Monday, February 28, 2011

How to Lie with Numbers

We're bombarded daily with statistics and numerical comparisons, usually in the context of someone making a case or supporting her perspective. More often than not, the numbers presented (even the accurate ones) are misleading, meaningless and/or irrelevant. And yet, people hear them, are impressed and then buy the argument. Sometimes they simply miss the fact that the numbers are meaningless, irrelevant and misleading and rather than asking, "What's that got to do with anything?", argue that the numbers must be wrong.

In a world where only some people know how to lie with numbers and others don't even realize that it's being done, well, it's... it's... not fair. Everyone should know how to lie with numbers or no one should. Since the latter horse has left the barn, I decided to write Doctor Tef's Guide to Lying with Numbers.

Percentage versus Absolute Value
The easiest and quickest way to transform an unimpressive number into an impressive one is to change it from an absolute value to a percentage or from a percentage to an absolute number.

For example, let's say that you want to impress someone with your increase in time spent exercising. Over the past 6 months, you've increased your time spent running from 4 minutes a day to 6-minutes.

Now, you could lead with an under-whelming, "Over the last 6 months, I've increased my daily running time by 2 minutes!" or you could super charge it with percentages. 2 minutes is half (or 50%) of the 4 you'd been running, so you could state the more impressive, "You know what? Over the past 6 months I've increased my running time by fifty-percent!"

Alternatively, if you want to torpedo the management of a large corporation that is struggling with financial results, you might transform the numbers from percentages to absolutes. Saying that a two-billion dollar company experienced a 5% loss in value is nowhere near as impressive as saying that the company lost $100,000,000.00. Five percent or one-hundred-million: same number, different effect.

As a rule of thumb, if you want to minimize the impression, use percentages with large numbers and absolute values with small numbers. If you want to maximize the impression, absolute values with large numbers and percentages with small ones.

Direction Matters
One of the things that confuses evened seasoned analysts is direction. If you start with 50 widgets and you end up with 150 widgets, that's an increase of 200%. How can that be? You start with 50 widgets You add 100 widgets which is 2 x 50 or 200%.

On the other hand, if you start with 150 widgets and end up with 50, you have a decrease of 66.6%. You lost 100 widgets which is two-thirds of what you started with or 66.6%. Same change in count, but completely different percentages.

This can get even more confusing when you intermix change and result. For example, the change from 50 to 150 is 200%; however, the result is that you have three times as many as you started with or 300%.

If I increase my monthly revenue from $1,000 to $3,000, I'm making three times as much as I was, but my increase was just 200%. On the other hand, if I decrease my revenue from $3,000 to $1,000, I end up making just a third of what I was with a reduction of 66%.

Transforming directionality is a technique shared by used car dealers and HR personel, alike. If I want to impress you with the discount I'm giving you on a car that I've reduced by $800 from $4,000 to $3,200, I don't say that I've reduced the price by 20% (800 divided by $4,000), I say that if I hadn't reduced the price, you'd be paying 25% more ($800 divided by $3,200).

If I want to minimize the impact of a pay reduction from $100 to $80 per week, I keep you focused on the the 20% reduction and steer you away from the realization that you used to make 25% more.

Ignore or Change Context
Of course, many of these techniques don't work unless you can successfully obfuscate context. Nothing spoils good number manipulation like someone saying something like, "25% of what?" or "What was the income before the loss of $100 million."

Obscuring context is a critical tool employed by hucksters, researchers, nutritionists, stock brokers, sports-casters, well, pretty much anyone who's using numbers to get what they want or to impress.

If you want to lie with numbers it's important to avoid questions that lead to context. For example, a statistic like "75% of people who tried thus and such saw an immediate improvement" sound impressive, but they don't actually mean anything without further context. What percentage of people qualified for the trial? How much improvement? Was it something only visible on a scope or something that people could see for themselves? Was the improvement sustainable?

She's a great CEO. She's taken a salary reduction of 50% until the economy gets better!

Sure, but what percentage of her overall compensation package is represented by salary? Does she have stock or options? Does she have other benefits?

Without context, the statistics don't mean anything.

Stats that Have No Place
One of the best ways to lie with stats is to use them in places where they have no business at all. This works particularly well when explaining to people why what they want to do won't work. Tell someone who is starting a business that 90% of new businesses fail. Tell a kid with skill, vision and opportunity that the odds of succeeding in life without completing college are terrible.

In cases like these, the statistic may be "factual", but they're not applicable because they don't take into account the character, the drive, the focus and skill set of the individual. Sure, there are phenomena that behave statistically, that are truly luck-of-the-draw in nature. In these cases, statistics can be useful: predicting the likelihood of drawing the cards you want, the chances of winning a contest or the likelihood of lighting striking a certain place.

However, resigning to the stats is a victim's position. It does not take into account all that you or someone else brings to the table that can beat the odds. In these cases, the attributes of the individual can far outweigh the stats and the statistics have no place.

Become a Great Manipulator of Numbers
You can win all your arguments and make lots of money by becoming a competent manipulator of numbers. It's fun and it's easy.
  1. Know when to use percentages and when to use absolute values
  2. Change the direction to make sure the numbers work for you
  3. Obfuscate context and leave out contextual "facts" that might lead to better perspective
  4. Roll out statistics where they have absolutely no place at all
Before you know it, you'll have enslaved those around you to your mastery of "the facts". Alternatively, you can use your newly acquired skill as a lying-numbers-detector.

Happy Monday,

1 comment:

  1. Very cool, Tef.

    Here’s a variation – expand or contract your scale to suit your intention. If you’re selling a $100/year extended warranty on a gizmo, and want to soften the blow, say “look, you can protect your investment for less than *a dollar a day*!” Conversely, if you’re a mortgage broker trying to convince a homeowner to refinance, you add up the estimated savings over the life of the loan (THOUSANDS of dollars!).


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