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Motor Vehicle Accidents

Hunjung Kim Melissa ManfredoniaHeidi Braunger Yaming LiuJo-Yu Mao Grace Lee

December 1, 2005

Econ 240A Project

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I. Rollover crashes Actual data vs. Condensed

ANOVA OLS Regression

Results

II. Alcohol-related crashes Actual vs. Condensed

Contingency Table ANOVA

Results

III. Conclusion

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I. Rollover Crashes

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Survival Rate in Rollover Crashes

Depends on…

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Number of Quarter Turns

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Vehicle Types

SUV

Pick-Up Truck

Van

Passenger car

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Complete Rollover Data

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Survivors vs. # of Rollovers & Vehicle Type

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ANOVA: two-factor w/o replication

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ANOVA: cont…

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Condensed Rollover Data

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Survivors vs.# of Rollovers &Vehicle Type(condensed data)

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ANOVA: two-factor w/o replication

SUMMARY Count Sum Average Variance

1.5 4 94077 23519.25 324966370.9

3.5 4 41504 10376 58549284.67

5.5 4 15859 3964.75 14588907.58

7.5 4 9090 2272.5 7318537.667

9.5 4 1893 473.25 287970.9167

11.5 4 454 113.5 18933.66667

13.5 4 155 38.75 2470.916667

15.5 4 42 10.5 387.6666667

>16 4 130 32.5 2524.333333

         

Passenger Car 9 76790 8532.222222 192860423.4

Sports Utility Vehicle 9 55348 6149.777778 132507267.7

Van 9 4005 445 519214.5

Pick-Up Truck 9 27061 3006.777778 32394135.19

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Source of Variation SS df MS F P-value F crit

Rows 1987881778 8 248485222.2 6.789472279 0.00011544 2.355081495

Columns 338839616.2 3 112946538.7 3.086088528 0.046303702 3.008786572

Error 878366548.8 24 36598606.2      

             

Total 3205087943 35        

ANOVA: cont…

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ANOVA Analysis

Ho: Two variables independent (ie: µp = µs = µv = µt) Ha: Two variables dependent (ie: at least two means differ)

α = 0.05 Differences between the number of quarter turns taken (ROW)

F-statistic = 5.785 > F-critical = 1.859P-value of 1.041e-6

Therefore, Ho is rejected and we conclude that the number of survivors is dependent on the number of quarter turns.

Differences between the vehicle types (Columns)F-statistic = 3.660 > F-critical = 2.798P-value = 0.0187

Therefore, Ho is rejected and we conclude that the number of survivors is dependent on the type of vehicle.

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OLS Regression

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Survivors vs. # of Turns & Vehicle Type

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Cont…

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Cont…

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OLS with Dummy variable

SURVIVOR DUMMY1_PASS DUMMY2_SUV DUMMY3_VAN DUMMY4_TRUCK CON_QUART_TURN

41833.00 1.000000 0.000000 0.000000 0.000000 1.500000

17932.00 1.000000 0.000000 0.000000 0.000000 3.500000

9405.000 1.000000 0.000000 0.000000 0.000000 5.500000

6032.000 1.000000 0.000000 0.000000 0.000000 7.500000

1257.000 1.000000 0.000000 0.000000 0.000000 9.500000

311.0000 1.000000 0.000000 0.000000 0.000000 11.50000

20.00000 1.000000 0.000000 0.000000 0.000000 13.50000

0.000000 1.000000 0.000000 0.000000 0.000000 15.50000

0.000000 1.000000 0.000000 0.000000 0.000000 17.50000

33737.00 0.000000 1.000000 0.000000 0.000000 1.500000

15701.00 0.000000 1.000000 0.000000 0.000000 3.500000

3126.000 0.000000 1.000000 0.000000 0.000000 5.500000

2433.000 0.000000 1.000000 0.000000 0.000000 7.500000

126.0000 0.000000 1.000000 0.000000 0.000000 9.500000

103.0000 0.000000 1.000000 0.000000 0.000000 11.50000

13.00000 0.000000 1.000000 0.000000 0.000000 13.50000

2.000000 0.000000 1.000000 0.000000 0.000000 15.50000

107.0000 0.000000 1.000000 0.000000 0.000000 17.50000

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OLS with Dummy variable (cont.)

SURVIVOR DUMMY1_PASS DUMMY2_SUV DUMMY3_VAN DUMMY4_TRUCK CON_QUART_TURN

3587.000 0.000000 0.000000 1.000000 0.000000 1.500000

2033.000 0.000000 0.000000 1.000000 0.000000 3.500000

464.0000 0.000000 0.000000 1.000000 0.000000 5.500000

75.00000 0.000000 0.000000 1.000000 0.000000 7.500000

125.0000 0.000000 0.000000 1.000000 0.000000 9.500000

30.00000 0.000000 0.000000 1.000000 0.000000 11.50000

9.000000 0.000000 0.000000 1.000000 0.000000 13.50000

0.000000 0.000000 0.000000 1.000000 0.000000 15.50000

18.00000 0.000000 0.000000 1.000000 0.000000 17.50000

17256.00 0.000000 0.000000 0.000000 1.000000 1.500000

5838.000 0.000000 0.000000 0.000000 1.000000 3.500000

2864.000 0.000000 0.000000 0.000000 1.000000 5.500000

550.0000 0.000000 0.000000 0.000000 1.000000 7.500000

385.0000 0.000000 0.000000 0.000000 1.000000 9.500000

10.00000 0.000000 0.000000 0.000000 1.000000 11.50000

113.0000 0.000000 0.000000 0.000000 1.000000 13.50000

40.00000 0.000000 0.000000 0.000000 1.000000 15.50000

5.000000 0.000000 0.000000 0.000000 1.000000 17.50000

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Summary Output : OLS with Dummy Variables

Dependent Variable: SURVIVOR

Method: Least Squares

Date: 12/01/05 Time: 11:41

Sample: 1 36

Included observations: 36

Variable Coefficient Std. Error t-Statistic Prob.

DUMMY1_PASS 19408.97 3270.443 5.934662 0.0000

DUMMY2_SUV 17026.53 3270.443 5.206184 0.0000

DUMMY3_VAN 11581.30 3270.443 3.541204 0.0013

DUMMY4_TRUCK 13883.53 3270.443 4.245152 0.0002

CON_QUART_TURN -1144.921 233.0587 -4.912586 0.0000

R-squared 0.494077 Mean dependent var 4598.333

Adjusted R-squared 0.428796 S.D. dependent var 9554.442

S.E. of regression 7221.059 Akaike info criterion 20.73564

Sum squared resid 1.62E+09 Schwarz criterion 20.95557

Log likelihood -368.2415 F-statistic 7.568523

Durbin-Watson stat 0.904177 Prob(F-statistic) 0.000224

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Results of Wald Coefficient Test

Estimation Equation: SURVIVOR = C(1)*DUMMY1_PASSGER CAR + C(2)*DUMMY2_SUV + C(3)*DUMMY3_VAN + C(4)*DUMMY4_TRUCK + C(5)*CON_QUART_TURN

Wald Coefficient Test : C(1)=C(2), C(1)=C(3), C(1)=c(4), C(2)=C(3), C(2)=c(4), C(3)=c(4),

On the base of outcome from the EView, Only C(1) is different from c(3). Thus, Passenger car is safer than Van. In the other cases, we didn’t have enough evidence that which vehicle is safer than others

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Results

Number of survivors in rollover crashes has statistically significant dependence on Number of quarter turns Type of vehicle Passenger Car has the higher survival rate than

VAN Other cases we didn’t have enough evidence which

type of vehicle is safer

More variables need to be considered

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II. Alcohol-related Crashes

Connection Between Alcohol-Related Fatalities and Time of the Day and Day of the Week

Statistical Techniques: Contingency Table ANOVA

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Adjusted Data ( Source: Minnesota, 2003 )- Divide 4 classes by the time period of crashes (Remember Rule of Five) - Delete unknown data of the raw data for the convenience of analysis

　 Sun Mon Tues Wed Thurs Fri Sat Total　crashes

00:00-06:00

29 5 10 8 5 7 23 87

06:00-12:00

7 5 4 3 4 1 6 25

12:00-18:00

6 1 0 2 5 3 6 23

18:00-24:00

10 10 9 10 13 21 19 92

Total　 52 21 23 23 27 32 54 227

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Histogram: Alcohol-Related Fatal Crashes by Day of Week

Alcohol-Related Fatal Crashes by time period of Day

87

25 23

92

0

10

20

30

40

50

60

70

80

90

100

sub-total(00:00-06:00)

sub-total(06:00-12:00)

sub-total(12:00-18:00)

sub-total(18:00-24:00)

Time Period of Day

Nu

mb

er

of

Cra

sh

es

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Pie chart : Alcohol-Related Fatal Crashes by Day of Week

Alcohol-Related Fatal Crashes by Day of Week(Minnesota 2003)

sunday, 53, 23%

Monday, 16, 7%

Tuesday, 23, 10%

wendesday, 23, 10%Thursday, 27, 12%

Friday, 32, 14%

Saturday, 54, 24%

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Contingency Table: we are testing the independence between the time of day and the day of week against the alternative hypothesis that these variables are

dependent.

Sun Mon Tues Wed Thurs Fri Sat TOTAL

00:00-06:00 29 5 10 8 5 7 23 87

06:00-12:00 7 5 4 3 4 1 6 30

12:00-18:00 6 1 0 2 5 3 6 23

18:00-24:00 10 10 9 10 13 21 19 92

TOTAL 52 21 23 23 27 32 54 232

chi-squared Stat

33.0897

df 18

p-value 0.0163

chi-squared Critical

28.8693

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1. Hypotheses Ho: Two variables (time of the day and day of week) are independent Ha: not Ho

2. Test stat: χ2 statistic : 33.0897 3. Critical χ2 statistic : 28.8693 (α = 0.05, df = 3*6 = 18) 4. Computed χ2 statistic > Critical χ2 statistic 5. We can reject Ho, therefore two variables are dependent

CONCLUSION:Two variables are dependent. The observed number of crashes are different from the expected numb

er of crashes.

Null Hypothesis Test:for the Contingency Table

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ANOVA: Two-Factor without Replication

SUMMARY Count Sum Average Variance

sub-total(00:00-06:00) 7 87 12.42857 91.95238

sub-total(06:00-12:00) 7 30 4.285714 3.904762

sub-total(12:00-18:00) 7 23 3.285714 5.904762

sub-total(18:00-24:00) 7 92 13.14286 23.80952

Sun 4 52 13 116.6667

Mon 4 21 5.25 13.58333

Tues 4 23 5.75 21.58333

Wed 4 23 5.75 14.91667

Thurs 4 27 6.75 17.58333

Fri 4 32 8 81.33333

Sat 4 54 13.5 77.66667

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ANOVA

Source of Variation SS df MS F P-value F crit

Rows 572.2857143 3 190.7619 7.501873 0.001844 3.159908

Columns 295.7142857 6 49.28571 1.938202 0.129221 2.661305

Error 457.7142857 18 25.42857

Total 1325.714286 27

ANOVA: Two-Factor without Replication

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ANOVA Analysis

The alcohol-related crashes may be affected by two factors:

Factor 1: the time of day

Factor 2: the day of week

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Factor 1

1. Hypotheses

Ho: No difference from time period of day

Ha: not Ho

2. Test stat: F-stat = 7.50

3. Critical F-stat: F=3.16 (α = 0.05, df = 3, 18 )

4. Computed F-stat > Critical F-stat

5. We can reject Ho, therefore there is a difference in the time of day.

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Factor 2

1. Hypotheses

Ho: No difference from day of week

Ha: not Ho

2. Test stat: F-stat=1.94

3. Critical F-stat: F=2.66(α = 0.05, df = 6, 18)

4. Computed F-stat< Critical F-stat

5. We can’t reject Ho, therefore there is no statistical difference among the days of the week.

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Results

The contingency table only suggested two

variables are not independent.

The ANOVA table illustrated a statistically

significant difference between time of day

and fatal alcohol-related crashes, however,

there’s no difference between the days of

the week and fatal alcohol-related crashes.

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III. Conclusion

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Rollover & Alcohol-related crashes

No significant conclusion can be drawn between the two data sets

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Future Application

Rollover crashes Survival rate on each type of vehicle

Alcohol-related crashes Survival rate on day of the week

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Moral of the Story…

Vehicles are not 100% “DEATH PROOF” DON’T drink and drive!