Sunday, February 12, 2012

Men from Venus, and other confusions solved by statistics

I remember that after starting college in my late teens I was sometimes bothered by generalised descriptions classmates made about men and women, rich and poor, Irish and British and so on. When people said that 'women' had one characteristic and 'men' had another I was full of doubts because I saw exceptions everywhere. There were gentle men and aggressive women, grasping women and submissive men, monogamous men and promiscuous women. Classmates based entire arguments on their understanding of 'human nature', but there were selfish people and selfless people, homicidal people and suicidal people. Which of these represented the 7 billion others?

I thought: generalisations are useless because when one meets a member of a particular group one cannot know if this individual is typical of the group, or an exception. I dismissed off-hand any argument based on human nature because I thought no single human nature could exist when individuals were unpredictable, behaving in diverse ways.

It was easy to take this perspective because the generalisations being made were often clumsy and did not match my own experiences. I remembered being irritated listening to some radio pundit remark that: 'I think all teenagers hate their parents.' I didn't! It was common to hear unsupported generalisations about nationalities, classes, and age groups, especially winking and back-slapping over the heavy alcohol-use associated with Irish culture. I didn't drink at all at that stage so this stereotyping seemed ridiculous.

Yet I did see that lots of Irish people did drink a lot, and short trips to France and Italy showed me that this particular culture of binge-drinking was not universal. So is it true to say that 'the Irish' drink heavily or not?

Statistics to the rescue
It took me a long time to reconcile the fact that there are both trends and exceptions and that, if I'd been honest with myself, my day to day life took account of both already.

Let's go back to alcohol with the Survey of Lifestyle, Attitudes and Nutrition in Ireland; A profile of drinking patterns and alcohol-related harm from SLÁN 2007. Respondents to this survey were asked how often they had an alcoholic drink over the previous year.
The left-most bar of people saying they consumed no alcohol in the previous year is the one I used to belong to. It seems to be quite a big exception: 19%. One in five Irish people don't drink! This would bring me back to my initial concern with generalising: how can people say that 'the Irish' like to drink when a fifth of the adult population have not touched the stuff over the last 12 months?

But there's more to it than that. First, drinking patterns differ between men and women. Only 15% of men reported never drinking, compared with 23% of women, so as a man who didn't drink I was in a slightly smaller minority.

Next, age. Below are two graphs, the first showing drinking rates for people between 18 and 29, the second showing rates for people over 65:

Only 11% of the younger group said they drank no alcohol in the previous year. So instead of belonging only to the fifth of Irish people who didn't drink, I also belonged to the tenth of young people who didn't drink. This again showed that I was yet more unusual, to be young and male and still never drinking.

(The comparison with the drinking trends for older people is interesting for a few reasons. First, why the discrepancy? Do people drink less as they age, and they move out of the binge-drinking party culture? Are older people carrying on the cultural patterns of another time, when people drank less? Or did the heavy drinkers just die off before they hit 65? Perhaps the moderate drinkers did if not the heavy - the proportion of people who drink over four times a week is actually higher among the elderly group than among the young.)

Seeing the stark differences between the old and the young, is it fair to say that younger people 'drink more' than older people?

Nah, not really, and it's that kind of generalisation that irritated me when I was younger. On encountering a young man we still don't know if he is part of the 11% who never drink or the 34% who drink 2-3 times a week. That older lady we bump into could be one of the 10% of over-65s who drink four or more times a week and has a hip flask buried in her handbag. How would we know?

Chances are
The answer is probability. If we know of an individual who is Irish, our best guess is that there is a one in five chance that he or she did not drink any alcohol over the last year. With extra information we can narrow it down. Is the person male? Then only a 15% chance of not drinking over the previous year. Is he young? The chance decreases further. Piling on additional information gradually improves our estimate for how an individual can be expected to behave.

We are still uncertain. Now, though, we can quantify our uncertainty a bit better, work out the likelihood that our individual shirks the trend or not.

Of course I was doing this already. If I had to enter a street with a group of female pensioners on one side and a group of teenage boys on the other, I would probably have made a snap decision to join the pensioners because deep down I judged the teenagers a greater risk. Rightly, of course: the vast majority of violent crimes are committed by young men. With further information I might reverse that decision: if the teenagers seemed quiet, or the pensioners drunk and noisy, I might push on through the youngsters.

There will always be exceptions and as children we had also always been taught not to base guesses about a person's probable behaviour on such things as race or sex. In the classroom we were given grim stories about slavery and the Holocaust and told that discrimination was wrong, but outside we got informal messages about spotting trouble by people's appearances. So I had always been weighing up our cultural aversion to discrimination against impulsive common-sense guesses about how people will behave.

Perhaps this all seems obvious - really I'm saying that most members of a group may have certain characteristics, but not all - but some of the subtlety is lost in public debates. When, for example, wage differences between men and women are discussed, it is the mean wages that are considered. The mean is made of data from the combined incomes of a great many individuals, divided by the number of individuals. That the male mean is higher than the female mean does not mean that 'men earn more than women' because there will be high-income women and low-income men. But, knowing nothing more than a person's sex, our guess about their likely income is slightly improved. The probability of finding a high-income man is higher than that of finding a high-income woman, more or less. So generalisations can be useful, so long as the extent of uncertainty is considered.

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