I always thought this was an eerie echo of what has happened in our information age, which could not possibly have been foreseen by Rand. We have perfect knowledge available to us, like never before in history. But that access is limited by the knowledge's source. Google: Santorum. Perfect knowledge. Devastating result - that is, if you want intelligent answers.
Numbers are the perfect medium through which to propagate misinformation. Quoting numbers is like quoting an irrefutable, dispassionate expert, someone who is not there but has complete authority - and because you are the source of which numbers you report, you may as well be writing the words your expert is saying.
Consider a marketing campaign for the cigarette brand Triumph. Merit cigarettes were a popular national brand, and if you are the VP of marketing for Triumph, you might think that a 'taste test'(cough, hack, I know, right?) of the two would be a good idea.
Triumph did exactly that - a taste test vs. their competitor Merit brand cigarettes. Their results for stated preference were:
- Triumph - preferred by 36%
- Merit - Preferred by 40%
- No difference - 24%
If you are Triumph's VP of marketing, these results are not what you were looking for. But these are numbers, remember? You can work with this, even though your brand was actually preferred by less people. Triumph boasted the results in their campaign:
"An amazing 60 percent said Triumph was as good or better than Merit"
Isn't that neat? A fantastic example of how you can take perfectly good numbers and use them to your advantage. You may call this "lying", but I assure you it's a kind of creativity we often reward in our society. If you were that Triumph VP, do you think "We're about the same as Merit, really" would have been a better choice of campaign?
How could using average be bad?
An easy illustration is something called the Bill Gates example. Imagine a homeless shelter filled with 50 homeless people. Average income, say 3,000 per year. If Bill Gates walks into that homeless shelter, the average income of everyone in that homeless shelter would skyrocket to an estimated $152 MILLION dollars. But that's not exactly fair, is it? In this case, the mean or median would be much more fair. Explained another way here.
I don't mean to entirely bash numbers. I LOVE numbers. Good statistics are an excellent way to understand a subject at it's core. The problem is that confirmation bias is so strong that people often see what they want to see in those numbers. Worse, ad agencies, politicos and Media representatives may want to prove something they are saying, and in an effort to support their story they may slant those numbers. It's not hard to do. It's actually harder to resist doing it, as anyone who has ever written a paper knows.
Change your assumptions, change your results
The first two examples are quite simply, selective reporting - touting one number as important while discarding relevant information. But it's also possible to completely change the outcome of the numbers based on assumptions that you, well, make up out of thin air.
Businesses do this all the time, and they have to. Forecasting sales of a new product is a flight of fancy - I know, I've done this several times, and sometimes it feels a bit like witchery or an ouija board. I prefer dice. But really, how can you predict a result for something that hasn't happened? I am not sure. Let's ask the guys that forecast sales for New Coke.
Easy example: government budgets. If you travel on over to the CBO you'll see their budget forecasts for the next year. Dig a little deeper into those forecasts and you'll see that those forecasts are based on assumptions. Of COURSE they have to be. Will the next congress renew those expiring tax breaks? Pass the proposed budget as proposed or with amendments? Hard to say. But if you want to lie outright, you could use those numbers and change a few of the assumptions, thereby changing the result pretty quickly. When dealing with large delicate numbers systems, tiny changes - say a 1% tax rate change based on an expiration date that never happens in actuality - can make a gigantic difference in the numbers.
Creating your own actual factual statistics that have a numbers-y feel without being really real at like, all.
The last, favoritest and bestest way to lie with numbers is to just go completely batcrunch crazy with your associations. This is more logic-based than numbers-based, but it sure is fun, and you can do it yourself!
1) Notice something
2) Notice something else about that something
Conclude that the two must be related for no other reason than the two coexist in the same space.
For instance, I was at Starbucks today. A group of wine representatives were having a meeting there. There were 10 total people in the store, 6 of which are wine reps, I therefore logically conclude that 60% of Starbucks' customers are wine reps.
FUN, RIGHT? By the same logic I have concluded just now that
- 33% of all backpacks belong to second graders(n:3)
- 100% of wives enjoy wine(n:5)
- Electric banjos outsell trumpets in America by an infinite margin (n:1)
- 100% of American households contain hundreds of legos(n:1)
- The average ear contains some 10+ small, irritating hairs on it(n:2)
- The median number of bananas in kitchens across america is 11.(n:1)
- 100% of dads are supremely cool (n:1)
(for accuracy, I included "n" - the statistical sampling size used in these conclusions)
These are ALL sample size problems, as you have probably guessed - there just isn't enough data to conclude anything. This is why Pharmaceutical companies conduct trials on hundreds of patients before their findings even approach any kind of validity.
Graphs lie effectively 100% of the time
I'll leave you with the below graph, which illustrates another excellent way to lie: using scaling in a graph. See if you can figure out the two main reasons that the graph below is painfully misleading! And good luck lying with numbers! :D