How to Lie with Statistics

Statistics is hard.  Let’s all go to the beach.

You know, I really enjoy being an information analyst.  Statistics has been a very rewarding career choice.  Over time I’ve learnt to swim through data like a fish dives through water.  In fact, remove me from statistics and I’d probably flap around gasping to breathe just like a landed fish.  But after many years I’ve come to accept that the vast majority of the population simply don’t “trust” statistics.  I admit not without good reason.  On the one hand we’re bombarded with statistics every day, mostly from the media (both “as reported” and by advertising).  On the other hand statistics are too often twisted, corrupted, misrepresented, biased, misused, falsified, misreported or sometimes simply ignored (not by me of course, heh).  No wonder some people throw up their hands and declare it’s all too hard.  Why bother paying attention anyway when 83.7% of all statistics are simply made up on the spot?

With that in mind I’ve just finished reading How to Lie with Statistics by Darrell Huff.

I understand that How to Lie with Statistics is one of the, if not the highest selling books on statistics ever written.  An extraordinary achievement, especially considering Huff had no formal training in statistics.  The concepts are all too familiar to me, but of course How to Lie with Statistics is not aimed at the professional.  It’s very much an introductory text aimed squarely at a non-technical audience.  My copy was a mere 124 pages long, making How to Lie with Statistics something that can be digested in just a couple of hours.  First published in 1954 it’s striking how, even though some of the language has dated terribly (“Negro”? “Mongolism”?), the basic ideas expressed inside are timeless.  Warning people to beware of such things as hidden bias, inappropriate sampling, “conveniently” omitted details, and inappropriate measures (e.g. using mean when median is more appropriate) remain as relevant in 2009 as in 1954.  They’ll still be relevant in 2059.

Duff certainly writes entertainingly and with good humour throughout, making How to Lie with Statistics a very accessible and enjoyable read.  More than 50 years after first being published, many of the statistical “sins” highlighted by Huff in his book are still being committed today.  By way of example – correlation being used to imply causation, graph scales used to exaggerate minor differences and “OK names” being used to mask dodgy sources.  In conclusion, How to Lie with Statistics will help the average reader identify the various statistics “sharks” that can lurk in these waters.

Safe swimming.

In future blog entries I’d like to expand further on some of the concepts that Huff wrote about in How to Lie with Statistics, hopefully using some real world examples.

Further reading:


The Wisdom of Gummy Bears

A couple of weeks ago I reviewed James Surowiecki’s The Wisdom of Crowds.  To briefly recap:

Under the right circumstances, groups are remarkably intelligent, and are often smarter than the smartest people in them.  Groups do not need to be dominated by exceptionally intelligent people in order to be smart.  Even if most of the people within a group are not especially well-informed or rational, it can still reach a collectively wise decision.

The book opens with an example of an impromptu experiment conducted by the scientist Francis Galton in 1906:

Galton was at a country fair where a live ox was placed on display.  Fairgoers were invited to guess the weight of the ox after it had been slaughtered and dressed.  Eight hundred ordinary people from all walks of life tried their luck.  They included experts such as butchers and farmers, as well as non-experts.  Out of interest, when the contest was over, Galton collected the used tickets and averaged the punters’ individual guesses.  This figure represented the “wisdom of the crowd”, and in this case the crowd had guessed the ox would weigh 1197 pounds.  After it had been slaughtered and dressed the ox weighed 1198 pounds.  The crowd’s judgement was essentially perfect.

I think this is amazing.  The “experiment” was a success because the “crowd” in this example had met Surowiecki’s conditions for making a “wise” decision. That is, they:

  1. were diverse, from a range of backgrounds, including experts and non-experts
  2. understood the process and outcome.  That is, the task was simply to guess the weight of an ox.
  3. acted independently using their own judgement to come to a personal decision, free of undue external influence
  4. made a decision that was aggregatable, in this case via Galton’s calculation of the average
  5. produced a result. The competition was run and when it was over there was a definitive winner.

Several weeks ago I had an opportunity to re-create Galton’s 100+ year old experiment.  I was at a party and one of the games was to guess the number of gummy bears in a big glass jar.  Like Galton in 1906 I was curious to test the decision making ability of a group of people.  So after the competition was over I asked the host for a list of all the contestants’ individual guesses.  A total of twenty three people had participated in the game and made the following estimates.

Contestant Contestant’s Guess
A 203
B 215
C 306
D 295
E 237
F 500
G 251
H 1000
I (winner)
J 450
K 150
L 300
M 1002
N 462
O 200
P 174
Q 295
R 187
S 305
T 420
U 483
V 250
W 1200
Average 402

In fact there were 387 gummy bears in the jar.  So contestant “I” was the clear winner (it wasn’t me, by the way!) with a guess of 369 gummy bears.  Not a bad effort.  Only 18 away from the true value.  But the really striking outcome for me was that the “crowd” faired even better.  The average of everyone’s guesses was 402, just 15 off the actual number.  In other words, the crowd was smarter than the smartest individual member.

An extraordinary result.

It also leads to an optimum strategy, if you ever find yourself participating in one of these “guess how much/how many” kind of games.  Wait until the last minute and take an average everybody else’s guesses.  In all likelihood that will be closer than any other individual estimate.

I didn’t follow my own brilliant strategy, by the way, which is why I’m not eating gummy bears at the moment.

The Wisdom of Crowds

James Surowiecki’s The Wisdom of Crowds turned the way I view the world completely on its head.  Concise, well thought out, and sharply written the premise behind The Wisdom of Crowds is this:

Under the right circumstances, groups are remarkably intelligent, and are often smarter than the smartest people in them.  Groups do not need to be dominated by exceptionally intelligent people in order to be smart.  Even if most of the people within a group are not especially well-informed or rational, it can still reach a collectively wise decision.

Obvious?  No.  This is a contradiction to the way many of us think of crowds.  Most of us, myself included before I read the book, might consider an individual person quite clever but would never describe a crowd as “wise”.  No doubt this is because we typically equate crowds with mobs.  And (as Surowiecki himself emphasises early on in the piece) a mob, of course, is profoundly stupid.  However stop to consider situations where crowds prove to be very astute decision makers.  A classic example of this is horse race betting.  It is no accident that the shorter-odd horses consistently finish so well.  Rather, a group of people is making a collective decision on an uncertain outcome that, time and time again, turns out to be remarkably accurate.

Which leads me to the critical conditions underlying Surowiecki’s hypothesis.  For a crowd to be “wise” it must be under the right circumstances.  In order for a group of people to come to a collectively good decision, it must:

  1. Be diverse. That is, a wide range of backgrounds is essential, including experts and non-experts.
  2. Have a basic grasp of the process and outcome. You wouldn’t necessarily ask a group of non-doctors to make a decision on a surgical procedure.  Not the same way you would on the outcome of a horse race at least.
  3. Act independently. That is, individuals in the group must be allowed to use their own internal judgement systems to come to a personal decision, without influence from each other and “outside”.
  4. Aggregate-able. There must be some way of crystalising the crowd’s collective “decision”.  In the horse racing example the aggregating system is via odds calculation.  The horse with the shortest odds is the group’s pick of the winner.
  5. Produce a result. For example, a race will be run and when it’s over there will be a definitive winner.  The stock market, on the other hand, isn’t as suitable as it’s in perpetual motion.

In essence Surowiecki details where group decision making can work, when it can work best, but also how it can fail.  Based on a simple but counter-intuitive theory that seems obvious by the end, it presents a compelling argument.  You don’t need a degree in statistics to enter.  The Wisdom of Crowds is aimed squarely at the non-technical audience and it hits that target.  Included is plenty of supporting evidence and examples in the form of entertaining anecdotes highlighted to press home its case.  It’s a great read, a real page-turner, and I highly recommend it.  If you’re looking for gift ideas this Christmas then The Wisdom of the Crowds would be an excellent addition to the wish list.


“Meet me by the tram stop.  I’ll be the one wearing a hat.”