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

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 I. Rollover Crashes

4 Survival Rate in Rollover Crashes Depends on…

5 Number of Quarter Turns

6 Vehicle Types SUV Pick-Up Truck Van Passenger car

7 Complete Rollover Data

8 Survivors vs. # of Rollovers & Vehicle Type

9 ANOVA: two-factor w/o replication

10 ANOVA: cont…

11 Condensed Rollover Data

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

13 ANOVA: two-factor w/o replication SUMMARYCountSumAverageVariance > Passenger Car Sports Utility Vehicle Van Pick-Up Truck

14 Source of VariationSSdfMSFP-valueF crit Rows Columns Error Total ANOVA: cont…

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 = > F-critical = 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 = > F-critical = P-value =  Therefore, Ho is rejected and we conclude that the number of survivors is dependent on the type of vehicle.

16 OLS Regression

17 Survivors vs. # of Turns & Vehicle Type

18 Cont…

19 Cont…

20 OLS with Dummy variable SURVIVORDUMMY1_PASSDUMMY2_SUVDUMMY3_VANDUMMY4_TRUCKCON_QUART_TURN

21 OLS with Dummy variable (cont.) SURVIVORDUMMY1_PASSDUMMY2_SUVDUMMY3_VANDUMMY4_TRUCKCON_QUART_TURN

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_PASS DUMMY2_SUV DUMMY3_VAN DUMMY4_TRUCK CON_QUART_TURN R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid1.62E+09 Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic)

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 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 II. Alcohol-related Crashes

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

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- 12: :00- 18: :00- 24: Total

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

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

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: :00-12: :00-18: :00-24: TOTAL chi-squared Stat df 18 p-value chi-squared Critical

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 : Critical χ 2 statistic : (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 ANOVA: Two-Factor without Replication SUMMARYCountSumAverageVariance sub-total (00:00-06:00) sub-total (06:00-12:00) sub-total (12:00-18:00) sub-total (18:00-24:00) Sun Mon Tues Wed Thurs Fri Sat

33 ANOVA Source of VariationSSdfMSFP-valueF crit Rows Columns Error Total ANOVA: Two-Factor without Replication

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 Factor 1 1. Hypotheses H o : No difference from time period of day H a : not H o 2. Test stat: F-stat = 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 Factor 2 1. Hypotheses H o : No difference from day of week H a : not H o 2. Test stat: F-stat= 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 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 III. Conclusion

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

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

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