# Something Amiss in Robinson (1996)

A 1996 article titled “Head Injuries and Bicycle Helmet Laws” published in Accident Analysis and Prevention is one of the most highly cited papers assessing the effect of helmet legislation.[1] (148 citations, Google Scholar, 4 Sept 2014) Additionally, this seems to be the first article purportedly demonstrating a negative impact of such laws. The conclusions of this paper state

Consequently, a helmet law, whose most notable effect was to reduce cycling, may have generated a net loss of health benefits to the nation.

In this paper, secondary analyses were performed on data contained in other reports. I’ve pointed out in a previous paper[2] that NSW adult cycling counts exist from sources cited in this paper although they are not presented. This is curious because the counts of adult cyclists from NSW helmet use surveys increased from pre- to post-helmet legislation which contradicts the conclusions of this paper. Adult cycling also increased by 44% in Victoria following helmet legislation.[3]

Linda Ward has pointed to another issue with this paper regarding a comparison of the proportion of head injury hospitalizations to cyclists before and after legislation in Victoria. Some of the relevant data is given in Table 6.[1] In this table, the proportion of head injuries are 31.4% for 1989/90 and 27.3% for 1990/91 for hospital admissions in Victoria. During this period, there are a total of n=2300 cycling hospitalizations. The author notes a comparison of these proportions is non-significant by a chi-square test.

The 2×2 table for this data can be reproduced using the source material.[4] Figure 25 of this report gives “All Other Injuries” of about 900 for year 1989/90. This allows us to fill in the rest of the table given below.

 Year Other Injury Head Injury 1989/90 900 412 1990/91 718 270

The frequencies of the other cells seem to correspond to the other values in Figure 25. The chi-square test for this table results in $\chi^2=4.49$, $p=0.03$ and $OR=0.82$. This result could be influenced by the need to estimate the number of cases from a plot. We can assess the influence of this estimate by repeating the analysis for other values near 900. Choosing values from 890 to 910 results in the plot of p-values below.

As you can see, there is a statistically significant decline in head injury in each instance for cycling injury in Victoria before and after helmet legislation. R code to reproduce these results is given below.

n=2300
p1=0.314
p2=0.273

a=900
n1=round(900/(1-p1))
b=n1-900
n2=n-n1
d=round(n2*p2)
c=n2-d

tab=matrix(c(a,b,c,d),nrow=2,byrow=T)
rownames(tab)=c(‘1989/90′,’1990/91’)