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with redistribution of wealth. If taxes were high but all benefits were paid in cash rather than state
services, then disposable income would accurately reflect consumption capacp. 137ity, and relative
income would be a reasonable basis for evaluating relative poverty. The further a society moves from the
“all cash” model toward an “all state services” model, the worse is the disposable income measure of
poverty. And Britain is very far from the “all cash” model.
When presented with a statistic involving something hard to measure, such as poverty, happiness, or
beauty, you should always check the measure used. Often it will be a crude approximation, acceptable
for some purposes but not others. Sometimes it will be plain wrong.
Having alerted you to the danger, however, I can offer no general guidance on how to tell good
measures from bad. Each measure must be examined as it is encountered. This will often be difficult,
since alleged statistical facts are usually served up plain by newspapers, politicians, and businesspeople,
with little information about the precise measure used. Then the proper attitude is open-minded
skepticism.
Switching Banks and Other Lies
The higher you price the products you sell, the greater the profit you make on each sale (unit profit). So
why not just set outrageously high prices? Because you would have no sales. Unlike unit profit, sales
volumes decrease as prices rise. If you want to maximize your aggregate profit, as most business owners
do, the best price is the one that finds the right trade-off between unit profits and sales volume.
To work out this best price, you need to know the unit profit at any given price and the volume at that
price. The former isp. 138simple when you know your costs.[11.1]But knowing how price affects
volume requires you to understand the price sensitivity of customers. And that is more difficult.
Experimenting can be dangerous. You might guess wrong and end up losing all your customers or giving
away unit profits without gaining volume, which is why companies often conduct market research before
making any price changes. Alas, such research often gives misleading results, for a simple reason: people
lie. Specifically, they claim to be more price sensitive than they really are.
I recently commissioned a survey of the managers of small businesses in Holland regarding the size of
discount required to make them change banks. “How likely would you be to switch to a bank offering a
rate of interest on your overdraft 0.25 percent lower than your current bank? Certain, very likely, maybe,
very unlikely, certainly not? What about 0.5 percent . . .”
If you took the results of the survey at face value, even the slightest discount would have most Dutch
small business managers switching banks in an instant. But small discountsare available from some Dutch
banks, who do not in fact experience long lines of small businesspeople wanting to open accounts.
The good reason managers don’t switch banks for small discounts is that switching banks costs more in
time and bother than the discount is worth. On a $20,000 overdraft, 0.25 percent is only $50 a year, and
changing banks is a big hassle.
p. 139So, why do they say they would switch? I can’t be sure. But my guess is that they like to think of
themselves as astute businesspeople who would not pass up opportunities for a better deal. And saying
you would switch banks involves none of the time or hassle of actually doing it.
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It is generally best to be skeptical about the results of surveys that get their data merely by asking people
about their inclinations or habits. People have all sorts of reasons to misrepresent themselves. They
usually don’t mean to deceive, but even if they are only lying to themselves the results will still be
unreliable. If you want to know about the sexual prowess of men, for example, I wouldn’t advise
gathering your information just by asking them.
It is difficult to know in advance what people will misrepresent. For example, you would think that voting
intentions are something on which you could take anyone’s word. But they aren’t. The U.K.
Conservative Party’s 1992 general election victory came as a surprise to opinion polling organizations,
most of which had forecast a comfortable victory for Labour. Their post-election analysis of how they
got it so wrong revealed that many people who vote Conservative are reluctant to admit it, even in an
anonymous poll. So, be warned. If even Tories can’t be relied upon secretly to admit it, there is little you
can take at face value.
Dope with Dad?
It is always refreshing to discover a good news story in the paper. I thought I had encountered one in the
London Times (Feb. 24, 2003, p. 2) under the headline “Drug Parents.” It announced that “nearly a
quarter of young drug users have smoked cannabis with a parent.” Family life is not dead in Britain after
all.
p. 140Alas, I read on and discovered that the statistic couldn’t be trusted. It was the outcome of “a
survey completed by 493 readers of rave magazineMixmag .” You will see the problem. Even if those
who complete surveys inMixmag can be relied upon to tell the truth about their drug-taking habits, they
are hardly a representative sample of young drug users. They are, for a start, people who want to share
information about their drug-taking habits, which makes them more than usually likely to take drugs with
their parents. Then, there is the simple fact that they read a magazine about the rave scene, which is
notoriously drug-riddled. These aren’t typical young drug users; they are enthusiasts, the train-spotters of
the drug world.
This statistic is a result of what is known assample bias. The sample was not characteristic of young
drug users more generally, and was uncharacteristic in a way that made it more likely to give the result in
question.
The need to avoid sample bias when collecting statistics is well-known. The mistake is widespread
nevertheless. Newspapers such as theLondon Times should certainly know better, because they
frequently publish the results of political polls and sometimes even conduct them. Yet, if it gives a good
headline, they are happy to publish the results of a badly biased survey, as the example illustrates.
Our drugs statistic is an example of a common way of ending up with a biased sample, namely, letting
the sample choose itself. Those who volunteer to participate in surveys about something are not normal
citizens with respect to that something. They are more passionate than most. So, what is true of them is
not likely to be true of the wider population.
p. 141About ten years ago, the radio and newspapers were thrilled to announce that 40 percent of
British women who go on holiday in Spain have sex with someone they had not previously met within five
hours of arriving in the country. This statistic was gathered from a survey conducted by a women’s
magazine. They had invited readers with interesting holiday sex experiences to participate.
More broadly, self-selection bias explains why politicians cheerfully ignore the views of protest
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