4. (10 points) Two staff analysts of the Bismark Municipal Transit Authority are

Question

4. (10 points) Two staff analysts of the Bismark Municipal Transit Authority are locked in debate regarding the relationship between driver experience and accidents on bus routes. From authority records they have coded drivers experience into the following categories: low (less than five years driving a bus), medium (5 to 19 years), and high (20 or more years); accidents have been coded as none, one, and more than on. These data are cross-tabulated below. Driver Experience Accidents Low Medium High None 31% 52% 18% One 41% 26% 19% More than one 28% 22% 63% 100% 100% 100% Gamma = .05 Lambda = .48 One analyst insists that these two variables are related while the other analyst insists that they are not related. Analyze the relationship between driver experience and accidents, explain the source of disagreement between the two analysts, and resolve their debate.

Explanation / Answer

<Please rate and comment in case of any queries>

The data has already been summarized in form of the 2 major coeffecients to assess correlation.

First point to understand is the data is ordinal in nature ,i.e. there is an inherent ordering in the values of the variable, e.g. experiance of driver is ordered as low < medium < high and also the number of accidents is categorized as None < one < more than one. When the data is ordinal in nature then it is always better to consider those measures of association which take ihnto account the ordering of the data points.

Gamma coeffecient matches the total number of pairs of data points against the difference between number of concordant and discordant pairs. Gamma = N(c) - N(d) / N(c) + N(d), consider a pair as driver experiance = low and accident level none to driver level = medium and accident level = one, then this is a discordant pair because the experiance has improved but accident level has also increased (against the expectation). In the same way we calculate the number of noncordant and discordant pairs and calculate Gamma. Gamma takes values between -1 to 1. Here Gamma is close to 0 which indicates almost no correlation.

On the other hand, lambda is a measure of association for nominal variable where there is no ordering between the variables considered. (which is not the case here). Lambda = 0.48 indicates there is strong relation between the 2 variables but do not gurantee any particular direction. Hence lambda is not useful in this type of analysis.

One of the analysts is following Lambda while the other one is following Gamma. The one following gamma will reach the correct interpretation. So since Gamma is close to 0 we will comment that there is no directional correlation between the driver experience and accident prone driving.

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.