Radar Detectors and Speeding

In describing their methods Teed, Adrian, and Knoblauch state that:

“Data for both studies were gathered during clear weather on a mostly level stretch of rural Interstate 70 west of Hagerstown, Maryland. Speed limits were 55 mph for all vehicles. Citizens band (CB) radio was monitored to determine the degree to which drivers with radar detectors alerted other drivers to the presence of radar signals and to assure that the study area was free of police enforcement or construction activities that might affect vehicle speeds.”

What is the purpose of the methodology described in this paragraph?

• Understand the notion of confounding.
• Understand how randomization of group assignments yields comparison groups that are similar with respect to confounding factors.

The researchers could not control which cars came into their sample so this was an observational study making it important to control for obvious confounding factors. In this case the investigators wanted to argue that when the cars slowed down it was in response to the hidden radar and not to alternative explanations like the weather, curves in the road, city traffic, a changing speed limit, warnings from other motorists, seeing a patrolling police car, or highway construction.

Using the data from the second study, make a plot which compares how the average speed depends on a vehicle's distance from radar for cars presumed to be with and without detectors.

Table 2: Second Study Results
          

• Be able to use your software to make a scatterplot.
• Be able to interpret the display (for example, recognizing patterns or spotting outliers).
  

The data from the table is plotted below (cars presumed to have radar detectors are indicated by blue o's; cars presumed to not have detectors are indicated by red x's):

Using the data from the first study make a 90% confidence interval for the percentage of cars that reduce their speed from greater than 65 mph to less than 65 mph when exposed to police radar. Describe any assumptions that you need to make for your interval to be valid and comment on their appropriateness.

Table 1: First Study Results
          

• Be able to make confidence intervals for proportions and means from a simple random sample.

With such a large number of observations we can use the normal approximation. There was a 44 − 32 = 12% reduction in the percentage of cars going faster than 65 mph. The standard error for this estimate is estimated to be 0.0092. Thus, the 90% Confidence Interval is 12% ± 1.645(0.92)% or 12% ± 1.5%. For this interval to be valid we need to assume that each car behaved independently. This may not be appropriate if the entire flow of traffic is slowed. The researchers tried to avoid this by using a rural stretch of road where cars are fairly isolated (from the data we note that they saw about 270 cars per hour). Also we cannot say with any certainty that the observed reduction in speeders was due to the exposure to police radar since any attribute of the location with the embedded speed-measuring devices could provide an alternate explanation.

Data from 14 of the 70 possible hours of observation in the first study were not used because of bad weather, unscheduled police patrols, and construction activities. Comment on what effect this may have on interpreting the conclusions of the study and suggest ways that this effect may have been avoided.

• Be able to identify problems with poorly designed experiments.
• Be able to identify potential sources of bias.

Any conclusions from the study that are related to factors that caused this data to be missing will be affected. For example, weather, police patrols and construction activities are more likely to happen at certain times of day. We can see this from the data since there were clearly more observations missing at the time of day that the "5 miles after radar" measurements were taken. Since time of day may also be related to vehicle speed, the study's conclusions are affected. This problem could have been avoided at the design stage by randomizing the location of the police radar throughout the day rather than using the systematic approach. The problem could also be partially controlled for in the analysis stage by comparing the radar data with the no radar data at the adjacent hours.

In describing the results from the second study, the researchers state that "Those vehicles with radar detectors were significantly faster than those without them before radar exposure (p < 0.01) ... and significantly slower immediately after (p < 0.0001) ..." Discuss the validity of these inferential statements.

• Understand that carrying out the mechanics of a significance test cannot make up for a poorly designed study.
• A valid significance test is based on the randomization used to collect the data.

 

It was not really known which cars had radar detectors and which did not. Cars were presumed to have radar detectors when their speeds were reduced by at least 5 mph in the presence of radar exposure. Thus, it is not fair to test the foregone conclusion that the cars classified as having radar detectors would have a slower average speed immediately after radar exposure.