A California Modern Roundabout Safety Effectiveness Evaluation

A Highway Safety Manual Section 9-35 Empirical Bayes California Modern Roundabout Safety Effectiveness Evaluation (M.R.S.E.E.) is an observational paired study with three (3) or more years of before and after crash and traffic volume data. The markdown compares the EB method with the naive method to demonstrate the difference between the two approaches. A few tables have a subscript “.1”, which means crashes in the “after” periods.

The package that was used to perform HSM Section 9-35 EB analysis is available on github. The data for this study is also available under “SWITRS.RData”¹.

Data, Analysis, and Results²

Meta Analysis³

Total Crash Meta Analysis Summary

Author	State	Date	No. of Sites	Total Years in the Before Period	Total Years in the After Period	Total Observed Crashes in the Before Period	Total Expected/Observed Crashes in the After Period	RTM	MCF	Safety Effect	Standard Deviation	CMF	Lower CL	Upper CL
Angshuman, G.	Georgia	2019	23	102.0	111.0	145	95	0.25	1.2	34.482759	0.0204813	0.6551724	0.6346911	0.6756538
MDOT	Maine	NA	13	23.0	32.0	44	30	0.25	1.2	31.818182	0.0364373	0.6818182	0.6453809	0.7182555
Derek, L.	Minnesota	2017	104	279.0	622.0	225	127	0.25	2.2	43.555556	0.0187143	0.5644444	0.5457302	0.5831587
Khan, G.	Wisconsin	2011	24	3.0	3.0	229	292	0.25	1.2	-27.510917	0.0638083	1.2751092	1.2113008	1.3389175
Mamlouk, M.	Arizona	2016	5	1.0	1.0	27	16	0.75	5.0	40.740741	1.0767668	0.5925926	-0.4841742	1.6693593
Isebrands, H.	Iowa	2011	18	98.2	98.2	97	98	0.10	1.2	-1.030928	0.0225203	1.0103093	0.9877889	1.0328296

Fatal and Injury Crash Meta Analysis Summary

Author	State	Date	No. of Sites	Total Years in the Before Period	Total Years in the After Period	Total Observed Crashes in the Before Period	Total Expected/Observed Crashes in the After Period	RTM	MCF	Safety Effect	Standard Deviation	CMF	Lower CL	Upper CL
Derek, L.	Minnesota	2017	104	279.0	622.0	114	52	0.25	2.2	54.385965	0.0188324	0.4561404	0.4373079	0.4749728
Khan, G.	Wisconsin	2011	24	3.0	3.0	80	80	0.25	1.2	0.000000	0.0565625	1.0000000	0.9434375	1.0565625
Mamlouk, M.	Arizona	2016	5	1.0	1.0	71	66	0.75	5.0	7.042254	0.9953403	0.9295775	-0.0657629	1.9249178
Isebrands, H.	Iowa	2011	18	98.2	98.2	60	50	0.10	1.2	16.666667	0.0245556	0.8333333	0.8087778	0.8578889

Summary Effect for Total Crashes

Total Crash Summary Effect	Standard Error	Lower Confidence Level	Upper Confidence Level
0.7298881	0.011036	0.7188521	0.7409241

Summary Effect for Fatal and Injury Crashes

FI Summary Effect	Standard Error	Lower Confidence Level	Upper Confidence Level
0.6222684	0.0144464	0.6078221	0.6367148

Forest Plot of Crash Modification Factors⁴ Data Section⁵

Geographic Locations of traditional Stop (ST) or Signalized (SG) controlled intersections converted to Modern Roundabouts (RA).⁶ Minor Traffic

Average Annual Daily Minor Approach Traffic

ID	Date	Minor_08	Minor_09	Minor_10	Minor_11	Minor_12	Minor_13	Minor_14	Minor_15	Minor_16	Minor_17	Minor_18
1	2012	1,025	1,025	1,025	2,188	2,188	2,188	2,188	6,900	6,120	1,025	NA
2	2012	4,465	4,465	4,465	4,373	4,373	4,373	4,373	4,373	4,376	4,465	NA
3	2012	11,765	11,765	11,765	1,840	1,840	1,840	1,840	1,840	11,530	11,765	NA
4	2012	11,765	11,765	11,765	11,765	11,765	2,320	1,750	1,750	794	11,765	NA
5	2012	4,403	4,403	4,403	11,765	11,765	11,765	4,889	2,188	4,315	4,403	NA
6	2013	5,492	5,492	5,492	4,891	4,891	4,891	4,891	4,891	4,891	5,492	NA
7	2013	1,035	1,035	1,035	8,200	8,200	8,200	8,200	8,300	1,014	1,035	NA
8	2014	7,376	7,376	7,376	1,035	1,035	6,999	6,999	1,609	7,228	7,376	7,376
9	2014	9,981	9,981	9,981	7,376	7,376	7,376	9,690	9,690	9,738	9,981	9,981
10	2014	17,400	17,400	17,400	13,200	13,200	13,200	13,200	17,400	17,400	17,400	17,400
11	2014	17,400	17,400	17,400	13,200	12,500	12,500	13,100	17,100	19,200	17,400	17,400
12	2014	5,994	5,994	5,994	17,400	17,400	3,440	6,113	6,113	1,593	5,994	5,994

Major Traffic

Average Annual Daily Major Approach Traffic

ID	Date	Major_08	Major_09	Major_10	Major_11	Major_12	Major_13	Major_14	Major_15	Major_16	Major_17	Major_18
1	2012	12,170	12,170	12,170	6,330	6,330	6,330	6,330	41,962	74,000	12,170	NA
2	2012	10,723	10,723	10,723	10,001	10,001	10,001	10,001	10,001	10,509	10,723	NA
3	2012	16,323	16,323	16,323	13,400	13,400	13,400	13,400	13,400	15,997	16,323	NA
4	2012	16,323	16,323	16,323	16,323	16,323	11,637	22,800	22,800	15,997	16,323	NA
5	2012	11,752	11,752	11,752	16,323	16,323	16,323	27,613	27,613	11,517	11,752	NA
6	2013	5,767	5,767	5,767	7,390	7,390	5,350	5,350	5,350	5,767	5,767	NA
7	2013	6,800	6,800	6,800	11,700	10,250	11,700	11,700	12,000	6,664	6,800	NA
8	2014	17,575	17,575	17,575	6,800	6,800	14,874	14,874	6,900	17,349	17,575	17,575
9	2014	10,500	10,500	10,500	17,575	17,575	17,575	10,500	10,500	9,781	10,500	10,500
10	2014	19,200	19,200	19,200	16,300	17,600	17,600	19,800	18,800	19,200	19,200	19,200
11	2014	19,200	19,200	19,200	16,300	17,600	17,600	19,800	18,800	24,500	19,200	19,200
12	2014	6,656	6,656	6,656	19,200	19,200	5,600	9,802	9,802	4,943	6,656	6,656

Crash Severity Levels by Site⁷

Abbreviations for Traditional and Roundabout Intersection Types

Highway Safety Manual and NCHRP 888 Base Conditions	Acronym
State Highway System	SHS
Four All Way Stop	U4STAW
Four Way Approach One to Two Way Stops	U4ST
Three Approach Stop	U3ST
Signalized	USG
Four Approach Dual Lane Roundabout	4SDRA
Four Approach Single Lane Roundabout	4SRA

California Highway Patrol Acronyms for Crash and Severity Types

Definition	Acronym
Fatal Injury	K
Serious Injury	A
Visible Injury	B
Compliant of Pain	C
Property Damage	O
Head On	A
Sideswipe	B
Rear End	C
Broadside	D
Hit Object	E
Overturned	F
Vehicle/Pedestrian	G
Other	H
Not Defined	O

Severity Levels

ID	Roundabout Type	Traditional Intersection Type	K	A	B	C	O	K.1	A.1	B.1	C.1	O.1
1	U3SRA	U3ST	0	0	1	1	2	0	0	1	3	4
2	U4SRA	U4STAW	0	0	1	0	0	0	0	0	1	15
3	U4SRA	U4STAW	0	0	1	0	1	0	0	2	0	3
4	U4SRA	U4ST	0	0	2	0	4	0	0	1	1	7
5	SHS_U4DRA	SHS_U4SG	0	0	5	11	27	1	0	1	8	26
6	SHS_U4SRA	SHS_U4ST	0	0	1	1	3	0	0	0	0	5
7	SHS_U4SRA	SHS_U4ST	0	0	0	1	4	0	0	0	1	4
8	U4SRA	U4STAW	0	0	0	1	0	0	0	0	1	5
9	U4SRA	U4SG	0	0	2	0	4	0	1	0	0	1
10	U4SRA	U4SG	0	0	0	1	10	0	1	1	1	13
11	U4DRA	U4SG	0	0	1	3	2	0	1	2	11	103
12	SHS_U4SRA	SHS_U4ST	0	0	1	3	4	0	0	0	0	6

Total Severity Crash_Types by Site⁸

Total Crash Types

ID	Roundabout Type	Traditional Intersection Type	A	B	C	D	E	F	G	H	A.1	B.1	C.1	D.1	E.1	F.1	G.1	H.1
1	U3SRA	U3ST	0	0	0	3	1	0	0	0	1	0	2	0	5	0	0	0
2	U4SRA	U4STAW	0	0	0	0	1	0	0	0	0	0	3	0	12	0	0	1
3	U4SRA	U4STAW	0	0	1	1	0	0	0	0	0	0	1	3	1	0	0	0
4	U4SRA	U4ST	1	0	4	0	1	0	0	0	0	0	1	1	6	1	0	0
5	SHS_U4DRA	SHS_U4SG	2	8	21	8	3	1	0	0	2	6	15	3	6	3	0	1
6	SHS_U4SRA	SHS_U4ST	0	2	1	2	0	0	0	0	0	1	2	0	2	0	0	0
7	SHS_U4SRA	SHS_U4ST	0	1	2	1	1	0	0	0	0	0	3	0	2	0	0	0
8	U4SRA	U4STAW	0	0	1	0	0	0	0	0	0	1	0	5	0	0	0	0
9	U4SRA	U4SG	0	2	2	1	0	0	1	0	0	0	1	0	0	0	1	0
10	U4SRA	U4SG	0	1	4	5	0	0	0	1	2	2	0	3	9	0	0	0
11	U4DRA	U4SG	1	0	2	2	0	0	0	1	1	83	11	10	12	0	0	0
12	SHS_U4SRA	SHS_U4ST	0	0	3	4	1	0	0	0	0	0	2	0	4	0	0	0

Fatal and Injury Crash Types by Base Condition⁹

Fatal and Injury Crash Types

ID	Roundabout Type	Traditional Intersection Type	A	B	C	D	E	F	G	H	A.1	B.1	C.1	D.1	E.1	F.1	G.1	H.1
1	U3SRA	U3ST	0	0	0	1	1	0	0	0	0	0	2	0	2	0	0	0
2	U4SRA	U4STAW	0	0	0	0	1	0	0	0	0	0	0	0	1	0	0	0
3	U4SRA	U4STAW	0	0	0	1	0	0	0	0	0	0	0	1	1	0	0	0
4	U4SRA	U4ST	0	0	2	0	0	0	0	0	0	0	0	1	0	1	0	0
5	SHS_U4DRA	SHS_U4SG	1	1	9	4	1	0	0	0	1	1	4	1	1	2	0	0
6	SHS_U4SRA	SHS_U4ST	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
7	SHS_U4SRA	SHS_U4ST	0	0	1	0	0	0	0	0	0	0	0	0	1	0	0	0
8	U4SRA	U4STAW	0	0	1	0	0	0	0	0	0	0	0	1	0	0	0	0
9	U4SRA	U4SG	0	0	0	1	0	0	1	0	0	0	0	0	0	0	1	0
10	U4SRA	U4SG	0	0	0	1	0	0	0	0	1	0	0	0	2	0	0	0
11	U4DRA	U4SG	1	0	1	2	0	0	0	0	1	7	2	3	1	0	0	0
12	SHS_U4SRA	SHS_U4ST	0	0	1	3	0	0	0	0	0	0	0	0	0	0	0	0

Total Crash Time Series by Site

Total Crash Severity Time Series Crash Data

ID	Intersection Type	Date	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018
1	U3ST	2014	0	0	0	1	1	2	0	5	2	0	1
2	U4STAW	2012	1	0	0	0	0	5	5	6	0	0	0
3	U4STAW	2012	0	1	0	1	0	3	1	1	0	0	0
4	U4ST	2013	0	0	2	3	1	0	4	3	2	0	0
5	SHS_U4SG	2014	0	0	0	13	10	20	0	11	17	6	2
6	SHS_U4ST	2014	0	0	0	2	2	1	0	0	3	0	2
7	SHS_U4ST	2014	0	0	0	3	2	0	0	0	2	0	3
8	U4STAW	2014	0	0	0	1	0	0	0	1	2	1	2
9	U4SG	2012	2	0	4	0	0	1	1	0	0	0	0
10	U4SG	2012	6	3	1	1	0	5	4	7	0	0	0
11	U4SG	2012	0	1	4	1	0	9	24	54	30	0	0
12	SHS_U4ST	2013	0	3	2	3	0	0	1	1	3	1	0

FI Crash Time Series by Site

Fatal and Injury Crash Severity Time Series Crash Data

ID	Intersection Type	Date	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018
1	U3ST	2014	0	0	0	1	0	1	0	2	2	0	0
2	U4STAW	2012	1	0	0	0	0	0	1	0	0	0	0
3	U4STAW	2012	0	1	0	0	0	2	0	0	0	0	0
4	U4ST	2013	0	0	0	2	0	0	2	0	0	0	0
5	SHS_U4SG	2014	0	0	0	5	6	5	0	3	6	1	0
6	SHS_U4ST	2014	0	0	0	1	0	1	0	0	0	0	0
7	SHS_U4ST	2014	0	0	0	1	0	0	0	0	1	0	0
8	U4STAW	2014	0	0	0	1	0	0	0	0	1	0	0
9	U4SG	2012	1	0	1	0	0	1	0	0	0	0	0
10	U4SG	2012	0	0	1	0	0	0	1	2	0	0	0
11	U4SG	2012	0	1	2	1	0	0	4	6	4	0	0
12	SHS_U4ST	2013	0	3	1	0	0	0	0	0	0	0	0

Simple Before and After Analysis and Results¹⁰

Crash Severity Trends¹¹

#> Analysis of Deviance Table
#> 
#> Model 1: Freq ~ Condition * Treatment
#> Model 2: Freq ~ Condition + Treatment
#>   Resid. Df Resid. Dev Df Deviance  Pr(>Chi)    
#> 1         0      0.000                          
#> 2         8     34.925 -8  -34.925 2.759e-05 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Crash Severity Trends : three conditions (no change, decrease, and increase) and the response variable is a five level categorical variable

	K	A	B	C	O
No Change	11	9	3	5	1
Decrease	0	0	6	3	2
Increase	1	3	3	4	9

Crash Type Trends¹²

#> Analysis of Deviance Table
#> 
#> Model 1: Freq ~ Condition * Treatment
#> Model 2: Freq ~ Condition + Treatment
#>   Resid. Df Resid. Dev  Df Deviance  Pr(>Chi)    
#> 1         0      0.000                           
#> 2        14     69.315 -14  -69.315 2.568e-09 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Crash Type Trends: three conditions (no change, decrease, and increase) and the response variable is a nine level categorical variable

	A	B	C	D	E	F	G	H
No Change	9	5	1	1	2	10	12	8
Decrease	1	4	6	7	0	0	0	2
Increase	2	3	5	4	10	2	0	2

Single Vs. Multi-Vehicle Crash Trends¹³

#> Analysis of Deviance Table
#> 
#> Model 1: Freq ~ Condition * Treatment
#> Model 2: Freq ~ Condition + Treatment
#>   Resid. Df Resid. Dev Df Deviance Pr(>Chi)   
#> 1         0        0.0                        
#> 2         2       12.7 -2    -12.7 0.001746 **
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Crash Type Trends: three conditions (no change, decrease, and increase) and the response variable is a two level categorical variable

	MV	SV
No Change	1	2
Decrease	7	0
Increase	4	10

Primary Collision Factor Crash Trends

#> Analysis of Deviance Table
#> 
#> Model 1: Freq ~ Condition * Treatment
#> Model 2: Freq ~ Condition + Treatment
#>   Resid. Df Resid. Dev  Df Deviance  Pr(>Chi)    
#> 1         0      0.000                           
#> 2        36     82.496 -36  -82.496 1.647e-05 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Primary Collision Factor Index Variables

Primary Collision Factor	Index Variable
BRAKES	A
Breaks	B
DRVR ALC|DRG	C
IMPROP PASS	D
IMPROP TURN	E
LANE CHANGE	F
NOT DRIVER	G
NOT STATED	H
OTHER EQPMNT	I
OTHER HAZ	J
OTHER IMPROP DRV	K
PED VIOL	L
R-O-W AUTO	M
STOP SGN|SIG	N
STRTNG|BCKNG	O
TOO CLOSE	P
UNKNOWN	Q
UNSAFE SPEED	R
WRONG SIDE	S

Primary Collision Factor Trends : three conditions (no change, decrease, and increase) and the response variable is a 18 level categorical variable

	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S
No Change	11	11	5	11	3	9	10	11	10	9	10	11	4	9	6	10	6	3	10
Decrease	0	1	2	0	1	1	0	0	1	2	1	0	3	3	1	1	4	4	0
Increase	1	0	5	1	8	2	2	1	1	1	1	1	5	0	5	1	2	5	2

Mosaic Plots¹⁴

Mosaic Plots under mutual independence.¹⁵ Mosaic Plots showing interactions.¹⁶ Severity Level Percent Changes (by site)

Severity Level Percent Changes (by site)

	K	A	B	C	O	Sum	K	A	B	C	O	Sum	K	A	B	C	O	Sum
1	0	0	1	1	2	4	0	0	1	3	4	8	0	0	0	-200	-100	-100
2	0	0	1	0	0	1	0	0	0	1	15	16	0	0	100	-100	-100	-1500
3	0	0	1	0	1	2	0	0	2	0	3	5	0	0	-100	0	-200	-150
4	0	0	2	0	4	6	0	0	1	1	7	9	0	0	50	-100	-75	-50
5	0	0	5	11	27	43	1	0	1	8	26	36	-100	0	80	27	4	16
6	0	0	1	1	3	5	0	0	0	0	5	5	0	0	100	100	-67	0
7	0	0	0	1	4	5	0	0	0	1	4	5	0	0	0	0	0	0
8	0	0	0	1	0	1	0	0	0	1	5	6	0	0	0	0	-100	-500
9	0	0	2	0	4	6	0	1	0	0	1	2	0	-100	100	0	75	67
10	0	0	0	1	10	11	0	1	1	1	13	16	0	-100	-100	0	-30	-45
11	0	0	1	3	2	6	0	1	2	11	103	117	0	-100	-100	-267	-5050	-1850
12	0	0	1	3	4	8	0	0	0	0	6	6	0	0	100	100	-50	25
Sum	0	0	15	22	61	98	1	3	8	27	192	231	-100	-100	47	-23	-215	-136

Severity Level Percent Changes (Traditional Intersection Type)

Severity Level Percent Changes (Traditional Intersection Type)

	K	A	B	C	O	Sum	K	A	B	C	O	Sum	K	A	B	C	O	Sum
SHS_U4SG	0	0	5	11	27	43	1	0	1	8	26	36	-100	0	80	27	4	16
SHS_U4ST	0	0	2	5	11	18	0	0	0	1	15	16	0	0	100	80	-36	11
U3ST	0	0	2	1	2	5	0	0	1	4	19	24	0	0	50	-300	-850	-380
U4SG	0	0	3	4	16	23	0	3	3	12	117	135	0	-100	0	-200	-631	-487
U4ST	0	0	2	0	4	6	0	0	1	1	7	9	0	0	50	-100	-75	-50
U4STAW	0	0	1	1	1	3	0	0	2	1	8	11	0	0	-100	0	-700	-267
Sum	0	0	15	22	61	98	1	3	8	27	192	231	-100	-100	47	-23	-215	-136

Severity Level Percent Changes (Roundabout Type)

Severity Level Percent Changes (Roundabout Type)

	K	A	B	C	O	Sum	K	A	B	C	O	Sum	K	A	B	C	O	Sum
SHS_U4DRA	0	0	5	11	27	43	1	0	1	8	26	36	-100	0	80	27	4	16
SHS_U4SRA	0	0	2	5	11	18	0	0	0	1	15	16	0	0	100	80	-36	11
U3SRA	0	0	2	1	2	5	0	0	1	4	19	24	0	0	50	-300	-850	-380
U4DRA	0	0	1	3	2	6	0	1	2	11	103	117	0	-100	-100	-267	-5050	-1850
U4SRA	0	0	5	2	19	26	0	2	4	3	29	38	0	-100	20	-50	-53	-46
Sum	0	0	15	22	61	98	1	3	8	27	192	231	-100	-100	47	-23	-215	-136

Severity Vs. Crash Type (Distribution of Crash Types and Severities) Crash Types by Time Period

Severity Level and Crash Types

	K.Before	A.Before	B.Before	C.Before	O.Before	Sum.Before	K.After	A.After	B.After	C.After	O.After	Sum.After
A	0	0	0	2	2	4	0	0	1	2	3	6
B	0	0	1	1	12	14	0	0	2	6	85	93
C	0	0	3	12	26	41	0	1	0	7	33	41
D	0	0	7	7	13	27	0	0	2	5	18	25
E	0	0	3	0	5	8	1	1	2	5	50	59
F	0	0	0	0	1	1	0	0	1	2	1	4
G	0	0	1	0	0	1	0	1	0	0	0	1
H	0	0	0	0	2	2	0	0	0	0	2	2
Sum	0	0	15	22	61	98	1	3	8	27	192	231

Severity Level Percent Changes

	K	A	B	C	O	Sum
A	0	0	-100	0	-50	-50
B	0	0	-100	-500	-608	-564
C	0	-100	100	42	-27	0
D	0	0	71	29	-38	7
E	-100	-100	33	-100	-900	-638
F	0	0	-100	-100	0	-300
G	0	-100	100	0	0	0
H	0	0	0	0	0	0
Sum	-100	-100	47	-23	-215	-136

Severity Level, Crash Types and Percent Changes

	K.Before	A.Before	B.Before	C.Before	O.Before	Sum.Before	K.After	A.After	B.After	C.After	O.After	Sum.After	K.Dif	A.Dif	B.Dif	C.Dif	O.Dif	Sum.Dif
A	0	0	0	2	2	4	0	0	1	2	3	6	0	0	-100	0	-50	-50
B	0	0	1	1	12	14	0	0	2	6	85	93	0	0	-100	-500	-608	-564
C	0	0	3	12	26	41	0	1	0	7	33	41	0	-100	100	42	-27	0
D	0	0	7	7	13	27	0	0	2	5	18	25	0	0	71	29	-38	7
E	0	0	3	0	5	8	1	1	2	5	50	59	-100	-100	33	-100	-900	-638
F	0	0	0	0	1	1	0	0	1	2	1	4	0	0	-100	-100	0	-300
G	0	0	1	0	0	1	0	1	0	0	0	1	0	-100	100	0	0	0
H	0	0	0	0	2	2	0	0	0	0	2	2	0	0	0	0	0	0
Sum	0	0	15	22	61	98	1	3	8	27	192	231	-100	-100	47	-23	-215	-136

HSM EMPERICAL BAYES BEFORE AND AFTER ANALYSIS, AND RESULTS¹⁷

Column Abbreviations for E.B. Tables

Definition	Abbreviations	Highway Safety Manual Equations
Calibration Factor	C	9A.1-1
Past Base Condition	Base_Past	9A.1-1
Current Base Condition	Base_Current	9A.1-12
Years in the Before Period	Y_b	9A.1-5
Average Minor AADT in the Before Period	Avg_AADTmin_b	9A.1-2
Average Major AADT in the Before Period	Avg_AADTmaj_b	9A.1-2
Predicted Crashes in the Before Period	P_b	9A.1-2
Observed Crashes in the Before Period	O_b	9A.1-5
Overdispersion Factor (Calibrated)	k	9A.1-5
Weight	w	9A.1-5
Expected Crashes in the Before Period	Nexp_b	9A.1-5
Average Minor AADT in the After Period	Avg_AADTmin_a	9A.1-3
Average Major AADT in the After Period	Avg_AADTmaj_a	9A.1-3
Predicted Crashes in the After Period	P_a	9A.1-3
Years in the After Period	Y_a	9A.1-3
Adjustment Factor	adj	9A.1-3
Expected Crashes in the After Period	Nexp_a	9A.1-4
Observed Crashes in the After Period	O_a	9A.1-3
Safety Effect (or Precent Reduction)	SE	9A.1-10
Odds Ratio	OR	9A.1-8
Variance	Var	9A.1-9
Variance of Odds Ratio	VarOR	9A.1-11
Standard Error	Std.Err	9A.1-12
Standard Error of the Safety Effect	Std.Err.SE	9A.1-12
Standard Error of the Odds Ratio	Std.Err_OR	9A.1-13
Test for Significance	Significance.test	9A.1-13
Crash Modification Factor (see Odds Ratio)	CMF	C-6
Confidence Level (65-70%)	CI	C-7, Table C-2

#>      California Highway Safety Information System AASHTO Safety Analyst SPF Total Crash Coefficients
#> Index Base Condition k    a      b    c   
#>     A U4ST           0.29  -3.12 0.27 0.16
#>     B U4STAW         1.24 -12.37 1.22 0.27
#>     C U3ST           3.18  -5.35 0.34 0.28
#>     D U4SG           0.38  -3.47 0.42 0.14
#>     E SHS U4SG       0.38  -3.47 0.42 0.14
#>     F SHS U4ST       0.29  -3.12 0.27 0.16

#>      California Highway Safety Information System AASHTO Safety Analyst SPF Fatal and Injury Crash Coefficients
#> Index Base Condition k    a      b    c    
#>     A U4ST           0.34  -4.35 0.29  0.19
#>     B U4STAW         1.95 -10.02 1.27 -0.22
#>     C U3ST           1.49  -8.45 0.49  0.39
#>     D U4SG           0.31  -5.11 0.49  0.16
#>     E SHS U4SG       0.31  -5.11 0.49  0.16
#>     F SHS U4ST       0.34  -4.35 0.29  0.19

EB Site Specific Results for Total Crashes

ID.	Base_Past	Base_Current	Y_b	Avg_AADTmin_b	Avg_AADTmaj_b	P_b	O_b	k	w	Nexp_b	Avg_AADTmin_a	Avg_AADTmaj_a	P_a	Y_a	adj	Nexp_a	O_a	Var.	VarOR	Std.Err_OR	SE	Std.Err.SE	test_statistic	Significance
2	U4STAW	U4SRA	3	2,188.00	6,330.00	5.880	1	1.24	0.012	1.060	3,684.200	28,158.40	64.707	3	11.005	11.666	16	126.804	0.968	0.984	29.001	98.393	0.295	N.S.
3	U4STAW	U4SRA	3	4,373.00	10,001.00	12.385	2	1.24	0.048	2.499	4,391.940	10,246.91	15.969	3	1.289	3.222	5	3.955	1.013	1.006	-12.366	100.637	0.123	N.S.
9	U4SG	U4SRA	3	1,840.00	13,400.00	19.298	6	0.38	0.086	7.143	5,762.940	14,503.91	27.989	3	1.450	10.360	2	13.734	0.021	0.144	82.885	14.405	5.754	95%
10	U4SG	U4SRA	3	2,320.00	11,637.00	18.788	11	0.38	0.086	11.667	3,675.800	17,911.31	28.091	3	1.495	17.444	16	23.848	0.110	0.332	14.945	33.150	0.451	N.S.
11	U4SG	U4DRA	3	4,889.00	27,613.00	29.979	6	0.38	0.076	7.825	4,136.788	21,221.59	31.946	3	1.066	8.338	117	8.209	22.296	4.722	-1,154.961	472.185	2.446	95%
4	U4ST	U4SRA	3	4,891.00	7,390.00	9.524	6	0.29	0.327	7.153	5,041.250	5,558.50	7.087	3	0.744	5.323	9	2.665	0.536	0.732	-54.533	73.211	0.745	N.S.
12	SHS_U4ST	SHS_U4SRA	3	8,200.00	11,410.00	11.629	8	0.29	0.312	9.133	4,637.325	9,291.00	7.598	3	0.653	5.967	6	2.682	0.228	0.477	6.490	47.700	0.136	N.S.
1	U3ST	U3SRA	3	6,999.00	14,874.00	8.911	4	3.18	0.054	4.264	5,897.370	14,849.75	5.527	3	0.620	2.645	8	1.552	2.597	1.611	-147.529	161.149	0.915	N.S.
5	SHS_U4SG	SHS_U4DRA	3	9,690.00	10,500.00	32.971	43	0.38	0.107	41.923	9,847.500	10,320.34	21.869	3	0.663	27.806	36	16.462	0.081	0.284	-26.768	28.378	0.943	N.S.
6	SHS_U4ST	SHS_U4SRA	3	13,200.00	16,733.33	16.701	5	0.29	0.222	7.601	17,400.000	19,100.00	12.062	3	0.722	5.490	5	3.083	0.227	0.477	17.377	47.695	0.364	N.S.
7	SHS_U4ST	SHS_U4SRA	3	12,966.67	16,733.33	16.652	5	0.29	0.219	7.550	17,775.000	20,425.00	12.310	3	0.739	5.581	5	3.223	0.221	0.470	18.814	46.981	0.400	N.S.
8	U4STAW	U4SRA	3	3,440.00	5,600.00	8.582	1	1.24	0.088	1.664	4,923.500	7,014.25	8.408	3	0.980	1.630	6	1.457	6.259	2.502	-137.730	250.177	0.551	N.S.

Naive Site Specific Results for Total Crashes

ID.	Base_Past	Base_Current	Y_b	Avg_AADTmin_b	Avg_AADTmaj_b	O_b	Avg_AADTmin_a	Avg_AADTmaj_a	O_a	Y_a	naive_ORi	naive_SEi	naive_Var.	naive_OR	naive_VarOR	naive_Std.Err_OR	naive_Std.Err.SE	naive_Statistic	naive_Significance
2	U4STAW	U4SRA	3	2,188.00	6,330.00	1	3,684.200	28,158.40	16	3	16.000	-1,500.000	1	8.000	136.000	11.662	1,166.190	0.600	N.S.
3	U4STAW	U4SRA	3	4,373.00	10,001.00	2	4,391.940	10,246.91	5	3	2.500	-150.000	2	1.667	2.917	1.708	170.783	0.390	N.S.
9	U4SG	U4SRA	3	1,840.00	13,400.00	6	5,762.940	14,503.91	2	3	0.333	66.667	6	0.286	0.063	0.252	25.198	2.835	95%
10	U4SG	U4SRA	3	2,320.00	11,637.00	11	3,675.800	17,911.31	16	3	1.455	-45.455	11	1.333	0.298	0.545	54.545	0.611	N.S.
11	U4SG	U4DRA	3	4,889.00	27,613.00	6	4,136.788	21,221.59	117	3	19.500	-1,850.000	6	16.714	57.107	7.557	755.693	2.079	95%
4	U4ST	U4SRA	3	4,891.00	7,390.00	6	5,041.250	5,558.50	9	3	1.500	-50.000	6	1.286	0.536	0.732	73.193	0.390	N.S.
12	SHS_U4ST	SHS_U4SRA	3	8,200.00	11,410.00	8	4,637.325	9,291.00	6	3	0.750	25.000	8	0.667	0.146	0.382	38.188	0.873	N.S.
1	U3ST	U3SRA	3	6,999.00	14,874.00	4	5,897.370	14,849.75	8	3	2.000	-100.000	4	1.600	1.200	1.095	109.545	0.548	N.S.
5	SHS_U4SG	SHS_U4DRA	3	9,690.00	10,500.00	43	9,847.500	10,320.34	36	3	0.837	16.279	43	0.818	0.035	0.187	18.697	0.972	N.S.
6	SHS_U4ST	SHS_U4SRA	3	13,200.00	16,733.33	5	17,400.000	19,100.00	5	3	1.000	0.000	5	0.833	0.333	0.577	57.735	0.289	N.S.
7	SHS_U4ST	SHS_U4SRA	3	12,966.67	16,733.33	5	17,775.000	20,425.00	5	3	1.000	0.000	5	0.833	0.333	0.577	57.735	0.289	N.S.
8	U4STAW	U4SRA	3	3,440.00	5,600.00	1	4,923.500	7,014.25	6	3	6.000	-500.000	1	3.000	21.000	4.583	458.258	0.436	N.S.

EB Fatal and Injury Site Specific Results

ID.	Base_Past	Base_Current	Y_b	Avg_AADTmin_b	Avg_AADTmaj_b	P_b	O_b	k	w	Nexp_b	Avg_AADTmin_a	Avg_AADTmaj_a	P_a	Y_a	adj	Nexp_a	O_a	Var.	VarOR	Std.Err_OR	SE	Std.Err.SE	test_statistic	Significance
2	U4STAW	U4SRA	3	2,188.00	6,330.00	2.205	1	1.95	0.029	1.035	3,684.200	28,158.40	17.308	3	7.850	8.122	1	61.918	0.015	0.123	93.649	12.313	7.606	95%
3	U4STAW	U4SRA	3	4,373.00	10,001.00	3.385	1	1.95	0.105	1.251	4,391.940	10,246.91	4.360	3	1.288	1.611	2	1.857	1.091	1.045	27.638	104.474	0.265	N.S.
9	U4SG	U4SRA	3	1,840.00	13,400.00	8.462	2	0.31	0.204	3.319	5,762.940	14,503.91	12.577	3	1.486	4.933	1	5.835	0.041	0.203	83.649	20.271	4.126	95%
10	U4SG	U4SRA	3	2,320.00	11,637.00	8.195	1	0.31	0.203	2.462	3,675.800	17,911.31	12.647	3	1.543	3.800	3	4.672	0.309	0.556	40.352	55.621	0.725	N.S.
11	U4SG	U4DRA	3	4,889.00	27,613.00	14.101	4	0.31	0.180	5.819	4,136.788	21,221.59	14.682	3	1.041	6.059	14	5.173	0.993	0.997	-102.514	99.670	1.029	N.S.
4	U4ST	U4SRA	3	4,891.00	7,390.00	4.292	2	0.34	0.481	3.102	5,041.250	5,558.50	3.179	3	0.741	2.297	2	0.884	0.433	0.658	25.423	65.833	0.386	N.S.
12	SHS_U4ST	SHS_U4SRA	3	8,200.00	11,410.00	5.369	4	0.34	0.463	4.633	4,637.325	9,291.00	3.416	3	0.636	2.948	0	1.008	NaN	NaN	100.000	NaN	NaN	NA
1	U3ST	U3SRA	3	6,999.00	14,874.00	4.492	2	1.49	0.195	2.487	5,897.370	14,849.75	2.766	3	0.616	1.531	4	0.759	2.958	1.720	-97.393	171.998	0.566	N.S.
5	SHS_U4SG	SHS_U4DRA	3	9,690.00	10,500.00	14.693	16	0.31	0.249	15.675	9,847.500	10,320.34	9.737	3	0.663	10.387	10	5.171	0.131	0.362	8.132	36.170	0.225	N.S.
6	SHS_U4ST	SHS_U4SRA	3	13,200.00	16,733.33	7.882	2	0.34	0.338	3.989	17,400.000	19,100.00	5.755	3	0.730	2.913	0	1.408	NaN	NaN	100.000	NaN	NaN	NA
7	SHS_U4ST	SHS_U4SRA	3	12,966.67	16,733.33	7.855	1	0.34	0.333	3.284	17,775.000	20,425.00	5.885	3	0.749	2.461	1	1.229	0.165	0.406	66.220	40.638	1.629	N.S.
8	U4STAW	U4SRA	3	3,440.00	5,600.00	2.563	1	1.95	0.193	1.302	4,923.500	7,014.25	2.139	3	0.835	1.087	1	0.732	0.846	0.920	43.200	91.987	0.470	N.S.

Naive Fatal and Injury Site Specific Results

ID.	Base_Past	Base_Current	Y_b	Avg_AADTmin_b	Avg_AADTmaj_b	O_b	Avg_AADTmin_a	Avg_AADTmaj_a	O_a	Y_a	naive_ORi	naive_SEi	naive_Var.	naive_OR	naive_VarOR	naive_Std.Err_OR	naive_Std.Err.SE	naive_Statistic	naive_Significance
2	U4STAW	U4SRA	3	2,188.00	6,330.00	1	3,684.200	28,158.40	1	3	1.000	0.0	1	0.500	1.000	1.000	100.000	0.500	N.S.
3	U4STAW	U4SRA	3	4,373.00	10,001.00	1	4,391.940	10,246.91	2	3	2.000	-100.0	1	1.000	3.000	1.732	173.205	0.000	N.S.
9	U4SG	U4SRA	3	1,840.00	13,400.00	2	5,762.940	14,503.91	1	3	0.500	50.0	2	0.333	0.250	0.500	50.000	1.333	N.S.
10	U4SG	U4SRA	3	2,320.00	11,637.00	1	3,675.800	17,911.31	3	3	3.000	-200.0	1	1.500	6.000	2.449	244.949	0.204	N.S.
11	U4SG	U4DRA	3	4,889.00	27,613.00	4	4,136.788	21,221.59	14	3	3.500	-250.0	4	2.800	3.150	1.775	177.482	1.014	N.S.
4	U4ST	U4SRA	3	4,891.00	7,390.00	2	5,041.250	5,558.50	2	3	1.000	0.0	2	0.667	0.667	0.816	81.650	0.408	N.S.
12	SHS_U4ST	SHS_U4SRA	3	8,200.00	11,410.00	4	4,637.325	9,291.00	0	3	0.000	100.0	4	0.000	NaN	NaN	NaN	NaN	NA
1	U3ST	U3SRA	3	6,999.00	14,874.00	2	5,897.370	14,849.75	4	3	2.000	-100.0	2	1.333	2.000	1.414	141.421	0.236	N.S.
5	SHS_U4SG	SHS_U4DRA	3	9,690.00	10,500.00	16	9,847.500	10,320.34	10	3	0.625	37.5	16	0.588	0.060	0.244	24.442	1.685	N.S.
6	SHS_U4ST	SHS_U4SRA	3	13,200.00	16,733.33	2	17,400.000	19,100.00	0	3	0.000	100.0	2	0.000	NaN	NaN	NaN	NaN	NA
7	SHS_U4ST	SHS_U4SRA	3	12,966.67	16,733.33	1	17,775.000	20,425.00	1	3	1.000	0.0	1	0.500	1.000	1.000	100.000	0.500	N.S.
8	U4STAW	U4SRA	3	3,440.00	5,600.00	1	4,923.500	7,014.25	1	3	1.000	0.0	1	0.500	1.000	1.000	100.000	0.500	N.S.

Emperical Bayes Total Crash Grouped Results for Traditional Intersections

Base_Past	No.Sites	O_b.grp.	O_a.grp.	Nexp_b.grp.	Nexp_a.grp.	Avg_AADTmin_b	Avg_AADTmaj_b	Avg_AADTmin_a	Avg_AADTmaj_a	Y_b	Y_a	OR.grp.i.	VAR.grp.	OR.grp.	VarOR.grp.	SE.grp.	Std.Err.OR.grp.	Std.Err.SE.grp.	test_statistic.grp.	Significance.test.grp.
SHS_U4SG	1	43	36	41.923	27.806	9,690.000	10,500.000	9,847.500	10,320.34	3	3	1.295	16.456	1.268	0.081	-26.770	0.285	28.547	0.938	N.S.
SHS_U4ST	3	18	16	24.284	17.038	11,455.556	14,958.889	13,270.775	16,272.00	9	9	0.939	8.982	0.859	0.082	14.059	0.286	28.563	0.492	N.S.
U3ST	1	4	8	4.264	2.645	6,999.000	14,874.000	5,897.370	14,849.75	3	3	3.025	1.551	2.476	2.803	-147.584	1.674	167.428	0.881	N.S.
U4SG	3	23	135	26.635	36.142	3,016.333	17,550.000	4,525.176	17,878.94	9	9	3.735	45.776	3.411	0.576	-241.077	0.759	75.878	3.177	95%
U4ST	1	6	9	7.153	5.323	4,891.000	7,390.000	5,041.250	5,558.50	3	3	1.691	2.665	1.545	0.563	-54.544	0.751	75.058	0.727	N.S.
U4STAW	3	4	27	5.223	16.518	3,333.667	7,310.333	4,333.213	15,139.85	9	9	1.635	132.246	0.866	0.971	13.366	0.986	98.550	0.136	N.S.

Naive Total Crash Grouped Results for Traditional Intersections

Base_Past	No.Sites	O_b.grp.	O_a.grp.	Avg_AADTmin_b	Avg_AADTmaj_b	Avg_AADTmin_a	Avg_AADTmaj_a	Y_b	Y_a	naive_ORi.grp.	naive_VAR.grp	naive_OR.grp	naive_SE.grp	naive_VarOR.grp	naive_Std.Err.OR.grp	naive_Std.Err.SE.grp	naive_test_statistic.grp	naive_Significance.test.grp
SHS_U4SG	1	43	36	9,690.000	10,500.000	9,847.500	10,320.34	3	3	0.837	16.879	0.830	17.036	0.026	0.161	16.066	106.042	95%
SHS_U4ST	3	18	16	11,455.556	14,958.889	13,270.775	16,272.00	9	9	0.889	6.507	0.841	15.911	0.065	0.255	25.483	62.437	95%
U3ST	1	4	8	6,999.000	14,874.000	5,897.370	14,849.75	3	3	2.000	1.455	1.833	-83.333	0.833	0.913	91.287	91.287	95%
U4SG	3	23	135	3,016.333	17,550.000	4,525.176	17,878.94	9	9	5.870	40.301	4.856	-385.564	2.694	1.641	164.136	234.906	95%
U4ST	1	6	9	4,891.000	7,390.000	5,041.250	5,558.50	3	3	1.500	2.235	1.412	-41.231	0.382	0.618	61.768	66.751	95%
U4STAW	3	4	27	3,333.667	7,310.333	4,333.213	15,139.85	9	9	6.750	123.696	0.312	68.773	42.032	6.483	648.317	10.608	95%

Emperical Bayes Total Crash Grouped Results for Roundabouts

Base_Current	No.Sites	O_b.grp.	O_a.grp.	Nexp_b.grp.	Nexp_a.grp.	Avg_AADTmin_b	Avg_AADTmaj_b	Avg_AADTmin_a	Avg_AADTmaj_a	Y_b	Y_a	OR.grp.i.	VAR.grp.	OR.grp.	VarOR.grp.	SE.grp.	Std.Err.OR.grp.	Std.Err.SE.grp.	test_statistic.grp.	Significance.test.grp.
SHS_U4DRA	1	43	36	41.923	27.806	9,690.000	10,500.000	9,847.500	10,320.34	3	3	1.295	16.456	1.268	0.081	-26.770	0.285	28.547	0.938	N.S.
SHS_U4SRA	3	18	16	24.284	17.038	11,455.556	14,958.889	13,270.775	16,272.00	9	9	0.939	8.982	0.859	0.082	14.059	0.286	28.563	0.492	N.S.
U3SRA	1	4	8	4.264	2.645	6,999.000	14,874.000	5,897.370	14,849.75	3	3	3.025	1.551	2.476	2.803	-147.584	1.674	167.428	0.881	N.S.
U4DRA	1	6	117	7.825	8.338	4,889.000	27,613.000	4,136.788	21,221.59	3	3	14.032	8.216	12.549	22.493	-1,154.908	4.743	474.272	2.435	95%
U4SRA	6	27	54	31.186	49.645	3,175.333	9,059.667	4,579.938	13,898.88	18	18	1.088	172.471	0.841	0.099	15.861	0.315	31.510	0.503	N.S.

Naive Total Crash Grouped Results for Roundabouts

Base_Current	No.Sites	O_b.grp.	O_a.grp.	Avg_AADTmin_b	Avg_AADTmaj_b	Avg_AADTmin_a	Avg_AADTmaj_a	Y_b	Y_a	naive_ORi.grp.	naive_VAR.grp	naive_OR.grp	naive_SE.grp	naive_VarOR.grp	naive_Std.Err.OR.grp	naive_Std.Err.SE.grp	naive_test_statistic.grp	naive_Significance.test.grp
SHS_U4DRA	1	43	36	9,690.000	10,500.000	9,847.500	10,320.34	3	3	0.837	16.879	0.830	17.036	0.026	0.161	16.066	106.042	95%
SHS_U4SRA	3	18	16	11,455.556	14,958.889	13,270.775	16,272.00	9	9	0.889	6.507	0.841	15.911	0.065	0.255	25.483	62.437	95%
U3SRA	1	4	8	6,999.000	14,874.000	5,897.370	14,849.75	3	3	2.000	1.455	1.833	-83.333	0.833	0.913	91.287	91.287	95%
U4DRA	1	6	117	4,889.000	27,613.000	4,136.788	21,221.59	3	3	19.500	6.300	16.596	-1,559.576	59.883	7.738	773.839	201.538	95%
U4SRA	6	27	54	3,175.333	9,059.667	4,579.938	13,898.88	18	18	2.000	159.932	1.109	-10.884	0.794	0.891	89.092	12.217	95%

Emperical Bayes Fatal and Injury Grouped Results

Base_Past	No.Sites	O_b.grp.	O_a.grp.	Nexp_b.grp.	Nexp_a.grp.	Avg_AADTmin_b	Avg_AADTmaj_b	Avg_AADTmin_a	Avg_AADTmaj_a	Y_b	Y_a	OR.grp.i.	VAR.grp.	OR.grp.	VarOR.grp.	SE.grp.	Std.Err.OR.grp.	Std.Err.SE.grp.	test_statistic.grp.	Significance.test.grp.
SHS_U4SG	1	16	10	15.675	10.387	9,690.000	10,500.000	9,847.500	10,320.34	3	3	0.963	5.175	0.919	0.135	8.132	0.368	36.757	0.221	N.S.
SHS_U4ST	3	7	1	11.906	8.322	11,455.556	14,958.889	13,270.775	16,272.00	9	9	0.120	3.642	0.104	0.015	89.612	0.123	12.313	7.278	95%
U3ST	1	2	4	2.487	1.531	6,999.000	14,874.000	5,897.370	14,849.75	3	3	2.613	0.760	1.973	3.377	-97.316	1.838	183.775	0.530	N.S.
U4SG	3	7	18	11.600	14.792	3,016.333	17,550.000	4,525.176	17,878.94	9	9	1.217	15.676	1.008	0.181	-0.762	0.426	42.575	0.018	N.S.
U4ST	1	2	2	3.102	2.297	4,891.000	7,390.000	5,041.250	5,558.50	3	3	0.871	0.884	0.746	0.488	25.424	0.698	69.846	0.364	N.S.
U4STAW	3	3	4	3.588	10.820	3,333.667	7,310.333	4,333.213	15,139.85	9	9	0.370	64.520	0.192	0.083	80.797	0.288	28.762	2.809	95%

Naive Fatal and Injury Grouped Results

Base_Past	No.Sites	O_b.grp.	O_a.grp.	Avg_AADTmin_b	Avg_AADTmaj_b	Avg_AADTmin_a	Avg_AADTmaj_a	Y_b	Y_a	naive_ORi.grp.	naive_VAR.grp	naive_OR.grp	naive_SE.grp	naive_VarOR.grp	naive_Std.Err.OR.grp	naive_Std.Err.SE.grp	naive_test_statistic.grp	naive_Significance.test.grp
SHS_U4SG	1	16	10	9,690.000	10,500.000	9,847.500	10,320.34	3	3	0.625	5.282	0.612	38.763	0.047	0.217	21.670	178.880	95%
SHS_U4ST	3	7	1	11,455.556	14,958.889	13,270.775	16,272.00	9	9	0.143	1.949	0.131	86.927	0.021	0.146	14.556	597.178	95%
U3ST	1	2	4	6,999.000	14,874.000	5,897.370	14,849.75	3	3	2.000	0.611	1.735	-73.501	1.530	1.237	123.692	59.422	95%
U4SG	3	7	18	3,016.333	17,550.000	4,525.176	17,878.94	9	9	2.571	8.967	1.802	-80.195	1.390	1.179	117.909	68.015	95%
U4ST	1	2	2	4,891.000	7,390.000	5,041.250	5,558.50	3	3	1.000	0.570	0.875	12.472	0.625	0.790	79.039	15.779	95%
U4STAW	3	3	4	3,333.667	7,310.333	4,333.213	15,139.85	9	9	1.333	61.883	0.062	93.835	1.996	1.413	141.297	66.410	95%

Emperical Bayes Fatal and Injury Crash Grouped Results for Roundabouts

Base_Current	No.Sites	O_b.grp.	O_a.grp.	Nexp_b.grp.	Nexp_a.grp.	Avg_AADTmin_b	Avg_AADTmaj_b	Avg_AADTmin_a	Avg_AADTmaj_a	Y_b	Y_a	OR.grp.i.	VAR.grp.	OR.grp.	VarOR.grp.	SE.grp.	Std.Err.OR.grp.	Std.Err.SE.grp.	test_statistic.grp.	Significance.test.grp.
SHS_U4DRA	1	16	10	15.675	10.387	9,690.000	10,500.000	9,847.500	10,320.34	3	3	0.963	5.175	0.919	0.135	8.132	0.368	36.757	0.221	N.S.
SHS_U4SRA	3	7	1	11.906	8.322	11,455.556	14,958.889	13,270.775	16,272.00	9	9	0.120	3.642	0.104	0.015	89.612	0.123	12.313	7.278	95%
U3SRA	1	2	4	2.487	1.531	6,999.000	14,874.000	5,897.370	14,849.75	3	3	2.613	0.760	1.973	3.377	-97.316	1.838	183.775	0.530	N.S.
U4DRA	1	4	14	5.819	6.059	4,889.000	27,613.000	4,136.788	21,221.59	3	3	2.311	5.171	2.025	1.041	-102.534	1.020	102.005	1.005	N.S.
U4SRA	6	8	10	12.471	21.850	3,175.333	9,059.667	4,579.938	13,898.88	18	18	0.458	75.909	0.275	0.050	72.547	0.223	22.289	3.255	95%

Naive Fatal and Injury Crash Grouped Results for Roundabouts

Base_Current	No.Sites	O_b.grp.	O_a.grp.	Avg_AADTmin_b	Avg_AADTmaj_b	Avg_AADTmin_a	Avg_AADTmaj_a	Y_b	Y_a	naive_ORi.grp.	naive_VAR.grp	naive_OR.grp	naive_SE.grp	naive_VarOR.grp	naive_Std.Err.OR.grp	naive_Std.Err.SE.grp	naive_test_statistic.grp	naive_Significance.test.grp
SHS_U4DRA	1	16	10	9,690.000	10,500.000	9,847.500	10,320.34	3	3	0.625	5.282	0.612	38.763	0.047	0.217	21.670	178.880	95%
SHS_U4SRA	3	7	1	11,455.556	14,958.889	13,270.775	16,272.00	9	9	0.143	1.949	0.131	86.927	0.021	0.146	14.556	597.178	95%
U3SRA	1	2	4	6,999.000	14,874.000	5,897.370	14,849.75	3	3	2.000	0.611	1.735	-73.501	1.530	1.237	123.692	59.422	95%
U4DRA	1	4	14	4,889.000	27,613.000	4,136.788	21,221.59	3	3	3.500	3.554	2.864	-186.379	3.102	1.761	176.117	105.827	95%
U4SRA	6	8	10	3,175.333	9,059.667	4,579.938	13,898.88	18	18	1.250	67.866	0.188	81.218	0.960	0.980	98.000	82.876	95%

Plots of Expected and Observed Frequencies by Traditional Intersection Groups Pooled Results¹⁸

Emperical Bayes Total Crash Pooled Results

group_type	No.Sites	O_b.grp.	O_a.grp.	Nexp_b.grp.	Nexp_a.grp.	Avg_AADTmin_b	Avg_AADTmaj_b	Avg_AADTmin_a	Avg_AADTmaj_a	Y_b	Y_a	OR.grp.i.	VAR.grp.	OR.grp.	VarOR.grp.	SE.grp.	Std.Err.OR.grp.	Std.Err.SE.grp.	test_statistic.grp.	Significance.test.grp.
control	12	98	231	109.482	105.472	6,249.722	12,685.14	7,264.468	14,883.41	36	36	2.19	207.676	1.929	0.109	-92.925	0.33	32.966	2.819	95%

Emperical Bayes Fatal and Injury Crash Pooled Results

group_type	No.Sites	O_b.grp.	O_a.grp.	Nexp_b.grp.	Nexp_a.grp.	Avg_AADTmin_b	Avg_AADTmaj_b	Avg_AADTmin_a	Avg_AADTmaj_a	Y_b	Y_a	OR.grp.i.	VAR.grp.	OR.grp.	VarOR.grp.	SE.grp.	Std.Err.OR.grp.	Std.Err.SE.grp.	test_statistic.grp.	Significance.test.grp.
control	12	37	39	48.358	48.149	6,249.722	12,685.14	7,264.468	14,883.41	36	36	0.81	90.657	0.614	0.042	38.602	0.204	20.375	1.895	90%

Meta Analysis Revisited

Total Crash Meta Analysis Summary

Author	State	Date	Safety Effect	Standard Error	CMF	Lower CL	Upper CL
TBA	CA	NA	-92.925298	0.3296567	1.9292530	1.5995963	2.2589096
Angshuman, G.	Georgia	2019	34.482759	0.0204813	0.6551724	0.6346911	0.6756538
MDOT	Maine	NA	31.818182	0.0364373	0.6818182	0.6453809	0.7182555
Derek, L.	Minnesota	2017	43.555556	0.0187143	0.5644444	0.5457302	0.5831587
Khan, G.	Wisconsin	2011	-27.510917	0.0638083	1.2751092	1.2113008	1.3389175
Mamlouk, M.	Arizona	2016	40.740741	1.0767668	0.5925926	-0.4841742	1.6693593
Isebrands, H.	Iowa	2011	-1.030928	0.0225203	1.0103093	0.9877889	1.0328296

Fatal and Injury Crash Meta Analysis Summary

Author	State	Date	Safety Effect	Standard Error	CMF	Lower CL	Upper CL
TBA	CA	NA	38.602343	0.2037462	0.6139766	0.4102304	0.8177228
Derek, L.	Minnesota	2017	54.385965	0.0188324	0.4561404	0.4373079	0.4749728
Khan, G.	Wisconsin	2011	0.000000	0.0565625	1.0000000	0.9434375	1.0565625
Mamlouk, M.	Arizona	2016	7.042254	0.9953403	0.9295775	-0.0657629	1.9249178
Isebrands, H.	Iowa	2011	16.666667	0.0245556	0.8333333	0.8087778	0.8578889

Summary Effect for Fatal and Injury Crashes Revisted

FI Summary Effect	Standard Error	Lower Confidence Level	Upper Confidence Level
0.622227	0.0144102	0.6078168	0.6366372

Summary Effect for Total Crashes Revisted

Total Crash Summary Effect	Standard Error	Lower Confidence Level	Upper Confidence Level
0.7312308	0.0110298	0.7202009	0.7422606

Forest Plots Revisited

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1. https://github.com/cn838/HSM.git↩︎

2. Performed and created using R Core Team (2020), https://www.R-project.org/↩︎

3. Meta Analysis performed by using the ‘Simple Before–After and Non-regression Cross-Section Studies performed’ (Bahar, G. 2010, “Transportation Research Circular E-C142” Literature Review Procedure pp.4-12). ↩︎

4. The dimensions of each point represents the sample size.↩︎

5. All Before and After tables read from Left (before) to Right (after). The “Date” column represents the estimated year for completed construction. Crashes that occurred during the Learning Curve and Construction periods were collected but were not reported or included in the analysis. Traffic Volumes, Modern Roundabout Locations, Property Damage Only (PDO) and Fatal and Injury (FI) Crash data was obtained from the Highway Performance Management System (HPMS), Kittelson Associates Modern Roundabout, California Highway Patrol (CHP) Statewide Integrated Traffic Records System (SWITRS), and University of California Berkeley’s Transportation Information Management (TIMS) databases, respectively. Property Damage Only (“PDO” or “O”) crashes were limited to the beginning of year 2010 and California Vehicle Code 2002 does not require these crashes to be reported. Fatal and Injury Crash data collected for the year 2018 may be incomplete, because the database was not achieved at the time of inquiry. See the Minimum Uniform Crash Criteria (M.M.U.C.C.) (CHP, 2017), for more details about crash type and severity definitions.↩︎

6. All locations are paired, which are bold colored diamonds. Each location has some amount of random variation, which was added to each location. Therefore, some points may not plot accurately at the provided scale. The base map were provided by Google® Earth™ .↩︎

7. Note: A subscript “1” indicates collisions occurring in the after period.↩︎

8. Note: A subscript “1” indicates collisions occurring in the after period.↩︎

9. Note: A subscript “1” indicates collisions occurring in the after period.↩︎

10. This method is also known as the Naive or observed differences method. Pedestrian and Cyclist crashes were collected as recommended by Ferguson, due to their paucity (Ferguson, et. al., 2019 p.54). Percent reductions were calculated using the HSM equation 9A.1-10 (Safety Effect). According to Eq. 9A.1-10 a negative reduction represents a increase and positive reduction (or percent change) represents an decrease in crashes. Eq. 9A.1-10 renders meaningless results when before or before and after periods have zero crashes, therefore, in cases where DIV/0! and b=0; zero change and the inverse (i.e. 100%(1-(a/b)^(-1)=100%(1-(a/0)^(-1)=-100%) were reported, respectively. These substitutions are debatable, which may effect followup analyzes or render the results useless (from a purely mathematical perspective).↩︎

11. Spine plots provide the interaction between crash severity and treatment conditions (or roundabouts). P-values greater than 0.05 are not significant and show no casual association. Meaning the roundabouts may have increased or decrease crashes or effects depending on the changes observed. The change in safety method was adopted from G., Khan 2011,p.19, ( or PDF page 27) and the Chi Square Tests and Spine plot methods were adopted from M. J. Crawley, ‘The R Book’ 2014. pp.623-624).↩︎

12. Spine plots show the Chi square test measures, which provide the interaction between crash severity and conditions. P-values greater than 0.05 are not significant and show no casual association.↩︎

13. Hit Object and Overturned, and Head On, Sideswipe, Rear End, Broadside, Vehicle/Pedestrian, are Single and Multi-Vehicle crash types respectively (California Highway Patrol, 2020).↩︎

14. There are two series of Mosaic Plots (three each), which used Before (B) and After (A) periods as well as other categorical variables as ordered factors. Property Damage and Fatal and Injury Crashes were treated as the response and the largest positive residuals appear in blocks that are colored blue. The first series shows the associations among all variables under the the assumption of mutual independence. The second series plots shows the combinations of the predictor factors that are colored blue are more likely to result in PDO or Fatal and Injury Crashes, which are a light blue color (this method was adopted from Bertin 1983 pp. 30-31 in ‘Discrete Data Analysis with R’ by Friendly, 2015 p.218).↩︎

15. See Friendly, 2015 pp.218↩︎

16. Mosaic plots of time, AADT and Primary Collision Factor show the interactions most likely to result in a FI or PDO crash(Friendly, 2015 pp.218). Variables on the right vertical axis labeled “A” and “B”, refer to “After” and “Before” periods for Roundabouts and Traditional Intersections, respectively.↩︎

17. This analysis does not report model fits. It was strictly an implementation of the 2010 Highway Safety Manual (HSM) Empirical Bayes (EB) section 9-35 method. The Safety Analyst (SA) Safety Performance Functions (SPF) were calibrated with a value of 1.00. The HSM overdisperion factors (k) were also calibrated. Those values are reported in the table as ‘k’. All calibrations were performed using FHWA Calibrator with Highway Safety Information System (HSIS) information. Eq. 9A.1-10 and Eq. 9A.1-11 render’s meaningless results when before, and before and after periods have zero crashes (ie !DIV/0=“No-Change” or “0” & -Inf=-100%), respectively.Naive Statistics were computed using the HSM procedure by substituting the Observed crashes in the after period for the Expected crashes in the after Period. Significant confidence levels are reported as 90% or 95% level of confidence levels. Levels that are Not Significant (N.S.) are reported. See HSM 2010 section 9-37 and 9-38 for more details. The validity of “Naive” or “Simple” computations has not been verified. Please refer to FHWA-HRT-10-063 for information about the HSM Safety Analyst and FHWA-HRT-17-084, FHWA-RD-99-128 for more information about intersection safety performance in CA.↩︎

18. Pooled across the sample. Each group has a different over dispersion factors or weights.↩︎