Statistical Applications in Traffic Studies.pptx

Statistical Applications is very important in traffic design

1. Statistical Applications in Traffic Studies

2. Statistical Applications in Traffic Studies A number of statistical methods are currently being applied in traffic engineering studies. These include: 1.Regression method 2.Poisson distribution 3.Normal distribution 4.Chi-squared test 5.Quality control method

3. Regression Methods The basic principle behind this method is that the expected number of accidents, on a certain road system during a given time period, is dependent in a linear way on factors which are supposed to be of significance for the determination of accident frequency. The number of accidents occurring on a certain day is itself assumed to be normally distributed, with a mean value being a linear function of regression variables, and a variance being constant an same for all days of a certain time period studied. The numbers of accidents on different days are assumed to be stochastically independent.

4. Some of the regression variables (independent variables) that could be considered are: Two wheeled vehicles involved in personal injury accidents as a proportion of all vehicles involved. Cost of safety improvements. Number of pedestrians Pavement width Number of junctions per km length of road.

5. Poisson Distribution

6. Normal Distribution Normal distribution is very useful in dealing with sampling, since it is found that irrespective of the distribution of the population, means of random samples taken from the population tend to assume a normal distribution. Normal distribution can also be used for approximating other types of distribution.

7. Chi-squared ( χ 2 ) Test The chi-squared χ 2 test is a very useful statistical tool and has many applications. Following are the important applications to the traffic engineering. They are: Testing of proportions with contingency tables Goodness-of-fit test A convenient application of the χ 2 tests is in testing the comparability of observed and expected values in two way tables, known as contingency tables

8. Another useful application of the chi-squared distribution is in the goodness-of-fit. In this test, the measure of the discrepancy between a set of observed data and the values that are to be expected if the results follow a hypothesis distribution is evaluated .