1. 1 Motor Vehicle Accidents Hunjung Kim Melissa Manfredonia Heidi Braunger Yaming Liu Jo-Yu Mao Grace Lee December 1, 2005 Econ 240A Project

2. 2 I. Rollover crashes Actual data vs. Condensed  ANOVA  OLS Regression Results II. Alcohol-related crashes Actual vs. Condensed  Contingency Table  ANOVA Results III. Conclusion

3. 3 I. Rollover Crashes

4. 4 Survival Rate in Rollover Crashes Depends on…

5. 5 Number of Quarter Turns

6. 6 Vehicle Types SUV Pick-Up Truck Van Passenger car

7. 7 Complete Rollover Data

8. 8 Survivors vs. # of Rollovers & Vehicle Type

9. 9 ANOVA: two-factor w/o replication

10. 10 ANOVA: cont…

11. 11 Condensed Rollover Data

12. 12 Survivors vs.# of Rollovers &Vehicle Type (condensed data)

13. 13 ANOVA: two-factor w/o replication SUMMARYCountSumAverageVariance 1.549407723519.25324966370.9 3.54415041037658549284.67 5.54158593964.7514588907.58 7.5490902272.57318537.667 9.541893473.25287970.9167 11.54454113.518933.66667 13.5415538.752470.916667 15.544210.5387.6666667 >16413032.52524.333333 Passenger Car9767908532.222222192860423.4 Sports Utility Vehicle9553486149.777778132507267.7 Van94005445519214.5 Pick-Up Truck9270613006.77777832394135.19

14. 14 Source of VariationSSdfMSFP-valueF crit Rows19878817788248485222.26.7894722790.000115442.355081495 Columns338839616.23112946538.73.0860885280.0463037023.008786572 Error878366548.82436598606.2 Total320508794335 ANOVA: cont…

15. 15 ANOVA Analysis  H o : Two variables independent (ie: µp = µs = µv = µt)  H a : 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 = 1.859 P-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 = 2.798 P-value = 0.0187  Therefore, Ho is rejected and we conclude that the number of survivors is dependent on the type of vehicle.

16. 16 OLS Regression

17. 17 Survivors vs. # of Turns & Vehicle Type

18. 18 Cont…

19. 19 Cont…

20. 20 OLS with Dummy variable SURVIVORDUMMY1_PASSDUMMY2_SUVDUMMY3_VANDUMMY4_TRUCKCON_QUART_TURN 41833.00 1.000000 0.000000 1.500000 17932.00 1.000000 0.000000 3.500000 9405.000 1.000000 0.000000 5.500000 6032.000 1.000000 0.000000 7.500000 1257.000 1.000000 0.000000 9.500000 311.0000 1.000000 0.000000 11.50000 20.00000 1.000000 0.000000 13.50000 0.000000 1.000000 0.000000 15.50000 0.000000 1.000000 0.000000 17.50000 33737.00 0.000000 1.000000 0.000000 1.500000 15701.00 0.000000 1.000000 0.000000 3.500000 3126.000 0.000000 1.000000 0.000000 5.500000 2433.000 0.000000 1.000000 0.000000 7.500000 126.0000 0.000000 1.000000 0.000000 9.500000 103.0000 0.000000 1.000000 0.000000 11.50000 13.00000 0.000000 1.000000 0.000000 13.50000 2.000000 0.000000 1.000000 0.000000 15.50000 107.0000 0.000000 1.000000 0.000000 17.50000

21. 21 OLS with Dummy variable (cont.) SURVIVORDUMMY1_PASSDUMMY2_SUVDUMMY3_VANDUMMY4_TRUCKCON_QUART_TURN 3587.000 0.000000 1.000000 0.000000 1.500000 2033.000 0.000000 1.000000 0.000000 3.500000 464.0000 0.000000 1.000000 0.000000 5.500000 75.00000 0.000000 1.000000 0.000000 7.500000 125.0000 0.000000 1.000000 0.000000 9.500000 30.00000 0.000000 1.000000 0.000000 11.50000 9.000000 0.000000 1.000000 0.000000 13.50000 0.000000 1.000000 0.000000 15.50000 18.00000 0.000000 1.000000 0.000000 17.50000 17256.00 0.000000 1.000000 1.500000 5838.000 0.000000 1.000000 3.500000 2864.000 0.000000 1.000000 5.500000 550.0000 0.000000 1.000000 7.500000 385.0000 0.000000 1.000000 9.500000 10.00000 0.000000 1.000000 11.50000 113.0000 0.000000 1.000000 13.50000 40.00000 0.000000 1.000000 15.50000 5.000000 0.000000 1.000000 17.50000

22. 22 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 VariableCoefficientStd. Errort-StatisticProb. DUMMY1_PASS19408.973270.4435.9346620.0000 DUMMY2_SUV17026.533270.4435.2061840.0000 DUMMY3_VAN11581.303270.4433.5412040.0013 DUMMY4_TRUCK13883.533270.4434.2451520.0002 CON_QUART_TURN-1144.921233.0587-4.9125860.0000 R-squared0.494077 Mean dependent var4598.333 Adjusted R-squared0.428796 S.D. dependent var9554.442 S.E. of regression7221.059 Akaike info criterion20.73564 Sum squared resid1.62E+09 Schwarz criterion20.95557 Log likelihood-368.2415 F-statistic7.568523 Durbin-Watson stat0.904177 Prob(F-statistic)0.000224

23. 23 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

24. 24 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

25. 25 II. Alcohol-related Crashes

26. Connection Between Alcohol-Related Fatalities and Time of the Day and Day of the Week Statistical Techniques: Contingency Table ANOVA

27. 27 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 SunMonTuesWedThursFriSatTotal crashes 00:00- 06:00 295108572387 06:00- 12:00 754341625 12:00- 18:00 610253623 18:00- 24:00 10 9 13211992 Total522123 273254227

28. 28 Histogram: Alcohol-Related Fatal Crashes by Day of Week

29. 29 Pie chart : Alcohol-Related Fatal Crashes by Day of Week

30. 30 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. SunMonTuesWedThursFriSatTOTAL 00:00-06:00 2951085723 87 06:00-12:00 7543416 30 12:00-18:00 6102536 23 18:00-24:00 10 9 132119 92 TOTAL522123 273254232 chi-squared Stat 33.089 7 df 18 p-value 0.0163 chi-squared Critical 28.869 3

31. 31 1. Hypotheses H o : Two variables (time of the day and day of week) are independent H a : not H o 2. Test stat: χ 2 statistic : 33.0897 3. Critical χ 2 statistic : 28.8693 (α = 0.05, df = 3*6 = 18) 4. Computed χ 2 statistic > Critical χ 2 statistic 5. We can reject H o, therefore two variables are dependent CONCLUSION: Two variables are dependent.  The observed number of crashes are different from the expected number of crashes. Null Hypothesis Test: for the Contingency Table

32. 32 ANOVA: Two-Factor without Replication SUMMARYCountSumAverageVariance sub-total (00:00-06:00)78712.4285791.95238 sub-total (06:00-12:00)7304.2857143.904762 sub-total (12:00-18:00)7233.2857145.904762 sub-total (18:00-24:00)79213.1428623.80952 Sun45213116.6667 Mon4215.2513.58333 Tues4235.7521.58333 Wed4235.7514.91667 Thurs4276.7517.58333 Fri432881.33333 Sat45413.577.66667

33. 33 ANOVA Source of VariationSSdfMSFP-valueF crit Rows572.28571433190.76197.5018730.0018443.159908 Columns295.7142857649.285711.9382020.1292212.661305 Error457.71428571825.42857 Total1325.71428627 ANOVA: Two-Factor without Replication

34. 34 ANOVA Analysis The alcohol-related crashes may be affected by two factors: Factor 1: the time of day Factor 2: the day of week

35. 35 Factor 1 1. Hypotheses H o : No difference from time period of day H a : not H o 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 H o, therefore there is a difference in the time of day.

36. 36 Factor 2 1. Hypotheses H o : No difference from day of week H a : not H o 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 H o, therefore there is no statistical difference among the days of the week.

37. 37 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.

38. 38 III. Conclusion

39. 39 Rollover & Alcohol-related crashes No significant conclusion can be drawn between the two data sets

40. 40 Future Application  Rollover crashes Survival rate on each type of vehicle  Alcohol-related crashes Survival rate on day of the week

41. 41 Moral of the Story…  Vehicles are not 100% “DEATH PROOF”  DON’T drink and drive!