In our last “Ask the Experts” article, we corresponded with Danish Engineer, Soren Jensen, to help clarify the findings from his study titled, “Road safety and perceived risk of cycle facilities in Copenhagen”. Local Vehicular Cyclists had attempted to cite the study as reason for not developing bicycle infrastructure. At the conclusion of the article, Soren summarized that if Dallas in fact added Cycle Tracks to its roadways, it would actually see “much higher ridership”, and “greater safety to bicyclists”.
In our dialog, Mr. Jensen referenced an important study from Public Health Consultant, Paul L. Jacobsen, titled, “Safety in Numbers”. This study has been the basis many US and European city planners have cited to increase bicycle infrastructure within their communities. The summary of the study states: “The risk of an individual pedestrian or bicyclist being hit by a motor vehicle decreases as the number of pedestrians or bicyclists increases, respectively.” When combined with the Soren study, which notes that implementation of Cycle Tracks increases bicycle ridership, a correlation can be inferred.
Within our comment section, commenter Steve-A, dismissed the Jacoben study, and linked to a Cycle*Dallas article he’d written citing “random numbers” could be used to achieve the same results. He drew his conclusions using a method noted in an article written by Vehicular Cycling advocate, John Forester, who questioned the study’s findings.
BFOC communicated with Paul L. Jacobsen in California, to explain his study and counter the claims made by Cycle*Dallas and Forester, and followed up once again with Author/Engineer Dr. Lon D. Roberts, to also shine some light onto the dispute.
First will start with Mr. Jacobsen:
This question comes up every 6 months or so. There’s a website out there with this argument.
First off, this is not the way I did the analysis. The folks saying the data is manipulated need to read the Methods section of my paper. (http://safetyinnumbers.notlong.com)
Secondly, having a variable on both sides changes the exponent by one, and that’s the issue that matters. The other variables change slightly. The key point is that injury rate is non-linear with the amount of walking and biking. Take a look at Table 1 in this recent paper. Lots of researchers have found the injury rate to be non-linear.
Soren Jensen provided the data used in Figure 2 of my SIN paper.
Next up, we asked Dr. Roberts to also review Forester’s argument:
The argument that some have posed that Jacobsen’s “Safety In Numbers” plots can be replicated by calculations involving random number is interesting but perhaps flawed — both mathematically and logically. For instance, the assertion that a plot created by paired data where the X-axis values are represented by the quotient of two uniformly distributed random variables, N divided by C, and the Y-axis values are represented by the quotient of two uniformly distributed random variables, C divided by P, results in a quasi-hyperbolic curve, “similar in shape” to Jacobsen’s, places undue emphasis on extreme outliers on both axes to dictate the shape of the curve. For instance, if N and C are randomly chosen values between 0 and 1, on average, half of the values for N will be 0.5 or less and half of the values for C will be 0.5 or less, if N and C are randomly chosen numerous times. Using Monte Carlo simulation to plot the value of N divided by C for 1000 samples in a run that I did, 75 percent of the values were less than 2, on the other hand the single most extreme value was 973. Since the theoretical values for N divided by C can range from zero to infinity, a computer generated plot of the “best fit” curve may vaguely resemble a hyperbolic function, if you choose to ignore the distribution of the data points, but it isn’t. (For any who are interested in how trend lines and correlation coefficients can be artificially manipulated, I would refer them to Anscombe’s Quartet.)