Read and summarize the chapter called “Shocking Statistics”. real life situation did you or someone you know ever find themselves in that was similar to

Read and summarize the chapter called “Shocking Statistics”. real life situation did you or someone you know ever find themselves in that was similar to what you read about in “Shocking Statistics.”  If not, imagine a scenario that you may find yourself in one day and talk about that. (150-200 words) Shocking Statistics tatistics are the chemical weapons of persuasion. All good
Spolitieians and businesspeople know this. Release a few sta-
tistics into the discussion and the effects will be visible within
moments: eyes glaze over, jaws slacken, and soon everyone will
be nodding in agreement. You can’t argue with the numbers. Yes you can. Even when the numbers are right, they often
don’t show what they are alleged to. For example, newspaper edi-
torialists are always leaping from statistics about changing behav-
ior to conclusions about changing, and usually worsening, values.
Behavior can change, however, not because values do but because
the circumstances do. Teenagers commit more street crime now
than in 1930. Is that because teenagers have less respect for pri-
vate Property or because there is now so much more to steal from
People on the street—most notably, their mobile phones! People
“at more now than they did in 1950. Is that because we have
become Sluttonous or because food is cheaper? 133 I34 CRIMES AGAINST LOGIC Drawing the wrong conclusion from statistics is an interest-
ing mistake, however, only if the statistics are right in the first
place. And often they are not. Consider the following statistics: 35 percent of British children live in poverty. 50 percent of small-business owners would switch banks
to receive a discount of 0.25 percent interest on their
overdrafts. 25 percent of young drug users have smoked cannabis
with a parent. 2 percent of young women suffer from anorexia nervosa,
and 20 percent of sufferers die from it. Each is from a reputable source. Each is also the result of a simple error of statistical method. (Sources don’t seem to become
reputable by being good at statistics! Understanding these errors is not difficult, as I hape this chap-
ter will show, but it is important. Widespread statistical naiveté
allows nonsense statistics like these to become the "hard facts”
that inform decision-making. British Poverty Soon after coming to power in 1997, the New Labour government
drew our attention to a shocking fact: 35 percent of children in
the United Kingdom live in poverty. Not absolute poverty, of
course; even the poorest are at no serious risk of going without
food, housing, schooling, or medical care. Rather, 35 percent of SHOCKING STATISTICS I 3 5 children live in relative pOVBIt)’: by the standards of modern Brit-
rain. the? are relatively poor. . 011 pages 99-102, I complained that the Labour government
played fast and loose With this ambiguity in the word poverty.
"We need to fight poverty, " they claimed. Why? Because poverty
is dreadful and there is so much of it. But this is merely a play on
words. Absolute poverty is dreadful [but rare]; relative poverty is
common [but not so dreadful). In this chapter, however, I want to set that issue aside and
examine only the claim that 35 percent of British children live in
relative poverty. This claim illustrates a common way in which
statistics can mislead: by being based on an improper measure of
the phenomenon in question. The government measures the number of people who live in
relative poverty as the number living in households with incomes
less than 60 percent of the national median income. We must
accept that 35 percent of children live in such households. Still,
why should we conclude that 35 percent live in relative poverty?
Why, in other words, is household income less than 60 percent
of the national median a good measure of relative poverty? The short answer is that it isn’t. In a country like the United
Kingdom, disposable income inequality is a hopeless way of
measuring relative poverty. To see this, consider two twelve-year-old boys who live
next door to each other. They live in the same quality of
house, attend the same school, go to the same doctor when
the? are sick, wear the same brand of athletic shoes, and so on.
Indeed, their material well-being differs in only one respect: x 136 CRIMES AGAINST LOGIC Jimmy’s parents give him £10 a week in pocket money, Timmy
gets only £5 pounds from his. Should we conclude that, since his
disposable income is only half of Iimmy’s, Timmy is a pauper rel-
ative to Jimmy! Obviously not. Jimmy and Timmy’s consumption is almost
identical. Let’s suppose that the housing, clothes, schooling, med-
ical care, and so on that they both receive are worth £100 per
week, and that both spend all of their pocket money. Then Jimmy
consumes £110 per week and Timmy consumes £105 per week.
Though Jimmy’s disposable income is double Timmy’s, he is only
5 percent better off. When a large percentage of consumption is not paid for out of
disposable income, differences in disposable income will always
exaggerate differences in the ability to consume. And it is the
ability to consume that is important with regard to poverty,
including relative poverty. 50 the govemment’s measure of relative household poverty is
wrong. Like Timmy and Timmy, British households need not pay
for much of what they consume out of their disposable incomes.
Most importantly, medical care and education are delivered by
the state, funded out of tax revenues. And, so far as the govern-
ment’s measure of poverty is concerned, housing is free too, since
it uses disposable income after housing costs. In a paternalistic society like Britain differences in disposable
income will overstate differences in consumption capacity and
hence in the number suffering relative poverty. This point has
nothing to do with redistribution of wealth. 1f taxes were high
but all benefits were paid in cash rather than state services, then
disposable income would accurately reflect consumption capac- snocxmc STATISTICS 137 ity, and relative income would be a reasonable basis for evaluat-
ing 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 somediing hard to
measure, such as poverty, happiness, or beauty, you should
always check the measure used. Often it will be a crude apprent-
imation, acceptable for some purposes but not others. Sometimes
it will be plain wrong. Having alerted you to the danger, however, lean offer no gen-
eral guidance on how to tell good measures from bad. Each mea—
sure 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 infor-
mation 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 set], the greater the profit
you make on each sale [unit profit). 50 why not just set outra-
8601-181)! high prices! Because you would have no sales. Unlike
“nit profit, sales volumes decrease as prices rise. If you want to
W” YOU-r 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 SiVen price and the volume at that price. The former is I 38 canoes AGAINST LOGIC simple when you know your costs.I 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 with-
out gaining volume, which is why companies often conduct mar-
ket research before making any price changes. Alas, such research
often gives misleading results, for a simple reason: people lie. Specif-
ically, 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? 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 man-
agers switching banks in an instant. But small discounts are
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 dis-
counts 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. 1. This is a simplification. Where a portion of costs is fixed [i.e., does not vary
with sales volume, such as television advertizingl, unit profit also depends on
volume, since average unit costs will vary inversely with volume. Most busi-
nesses have some fixed costs, so knowing unit profit at any given price also
requires knowing volumes at that price. But the point still holds: the difficIJlt
part is knowing how price affects volume. SHOCKING STATISTICS r 39 50′ 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 busi-
nesspeople 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. It is generally best to be skeptical about the results of surveys
that get their data merely by asking people about their inclina-
tions 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 misrepre-
sent. For example, you would think that voting intentions are
something on which you could take anyone’s word. But they
aren’t. The UK. Conservative Party’s 1992. general election vic-
WY 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, he warned. If even Tories can’t be relied
upon seeretly to admit it, there is little you can take at face value. Dope with Dad?
:1: always refreShing to discover a good news story in the paper.
. mgught I had encountered one in the London Times (Feb. 2.4,
"stall” 2) under the headline “Drug Parents." It announced that
” Pareztafiuarter 0f Vol-“’18 drug users have smoked cannabis with ‘ Family life is not dead in Britain after all. k I40 CRIMES AGAINST LOGIC Alas, I read on and discovered that the statistic couldn’t be
trusted. It was the outcome of “a survey completed by 493 read-
ers of rave magazine Minnag.” You will see the problem. Even if
those who complete surveys in Mixmag can be relied upon to tell
the truth about their drug-taking habits, they are hardly a repre-
sentative sample of young drug users. They are, for a start, peo-
ple 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 mag-
azine 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 as sample bias. The sample was not characteristic of young drug users more gener-
ally, 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. Newspa-
pers such as the London 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. SHOCKING STATISTICS I41 About ten years age, 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 marchers, letter-to-the-
editor writers, and even party members attending the annual con-
ierences. Only fanatics take part in such political activities, and
most voters aren’t fanatical. Most cases of sample bias are quite obvious but some are
difficult to detect. For example, you might think it reasonable
to take a “snap shot” approach to discovering the average dura-
tion of periods of unemployment. Contact some portion of the
unemployed population on one day of the year and ask them how
long they have been unemployed. Provided the sample is large
enough, its average is the average for all those who experience
unemployment. In fact, this sample would dramatically bias the result upward.
Pimple who are unemployed for long periods are much more
likely to be unemployed on any given day than people who are
Unemployed for only short periods. Lots of people who have been
unemployed for a week are back at work on the day of the poll.
S0 the? don’t get counted. But everyone who has been unem-
Ploi’ed for years is unemployed that day and so they all get
Counted. To avOid this bias, you need a sample of people, not who
are unemployed today, but who have been unemployed at some L I42- CRIMES AGAINST LOGIC time in the last, say, ten years. The average term of unemp10y_
ment in this sample gives a better answer.z Before moving on, I cannot resist mentioning a really egregious
case of sample bias. For many years now, it has been taken as a
well-established fact that 10 percent of Western men are homo.
sexual. Most believe this statistic but do not know its source. It
is Kinsey’s Sexual Behavior in the Human Male, published in
1948. Alas, 25 percent of the sample used for Kinsey’s survey
were prison inmates, despite the fact that prison inmates were
only 1 percent of the American male population. Since they live
in an all-male environment, prison inmates are more likely to
have homosexual sex than other men. It does not follow that less than 10 percent of men are homo-
sexual after all. There were competing forces at work in Kinsey’s
survey, especially the tendency of people to lie about what was
then a taboo activity. 50, for all Kinsey’s research tells us, we have no idea what percentage of men are homosexual.a Looking out the
window of my office, [would be inclined to think it is more than
10 percent. Then again, my office is in Covent Garden. Anorexia and Other Big Small Numbers The BMA called for the fashion industry and television
to stop focusing on “abnormally thin" celebrities, such 2. I owe this example to Steven E. Landsburg, The Armchair Economist lNW York, The Free Press, 1994], p. 132. I say a better answer rather than the right
answer because this sample may not reflect recent changes in average periods
of unemployment. 3. Better research by Edward Iaumarm in 1994 found the percentage 0′ men
who are consistently homosexual to be 4 percent. SHOCKING STATISTICS 143
as Kate Moss, Callista Flockhart, and Victoria Beckham
of the Spice Girls, and for the Government to set targets
on reducing the disease. Anorexia nervosa affects about
2 percent of young women and kills a fifth of sufferers.
-The London Times (May 31, 2000)
The British Medical Association (BMA) is always calling on
people to stop doing this or that on account of its dreadful effects
on the health. Normally, their mistake is in thinking that health
is all people care about. I may know that smoking is bad for me
but persist in any case, because I prefer a short and smoky life to
a long fresh one. On this occasion, however, they went wrong on
what should be their home ground, namely, on the medical facts
and figures. The idea that anorexia affects 2 percent of young
women and kills a fifth of sufferers is ridiculous.
There are 3.5 million British women between the ages of fif-
teen and twenty-five. If 2 percent of them suffer from anorexia
nervosa, that is 70,000. And if a fifth die from it, we should expect
14,000 young women to die from anorexia each year.* You will
begin to suspect that something has gone wrong when I tell you
that in 1999 the total number of deaths in women from this age
group, from all causes, including anorexia, was 855. Can anorexia
really kill sixteen times more young women than even die?
4. Death rates from a disease are normally expressed annually, i.e., as the per-
centage of sufferers who will die in a one year period. If the 20 percent death
rate of our example is not annual, but over some longer period, then the num-
ber of anorexia-caused deaths each year would be smaller, but not small enough
to save the alleged statistic from massive error. For example, if 20 percent die
in a ten year period, then the number of deaths each year in women from 15 to
35 should be 2,800. I44. CRIMES AGAINST LOGIC We need not flounder around in the dark. Causes of death are
recorded and the figures are available from the National Statis-
tics Office. We can check the number of anorexia-caused deaths
in young women. The BMA’s figure must be wrong, since no dis-
ease can kill more people than die. But how wrong is it? The figure of 14,000 is more than a thOusand times greater
than the truth. The number of young women who died from
anorexia nervosa in 1999 was 13. Not 13,000. 13. If I were Callista Flockhart, I’d have sued the BMA and the
Times. By encouraging the media to stop focusing on her, they
attempted to ruin her career, on the bogus allegation that look-
ing at her makes people die of anorexia. Millions of young Brit-
ish women watch Callista Flockhart and at most thirteen die
from it each year. That makes Ms. Flockhart safer than crossing
the road. I’m not Callista Flockhart of course, so I did not sue the BMA
or the Times. But I did write to the editor of the Times pointing
out their error. Neither my letter nor a correction was published, and I received no explanation of how they could have published
such a crazy number. So, I am left to guess at where things went
wrong. My suspicion is that Helen Rumbelow, who wrote the article,
suffers from an ailment that afflicts 25 percent of journalists and
makes a fifth of them talk nonsense.5 She has no sense of scale. When numbers get very small or very big, those afflicted lose all
sense of whether or not they are reasonable. We all suffer when the subject matter is unfamiliar. Is forty bil-
lion dollars a good price for a space shuttle, or is it a bit over the 5. If the BMA isn’t too good to make up statistics, nor am I. n: SHOCKING STATISTICS I45 mpg Most of us wouldn’t have a clue. Is 0.01 of a second a rea- gamble period of time for an electrical impulse to cross a synapse
in your brain? Again, unless you are a neuroscientiat, you’ll have
no idea. And anorexia deaths in young women! Well, 2 percent
isn’t very many. And if only a fifth of them die, that’s a very small
number: only 0.4 percent. Seems reasonable, doesn’t it? Usually, 0.4 percent is quite a small number. When it comes
to deaths in young women, however, its enormous. Young
women hardly ever die. Young men die a hit more. But, more or
1043; dying is the exclusive preserve of the old. That is something
you might have expected the BMA and a medical correspondent
from the Times to know, and they probably do know it in some general sense. But a very small number like 0.4 percent iust didn’t
ring the alarm bells. Just as small numbers can be bigger than they look, so big
numbers can be smaller. Barclays Bank’s profit announcement
prompts an outraged newspaper editorial every year. “Three bil-
lion pounds profit! And still they shut branches and sack staif.
Greedy bastards!” This misses the fact that Barclays is a very big
business with many thousands of shareholders. No single greedy
bastard gets that $3 billion. In 2002, £3 billion represented a
returnof only 15 percent on shareholders’ investment in the busi—
ness. That’s a reasonable return in these hard times, but hardly
scandalous. The same mistake is at work when you hear all those amaz- ing facts about the cost of repairing the damage done by a hurri-
cane, the economic value of joining the Euro, and so on. A cost 01 benefit that is spread across many individuals is summed up
ind Presented as a single, shockingly large number. Repairing
uni cane damage may cost an amazing $150 million, but it will I46 CRIMES AGAINST LOGIC be home by ten million Florida taxpayers, costing each of them
a much less amazing $15. Joining the Euro really might increase
the United Kingdom’s GDP by £3 billion per year, as the trea-
sury’s recent report claims. But sixty million participate in the
UK economy, so each benefits by only £50 per year, or £1 per week.6 Everyone enjoys being shocked by amazing statistics. But you
have to be able to believe them; the fun is wrecked by discover-
ing the statistics are bogus. The brief moment of elation I expe-
rienced upon hearing about the promiscuity of English women in
Spain was spoiled by discovering the shoddy sample selection
that lay behind it. If I hadn’t noticed the sample bias, I could have
enjoyed the alleged fact for longer. Ignorance is bliss, as they say.
But I console myself with the fact that I did not waste the price
of an airfare to Spain. Ignorance can also be expensive. That is the real value of learning to see through bogus statis-
tical claims. You don’t make the mistake of acting upon them,
by flying to Spain for unlikely sex or pointlessly lowering your
prices or supporting silly policies. 6. [owe this observation to an editorial by Anatole Kaletsky in the Times. lime
10, 2003.

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