Exploratory Analysis of Crash Data

1. Exploratory Analysis of Crash Data Spring 2013

2. Sampling Frame Sampling frame: the sampling frame is the list of the population (this is a general term) from which the sample is drawn. It is important to understand how the sampling frame defines the population represented. Example: If the study seeks to identify the safety effects of traffic signals, the sample frame should include a sample of signalized intersections in a given geographical area. If a control group is included, the sampling frame will include sites categorized under this group. Sig Int #2 Sig Int #1 Unsig Int #2 Unsig Int #1 Unsig Int #7 Sig Int #9 Signalized Unsignalized

3. Sampling Frame Map crashes for Year 1 Map crashes for Year 2

4. Sampling Frame Number of Crashes for Year 1 0 3 10 5 2 0 7 1 1 4 2 0 11 2 6 3 1 0 8 10 5 1 2 0 4 6 1 3 Number of Crashes for Year 2 6 0 3 7

5. Sampling Frame Signalized Intersections Database * ex: Nb of lanes, actuated signals, exclusive left-turn lane, etc.

6. Sampling Frame Signalized Intersections Database Crash Count 1 0 Intersection 1 Year 2 1 Crash Count 3 6 Intersection 9 Year 2 1

7. Sampling Frame Unsignalized Intersections Database * ex: Nb of lanes, actuated signals, exclusive left-turn lane, etc.

8. Histograms

9. Ogives Source: Washington et al. (2003)

10. Box Plots

11. Scatter Diagrams

12. Scatter Diagrams

13. Bar and Line Charts Source: Washington et al. (2003)

14. Two by Two Tables

15. Maps

16. Maps – GIS Information http://www.saferoadmaps.org/home/

17. Confidence Intervals Statistics are usually calculated from samples, such as the sample average X, variance s2, the standard deviation s, are used to estimate the population parameters. For instance: X is used as an estimate of the population μx s2 is used as an estimate of the population variance σ2 Interval estimates, defined as Confidence Intervals, allow inferences to be drawn about the population by providing an interval, a lower and upper value, within which the unknown parameter will lie with a prescribed level of confidence. In other words, the true value of the population is assumed to be located within the estimated interval.

18. Confidence Intervals Confidence Interval for μ and known σ2 95% CI Any CI 90% CI

19. Confidence Intervals Compute the 95% confidence interval for the mean vehicular speed. Assume the data is normally distributed. The sample size is 1,296 and the sample mean X is 58.86. Suppose the population standard deviation (σ) has previously been computed to be 5.5.

20. Confidence Intervals Compute the 95% confidence interval for the mean vehicular speed. Assume the data is normally distributed. The sample size is 1,296 and the sample mean X is 58.86. Suppose the population standard deviation (σ) has previously been computed to be 5.5. Answer

21. Confidence Intervals Confidence Interval for μ and unknown σ2 95% CI Any CI 90% CI Only valid if n > 30

22. Confidence Intervals Same example: Compute the 95% confidence interval for the mean vehicular speed. Assume the data is normally distributed. The sample size is 1,296 and the sample mean X is 58.86. Now, suppose a sample standard deviation (s) has previously been computed to be 4.41. Answer

23. Confidence Intervals Confidence Interval for a Population Proportion The relative frequency in a population may sometimes be of interest. The confidence interval can be computed using the following equation: ^ Where, p is an estimator of the proportion in a population; and, q = 1 – p. Normal approximation is only good when np > 5 and nq > 5. ^ ^

24. Confidence Intervals A transportation agency located in a small city is interested to know the percentage of people who were involved in a collision during the last calendar year. A random sample is conducted using 1000 drivers. From the sample, it was found that 110 drivers were involved in at least one collision. Compute the 90% CI.

25. Confidence Intervals A transportation agency located in a small city is interested to know the percentage of people who were involved in a collision during the last calendar year. A random sample is conducted using 1,000 drivers. From the sample, it was estimated that 110 drivers were involved in at least one collision. Compute the 90% CI. Answer

26. Population Proportion

27. Confidence Intervals Confidence Interval Population Variance When the population variance is of interest, the confidence interval can be computed using the following equation: Where, X 2 is Chi-Square with n-1 degrees of freedom Assumption: the population is normally distributed.

28. Confidence Intervals Taking the same example before on the vehicular speed, compute the confidence interval (95%) for variance for the speed distribution. A sample of 100 vehicles has shown a variance equal to 19.51 mph.

29. Confidence Intervals Taking the same example before on the vehicular speed, compute the confidence interval (95%) for variance for the speed distribution. A sample of 100 vehicles has shown a variance equal to 19.51 mph. Taken from Chi-Square Table Answer

30. The Chi-Square Goodness-of -fit Non-parametric test useful for observations that are assumed to be normally distributed. Need to have more than 5 observations per cell. The test statistic is If the value on the right-hand side is less than the Chi-Square with n-1 degrees of freedom, the observed and estimated values are the same. If not, the observed and estimated values are not the same. You can also perform this test for two-way contingency tables.