Variance in odds ratios for estimating the deterrent effect of darkness on cycling: Variation due to the choice of case and control hours

Comparing the counts of cyclists travelling at specific times of day is one approach to measuring the impact of ambient light level. Here we investigate one source of variance in the magnitude of change seen in previous research—the choice of case and control hour. This was done through an analysis of cyclist flows using data from multiple automated cyclist counters in five cities (Arlington, Bergen, Berlin, Birmingham and Leeds) to determine the odds ratios (OR) for each combination of case and control hour. The results tend to reveal odds ratios above 1.0 indicating that cycling can be deterred by darkness. The odds ratios varied with the choice of case and control hour. For two cities (Birmingham and Leeds), the impact was small, with little difference in ORs between any case and control hour combination. For three cities the variance in ORs was larger. To represent the impact of darkness on cycling flows across the range of case and control hours we suggest the Mantel-Haenszel pooled odds ratio is used, in which the odds ratio for each combination of case and control hour is weighted by the total number of cyclists in that combination. This suggested a statistically significant (p<0.001) deterrent effect of darkness in all five cities.