Saturday, 26 February 2011

The danger of headline statistics

One of the most common ways of misleading people with statistics is to carefully select a statistic from a larger data set, and then make inferences from that statistic as if it were representative of the data set. This can lead to headline statistics which imply the opposite of the underlying reality.

Being able to spot these and show up the misdirection is sometimes quite tricky.

For a (relatively straightforward) example, a statistic that often gets quoted in arguments about gender equality is that "over 80% of those dying in workplace accidents are men". I'll use this to illustrate some of the common problems with these sorts of headline statistics.

[trigger warning: workplace deaths, murders]

Problem 1: scoping of the statistic

There's no indication on this statistic of what country it's related to or when the data was gathered. I couldn't find a formal breakdown for the UK at all, and didn't feel like guessing from the names on the accident summaries. Looking at the available statistics for other rich industrialised English-speaking nations, the headline figure is almost certainly true, though.

However, not having a year or country specified makes it very difficult to look beyond the headline at the details - which details?

Specifying "workplace accidents" also statistically excludes those cases where someone is intentionally harmed while working, since that would be compartmentalised as a police rather than a health and safety matter. The various murders of sex workers would not, for instance, be counted, which significantly skews the gender balance of the statistics, but not of the actual workplace dangers.

Problem 2: implying a cause

The implied cause is that there is discrimination against men which causes them to die more in workplace accidents. There are actually several other factors involved.

Who can die in the workplace?

Firstly, more men than women have jobs at all. Here's the UK's Labour Force Survey.

In 1971, the ratio of men to women in employment was 3:2. 1

In 1992 - the first year for which detailed statistics are available - the ratio is closer to 5:4, but the detailed statistics show that almost all the men are in full-time employment, while only slightly over half of women are.

In 2010, the base ratio is around 8:7, but the full-time/part-time patterns are much the same. There has been a slight rise in the number of men working part-time, and a slight rise in the number of women working full-time, since 1992, but it's not a major difference.

If we assume on average that a part-time worker works half the hours of a full-time worker, that means that men are collectively working in paid employment between a third more and twice as many hours as women collectively work in paid employment (depending on the year)

So, some of the difference is caused by the difference in hours worked. Men are more likely to die at work because they collectively spend longer there. Note that greater male employment is generally not considered evidence of discrimination against men.

Who is likely to die at work?

Some jobs are considerably more dangerous than others. The Health and Safety Executive collects data on fatal injuries at work (including fatal injuries to members of the public who were in a workplace).

Many of the deaths of workers occurred in the Construction and Agriculture sectors, both of which mostly employ men and involve large amounts of heavy machinery.

There are a number of reasons for most employees in these sectors being men, but they are not reasonable to describe as discrimination against men.

Problem 3: missing the real problem

The problem with workplace deaths is not that men die in workplace accidents, it's that people die in workplace accidents. The correct thing to ask the magical society fairy for is an end to workplace accidents, not an equalisation of who dies in them by gender.

There can't be many accidents that wouldn't have happened if - all else equal - the worker in the unfortunate position hadn't been a man2. Nor are there likely to be many potential fatal accidents which were only avoided (or at least not fatal) because the worker wasn't a man.

So, primarily, the solution is to try to make workplaces safer. This - at least in the UK - is happening. Fatal workplace accidents have fallen to less than a half of their rate in the early 90s3. A combination of regulation and guidance of health and safety has helped make the UK one of the safest places in the world to work4 (though that's not the only reason, of course; see below).

Problem 4: not distinguishing between primary and secondary effects

There are privilege-related issues here - class, gender, immigration status, and disability, for instance, can all lead to situations where someone has to take a job which is less safe. Internationally, the UK is able to use its trading wealth to export a lot of the more dangerous work to other countries so that foreigners die on our behalf.

These are all important issues, with established campaigning groups for all of them, especially in the trade union movement.

For immigration status, it's a direct consequence of the harsh treatment we give to undocumented migrants - and the low value we place on their lives as a society - which makes it easy for unscrupulous employers to exploit them knowing that they can't easily report their employer to the authorities.

The danger they are in is a primary consequence of their immigration status, and so the solutions have to consider that: generally making workplaces safer won't help because there is no practical mechanism for enforcement against that employer (who is already breaking a vast range of laws and won't mind breaking health and safety law too).

For gender, the disparity in workplace accidents (not workplace deaths in general - see above - but accidents specifically) is not a primary consequence of the workers' gender, but a secondary effect from a number of gender-related issues:

  • Men are more likely to have paid work, and for more hours, due to well-documented discrimination against women, childcare being seen as primarily (or even only) a woman's job, and so on.
  • Men (especially working-class men) are encouraged into paid work requiring physical activity, whereas women are discouraged from this. This happens both at the stage of career choices, and in the workplace itself where hostile anti-women environments can be self-perpetuating. The "men's work" is generally better paid than the "women's work" for equivalent knowledge and experience.

As a consequence of these, there are more men in dangerous jobs than there are women - but it's a consequence of discrimination against women, not discrimination against men: all of the components that cause it are positive for men, even if this one side-effect is negative.


The headline statistic is often used to imply discrimination against men. The underlying data shows no such thing (though there are genuine issues related to gender and other aspects of discrimination).


1 As with all UK official statistics, the existence of people who are neither men nor women is ignored. Depending on the method by which statistics are collected, misgendering of at least some of the trans people in the sample is also extremely likely. The lack of useful data means that I can only discuss men and women for this post.

2 I've no idea about how you'd ethically go about testing this, but it's not a completely outlandish hypothesis that since men are socialised to be more confident than women, and get more tolerance for minor errors, they're more likely to cut corners on safety procedures as confidence shades into recklessness, and this accounts for a higher proportion of accidents in male-dominated workplaces.

3 Adjusted for the relative proportions of industries, the UK has the lowest fatal accident rate of all EU countries, and less than a third (per 100,000 workers) of the rate in the USA.

4 Naturally, rather than taking some pride in this achievement, many of the popular papers and politicians feel that we aren't, as a nation, killing enough workers, and want to see much of the protective regulations repealed. The people suggesting this generally do not work in jobs involving heavy machinery, steep drops, or other dangerous environments, where the trades unions representing the actual workers tend to be quite in favour of workplace safety.