9.33

Injury

1.79

4.8

4.84

Right-angle

0.55

3.93

1.82

Left-turn

0.55

1.6

0.95

Rear-end

0.89

17.2

3.97

Nighttime

2.92

Disobeyed signal

0.81

1Data source: Kowdla.(6)
2Data source: project database.
Rate = Crashes/intersection/year.
— Indicates no available data.

Table 2 and table 3 provide estimates of the required number of before- and after-period intersection-years for crash rates A, B, and C to achieve statistical significance at 95- and 90‑percent confidence levels, respectively. The minimum sample indicated the level for which a study seemed worthwhile (i.e., it was feasible to detect with the specified level of confidence the largest effect that one might reasonably expect based on current knowledge about the strategy). The research team based these sample size calculations on specific assumptions regarding the number of crashes per intersection and years of available data. Intersection-years is the number of intersections where the strategy was in effect multiplied by the number of years of data before or after implementation. For example, if a strategy was implemented at nine intersections and data were available for 3 years since implementation, then there was a total of 27 intersection-years of after-period data available for the study.

Table 2 . Minimum required before-period intersection-years for treated intersections at the 95‑percent confidence level.

Crash Type

Expected Percent Reduction in Crashes

Rate A

Rate B

Rate C

All

10

751

65

199

20

113

10

30

30

38

3

11

40

17

1

5

Fatal and injury

10

1,036

386

384

20

156

58

58

30

53

20

20

40

23

9

9

Right-angle

10

3,373

472

1,020

20

507

71

153

30

173

24

52

40

75

10

23

Left-turn

10

3,373

1,159

1,955

20

507

174

293

30

173

59

100

40

75

26

43

Rear-end

10

2,084

108

468

20

313

16

71

30

107

6

24

40

46

2

11

Nighttime

10

636

20

96

30

33

40

14

10

2,290

Disobeyed

20

344

30

117

40

51

Note: Assumes equal number of intersection-years for treatment and comparison intersections and equal length of before and after periods.
Boldface indicates the sample size values recommended in this study.
— Indicates no data.

Table 3 . Minimum required before-period intersection-years for treated intersections at the 90‑percent confidence level.

Crash Type

Expected Percent Reduction in Crashes

Rate A

Rate B

Rate C

All

10

467

41

124

20

78

7

21

30

27

2

8

40

12

1

4

Fatal and injury

10

644

240

239

20

108

40

40

30

37

14

14

40

16

6

6

Right-angle

10

2,096

293

635

20

351

49

106

30

122

17

37

40

53

7

16

Left-turn

10

2,096

721

1,215

20

351

121

203

30

122

42

70

40

53

18

31

Rear-end

10

1,296

67

291

20

217

11

49

30

75

4

17

40

33

2

8

Nighttime

10

395

20

66

30

23

40

10

Disobeyed

10

1,425

20

238

30

82

40

36

Note: Assumes equal number of intersection-years for treatment and comparison intersections and equal length of before and after periods.
Boldface indicates the sample size values recommended in this study.
— Indicates no data.

The sample size values recommended for this study are highlighted in bold in table 2 and table 3 . These were recommended based on conservative estimates of the anticipated effects of the treatment. As noted, the sample size estimates provided were also conservative in that the state-of-the-art EB methodology proposed for the evaluations would require fewer intersections than the less robust conventional before–after study with a comparison group. Estimates could be predicted with greater confidence or a smaller reduction in crashes would be detectable if there were more intersection-years of data available in the after period. The same holds true if the actual data used for the analysis had a higher crash rate for the before period than was assumed.

Case 2 considered the data collected for both the before and after periods. RLILs were installed at 108 signalized intersections between 2004 and 2010. The before and after periods varied across intersections depending on the year of treatment installation. The total intersection-years of data available was 365 for the before period for two-lane major roadways and 599 for the after period. From this, one can estimate the minimum percent reduction detectable for the two confidence levels (i.e., 90 and 95 percent). The results of these calculations are shown in table 4 . The calculations are based on the methodology in Hauer.(5)

Table 4 . Sample analysis for crash effects.

Crash Type

Intersection-Years
in Before Period

Intersection-Years
in After Period

Minimum Percent Reduction
Detectable for Crash Rate Assumption1
P
= 0.10

Minimum Percent Reduction
Detectable for Crash Rate Assumption
1
P
= 0.05

Total

365

599

5

10

Fatal and injury

365

599

10

10

Right-angle

365

599

10

15

Left-turn

365

599

15

15

Rear-end

365

599

10

10

Nighttime

365

599

10

10

Disobeyed

365

599

15

20

1Results were to nearest 5-percent interval, and the crash rate assumption was based on actual crash rate for the before period.

For the available data, the minimum percentage changes in crash frequency that could be statistically detected at the 95- and 90-percent significance levels were estimated using the before-period crash rates (Rate C) in table 1 . The results indicate that the data should be sufficient for detecting the anticipated crash reduction effects highlighted in table 2 (i.e., 10‑percent reductions for all crash types except left-turn and disobeyed signal crashes, if such an effect were present). Using these results, the project team decided to proceed with the evaluation using the data available at the time.

 

 

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