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.

Conclusion

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).

Footnotes

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.

Buses, and the point of public services

The local County Council has had a major budget cut from central government. Part of dealing with this involves reducing or removing the subsidy they provide for certain services which would not be commercially viable.

While they say that this does not necessarily mean the service will be withdrawn, both of the major bus operators have said that they cannot afford to continue more than a few of the services without a subsidy.

Sunday services and evening services are facing the majority of the cuts, mainly in rural parts of the county.

There are two things related to this that I want to draw attention to, and they apply to all sorts of cuts that the government is making or requiring local councils to make.

Firstly, as reported in the local free paper:

About a fifth of all bus services in the county are not commercially viable. But the council believes more than 95% of bus passenger journeys would be largely or entirely unaffected by the cuts.

Obviously most passenger journeys are not going to be affected. Most journeys are made on busy routes, which don't need a subsidy. The point of public subsidy of bus routes - and indeed public funding of many things - is to make affordable services that would not be possible on a pure market model, but which are necessary to many people. To say that most journeys will be unaffected is true, but not relevant.

Lots of people who rely on the bus services to get about are going to find their movement restricted, and that leads on to the second point: cuts to public services have a knock-on effect on the private economy.

We're told by the government that public spending is preventing private spending. Well, in this case that's clearly not true - it's not as if there would be private operators on these routes without the public subsidy: the private operators have said so themselves.

But furthermore, this public subsidy helps private spending. Cut the evening services, and people won't be able to get into the urban centres of the county then - or won't be able to get out later without spending several times the cost of a bus ticket on taxi fares.

So people going into towns in the evening for the nightlife are a bit stuck, as are people who go into town to work in the pubs and clubs providing that nightlife, or in other evening shift jobs in shops where they clock off after 8pm when many services are being withdrawn or cut back. The local private economy takes a dip as a result.

They could get a car and travel that way, but that's a large cost to themselves so won't be practical for a lot of people who were relying on the buses before, and it also increases congestion and exacerbates the lack of parking in town centres, which makes things worse for everyone. And, of course, having got the car, they then don't need the bus to get around on weekday mornings and afternoons either, so that's fewer bus passengers, and perhaps some of the more borderline unsubsidised bus routes start to slip out of profit too.

Reduced private expenditure leads to reduced tax revenue, so the whole cycle starts again.

By supporting necessary but not commercially viable services, public funding helps both the public and private sector, both of which are likely to take severe damage in the next few years.

In praise of unreasonableness

So, the Pope recently visited the UK, though thankfully not Durham, and there were numerous protests. As head of the Catholic church he's said a large number of extremely unpleasant things, and endorsed many anti-women and anti-LGBT views. Then there's the church hierarchy's treatment of numerous abuse cases across the decades. The protesting was hardly surprising.

One of the consequences of this, as well as the general justified sentiments against the Catholic church hierarchy and the Pope personally based on their roles in covering up abuse, recommending discrimination, and so on, has been various criticism of Catholicism and religion in general, and then from that general attacks on the idea of people believing in anything "supernatural" (including deities). There's a very short slippery slope from criticising the genuine problems with the Catholic hierarchy to anti-religious discrimination (protests are not a good place for fine distinctions like that, either, unless you're very careful).

The atheist criticism of religious belief is - in their¹ own words - that it is "not reasonable", "not rational" or "not based on the evidence". The three phrasings are given much the same meaning in practice, and the disablist connotations of irrational (and the general insult of unreasonable) are generally desired.

I entirely agree that there is not sufficiently strong scientific evidence for the existence of anything that could reasonably be described as a deity, but that's really besides the point, and the use of "not reasonable" or especially "not rational" as shorthands for "not based upon scientific evidence" is extremely problematic.

I'm going to use "unreasonable" (note the quote marks) as a shorthand for "not based on scientific views of evidence and logical conclusions from that evidence" to save space, because even though that's not quite the normal meaning of the word, it's the meaning given to it in these debates. It's true that given that definition, belief in any deity or non-deific supernatural² occurrence is "unreasonable". The problem is that so are rather a lot of other things that are commonly held beliefs and take place entirely within the natural realm.

Ethics and morals

Ethics and morals are unavoidably "unreasonable" (this is why straw-atheists don't have them). It is not possible to prove solely by the application of evidence and logic that a particular moral stance is superior to another stance.

Once you make some assumptions about what the purpose of having morals in the first place is - to keep society intact, or to maximise some measure of happiness, or to prevent certain behaviours, or whatever - you can then "reasonably" use evidence and logic to make a decision about the best ethical and moral decisions to achieve that purpose. But since your purpose was selected arbitrarily, and in practice based on socialisation and other factors external to your "reasonableness", it is itself "unreasonable".

Anything else that involves a values judgement - aesthetics, what to have for breakfast, etc. - ends up with the same situation.

The scientific method

The scientific method - in extremely concise outline - is that you make a theory to explain an aspect of nature, carry out experiments to test the theory, and refine or abandon the theory according to the results of the experiments. The idea is that over time the incorrect theories will be contradicted by experiment, and the correct ones won't, and the accuracy of the set of all current theories will therefore on average increase over time.

There's lots of added detail in practice to make sure that you don't throw out correct theories, or hang on to incorrect ones, in an attempt to get to the real right answer faster, but that's not really relevant here.

The scientific method is something I personally have a very strong belief in (the basic principle, anyway - I have quite a lot of criticism of some of the details of implementation, especially in some fields of study). It is, however, an "unreasonable" belief - I cannot prove, from the evidence, that the scientific method works.

I do have a straightforward circular argument in favour of the scientific method (summarised: "it seems to have worked so far"), but it's generally not considered "reasonable" - or indeed reasonable - to use circular arguments.

Free will

This might fall within the scope of "supernatural" for some people, but it need not. I believe that I have free will, and that so does everyone else. I don't even think it's philosophically interesting to discuss alternative situations where free will does not exist because I don't believe there's a self to exist without the existence of free will - there's just particles moving along their probabilistic paths.

I have no evidence of a scientific sort for this, and only a circular argument similar to Descartés "I think therefore I am" for non-scientific evidence. It's not a "reasonable" belief, but I think it's an entirely reasonable belief given the alternatives.

So, in praise of unreasonableness

The "sceptical atheist" community is right that religious beliefs and faiths are not "reasonable". Where they're wrong is the giant leap many of them take from that to "and therefore a sign of lack of intelligence / moral inferiority / mental illness / closed-mindedness / other insult of choice." and in the implication that one can get by entirely on "reasonable" beliefs.

This results in the usual problems that happen when one group of people believes another group to be inferior to it. These are all of course criticisms that can be applied to religions too, but atheists claim to be above the "irrational" actions of religion.

Firstly, while in the UK atheists don't have the structural power to discriminate against the default religion of Christianity (whatever the Pope might say), they are by a significant margin the second-most powerful belief group and so can quite happily contribute to the oppression of believers in religions lower down the local kyriarchy. See also France and the way an aggressive anti-religious message (masquerading as secularism) has been mixed with racism for a wholly counter-productive ban on Islamic veils.

Stereotyping the extremely diverse beliefs of a billion co-religionists to their most extreme members lends itself to being a cover for other forms of bigotry (most directly racism and disablism, and a claim that one is being "unreasonable" or "irrational" is an extremely common silencing tactic everywhere).

I don't want a situation where atheists end up at the top of the pile instead. This isn't going to happen any time this century even in a secularish country like the UK, but it shouldn't even be a goal - the goal should be to end religious privilege and discrimination, but that's a goal that many atheists would reject as treating "unreasonable" beliefs as valid.

Secondly, it makes it more difficult to get co-operation between atheists and religious people on mostly unrelated social justice matters. This also makes it harder to work together on matters related to the conduct of religious organisations where, to return to the start of this post for an example, the majority of both atheists and UK Catholics have serious disagreement's with the Catholic hierarchy's decisions on abortion, contraception, LGBT rights, women's rights, and so on.

You end up with the usual problem of intersecting oppressions, though perhaps with the default in the other place, where the existence and experience of Catholic LGBT people gets erased by both their own religious hierarchy and by their supposed allies, or action within religious communities in favour of women's equality is dismissed as irrelevant because it takes place within a religious setting.

There seems to be an attitude that because religious people have an "unreasonable" belief in one area, there's no point in trying to work with them in other areas despite this disagreement, but instead one must convince them of the truth of atheism first. This never ends well. It can also lead to an approach where people try to find scientific justifications for ethical decisions, and I've looked at one example of the problems with that approach before. Science is a valuable tool for humanity, but it's not supposed to be used for everything.

Thirdly, as I've said above, it misses the point. I don't believe in social justice because I have scientific standards of evidence that the world would be a better place without the kyriarchy - I don't even know what a non-kyriarchal world would look like in practice - but because I have what would be insultingly dismissed as "faith" that it would be better (according to my own ethical values) than what we currently have. I'm happy to hold that "unreasonable" belief and work towards it. Having decided "unreasonably" that this is a goal, my approach is going to be at times very much based on scientific evidence, of course, but that doesn't make the goal itself scientifically "reasonable".

Let's be "unreasonable", because there is too much that is important that cannot be dealt with "reasonably". Let's let other people have their own "unreasonable" beliefs, if they don't cause harm; and let's focus on the harm caused, not whether that harm has a scientific or an "unreasonable" backing³, if they do.

Footnotes

¹ While my personal beliefs in deities and other supernatural things are very similar to those of a sceptical atheist, and while I agree that there is no scientific evidence for deities and the supernatural, I don't at all agree with the conclusions generally drawn from this, so I'm not using "our" here.

² The definition of "supernatural" versus "natural" is hardly the dichotomy that it's made out to be - see Clarke's Third Law. Determining whether a "supernatural" event is really "outside nature" or just a sign that some previously reliable theories need refining would in practice keep people busy for centuries or longer. Meanwhile, by definition, anything genuinely supernatural would not be amenable to scientific study.

³ People asserting a scientific backing for their claims, when their claims do not meet general scientific standards, should be criticised for this, of course, and claims that are purported to be scientific can of course be meaningfully analysed by scientific methods.

Alternative vote and the flaws with proportionality arguments

One of the arguments that's used against adopting Alternative Vote (AV) is that it isn't a proportional system, and in some cases is "less proportional" than First Past the Post (FPTP).

This argument annoys me not because it's false - it's entirely true - but because it's not relevant.

You can apply second-preference polling to the First Past the Post result fairly easily - the BBC has a chart of the 1983-2005 general elections and my alternative vote swingometer uses roughly the same calculations for its 2010 base case.

You can tell from this fairly easily - play around with the AV swingometer if you're unconvinced - that AV ends up more proportional if the winning party of Conservatives and Labour has less Lib Dem support than the second-placed party (as happened in 2010) and less proportional in the opposite situation (as happened in 1997).

This doesn't actually make a lot of sense, though.

Firstly, it's not sensible to assume that first preferences under AV are the same as votes cast under FPTP. You're essentially assuming no tactical voting if you do this, and while the extent and impact of tactical voting is heavily debated, no-one denies that it does occur. At the moment, polling suggests that 5-10% of voters do not cast a FPTP vote for their AV first preference, but the nature of tactical voting means that these may be more concentrated in the marginal constituencies.

It's difficult to model accurately. I'm not too bothered about it in the AV swingometer yet, because there's very little useful polling, and the boundary changes will mean that it's not particularly useful for predicting an election result, as opposed to looking at the general impact of particular preference distributions, at the moment. However, for talking about "what ifs" for previous elections, it matters.

People will vote differently under different voting systems, as the polling shows. Parties will campaign differently under different voting systems, because the proportion of the electorate that they really need to appeal to for a majority changes, and even which parties can exist with a reasonable chance to get elected changes.

Secondly, in a preferential system, the concept of proportionality starts to break down. Proportional to first preferences is usually what is meant, but that's not necessarily meaningful either because the preference ordering doesn't tell you about the gap between the preferences.

At the last election, had it been AV, I would have taken a long time to decide which order to put the first two preferences in, and it would have been - as it was under FPTP - a very marginal decision. The third to sixth preferences would have been very easy as there would have been a wide margin. So for proportionality my vote should probably have counted in the ratio 50:45:3:2:0:0, but someone else casting a vote with the same preference order might mean it as 70:20:5:2:2:1

Thirdly, neither is designed as a proportional system - it's not possible to have a proportional system while keeping a strict one MP per constituency and not having top-up MPs (this isn't quite true, actually¹). Comparing AV and FPTP on proportionality, as well as depending on a number of false assumptions about voting habits and hidden definitions of proportionality itself, to me doesn't even make sense. It's like comparing two cars based on which one needs the shortest runway to land on.

A comparision between AV and FPTP should be based on the effect they will have at the constituency level, on campaigning methods and incentives, on the effect on political decisions, and so on. There may well still be consequences in that to make a supporter of proportional representation prefer FPTP over AV given that a PR system is not on offer (though that isn't my view).

¹ Single-seat proportionality

There is actually one voting system which will usually (it's not actually guaranteed, but with the hundreds of constituencies the UK has, it's fairly likely) give a significantly more proportional result than FPTP using the existing constituency set up.

I call it "Vote From Hat". You take all the votes cast within a constituency, discard those for which voter intent cannot be determined or are otherwise invalid, and put the remainder into a giant hat. Stir well. The Returning Officer then selects at random a ballot paper from the hat, and declares the candidate chosen by that ballot paper to be the winner.

For a large enough number of seats this is almost as proportional as a whole-country list system would be, provided that there aren't huge turnout differentials or size differences between seats.

A quick review of the advantages of this system.

• Generally proportional on both a regional and national level. Regional parties (the Northern Ireland parties, the SNP, Plaid Cymru, Mebyon Kernow, etc.) are represented roughly proportionally within their regions without significantly affecting the national proportionality of the nation-wide parties.
• Maintains a strong constituency link as there is one MP per seat.
• Strong incentive to vote - your vote could literally be the one that makes the difference, in any constituency.
• Easy to get rid of unpopular MPs. Actually, quite easy to get rid of popular ones, too. There is no such thing as a safe seat.
• Very quick to count, and no need for recounts.
• No incentive for tactical voting - you should always vote for the candidate you genuinely want to win.
• Election night is much more exciting - even if the government comes out, as it did in 2001, with much the same number of seats that it started with, that doesn't mean that they'll be the same seats or that prominent ministers won't have lost their seat.
• Shows that proportionality is not the sole criterion by which a voting system should be judged.

Sadly it's not on offer.

Fighting red herrings on abortion

In the news recently has been Cameron's statement that the time limit for abortion should be cut to 20 or 22 weeks. This is not surprising news - he voted for 22 weeks the last time (2008) the question came up in the Commons, and many Conservative MPs (as well as some from other parties) favour larger cuts.

He claims as the reason "the way medical science and technology have developed in the past few decades". Unsurprisingly, the general response has been the same as last time, to point out that the evidence he's using for that claim is wrong.

This is not the full story.

The problem is that currently the way the debate has been framed is that the time limit on abortions¹ in the UK is set with reference to the survival chances of premature babies born after an equivalent length of gestation.

Cameron and others claim that the survival rate of premature babies born in the 20-24 week period has improved significantly. Numerous doctors and scientists claim - with the support of the scientific literature - that this is not the case, although the proportion surviving who are born after 24 weeks has improved considerably.

It's a concern, definitely, if the leader of a political party is misinterpreting or unaware of the relevant research, and people are absolutely right to point this out.

The problem is that relatively few people are also pointing out that the entire basis of the argument is flawed. There is no good reason - historical inertia from the original legalisation I'd view as an "accurate" rather than "good" reason - why the survival of premature babies once born should be at all related to the time limit for abortion.

The original argument may have been to set a distinction between "alive" and "not alive" that wasn't fertilisation, conception, or birth - and if that was what was needed to get the original legalisation passed, that's fair enough. The distinction is absurd, though, and I think it's necessary to also point this out.

If medical science was to develop an incubator environment that could duplicate the uterus so well that not only did the survival rate for premature babies at any stage of development increase massively, but that babies could develop right from the embryo stage in this environment (which would be a massive boost for some branches of fertility treatment) this would hardly mean that abortion for non-medical reasons should be banned. Almost all the reasons why someone might want an abortion would still apply despite this technology existing.

Conversely, assuming that Parliament and scientific research could move rapidly enough, what about the case where a war or natural disaster significantly reduced the UK's medical and scientific resources and capabilities, to the point where survival of premature babies in the 24-30 week range became highly improbable. I doubt those now calling for a lower limit would support it being raised anyway, but it would be slightly absurd to do so even if they did.

Basing the abortion time limits on - effectively - how good the local health service is seems logically indefensible. It may have been a necessary thing to do politically at the time, and it's fortunate that the limit it provided then was a high one, but continuing to accept it as a correct way of deciding the limit will eventually be a very bad strategy. (While the reduction from 28 to 24 weeks in 1990 probably could not have been avoided in practice due to the size of the Conservative majority, it was done under exactly these grounds)

It's quite clear from the votes on 12-week and 16-week limits that some MPs would rather it was reduced significantly below any plausible limit this argument could provide, and would probably have voted for 0-week if the option had been there. If they don't accept it as a dividing line, I don't see why I should either when opposing them. The time limits at which abortion is available should be related to when it is necessary for the woman involved, not to what another woman's premature baby's chances of survival are.

So Cameron is wrong on the science, but he's even more wrong that the science is relevant in the first place.

¹ Excluding Northern Ireland, where abortion remains illegal and the government refuses to do anything about it, and excluding those medically necessary to save the mother's life or prevent serious (but not less serious) injury to her which can occur at any time.
Technically those within the 24 week period must be justified by the prevention of harm to the mother or her existing child(ren)'s health (physical or mental) but the majority of doctors correctly interpret this broadly.

Postscript

Other things that are infuriating about the way that the political debate over abortion is conducted in the UK:

• Northern Ireland. The UK Parliament has the authority to legalise abortion there (which in practice means legalising abortion for poor women there, rich women being able to afford the ferry/plane trip to one of the other UK countries) but not the courage to do so.
• "Free votes". All three major political parties give their MPs a "free vote" on abortion. I don't object to free votes as such, but this means that none of the three will ever include anything explicitly pro-choice in their manifesto, because this custom would stop them being able to require their MPs to follow it. They don't have to follow the custom, but for now they'll continue to do so. On other so-called "moral issues" the parties have quite happily set an official line. This seems to be a case where they're secretly happy to be bound by a pointless Westminster tradition.
• Parliamentary timing. The amendments to the HFE Act that would have reduced the time limit to 12, 16, 20 or 22 weeks all got debated and voted on. Two pro-choice amendments (one to remove the requirement for two doctors to agree, which is not required for any other medical procedure; one to bring Northern Ireland into line with the rest of the UK) were scheduled later and didn't make it to a vote. That hardly seems balanced, and if that pattern - with a Labour government mostly in control of the timing - continues, any erosions are going to be very hard to reverse.