Lies, damn lies, and statistics

Gaussian Distribution
Source: Wikipedia)

People often think they have intuitive grasp of statistics, and the reality is very few of us are any good at it. We usually end up answering the wrong question because of attribute substitution: we analyzed something ELSE that's NOT what's needed.

Here's an example. Let's say there's a genetic condition that affects 1 in 10000. There is a test for it, and it's 99% accurate. Now, let's say you tested person A, and the test comes back positive. So what's the chance that person A actually has this genetic condition?

99% you say?

Ah, but you'd be wrong!  The proper answer is: it depends on how big of a population we're talking about. 

Why? Let's first assume that there are a million people.

Out of that million, there's 100 that has this condition (1 in 10000)

For those 100 people, 99 of them will test positive (correctly), and 1 will test negative even though he does have it (false negative).

For the other 999899 people, 99% of them will test negative (correctly), while 9999 of them will test positive (false positive).

So for all the people who tested positive, that's 9999 + 99, only 99 actually has the condition.

So the answer is 0.99%. That's right, LESS THAN ONE PERCENT.

Not very intuitive, but that's because you forgot to take into account false positives and false negatives and how they muck with the results.

Scammers often use this sort of "bad calculations" to lead your mind astray into thinking the "opportunity" is profitable.




Peter Donnelly explains how stats will fool juries

http://www.ted.com/talks/peter_donnelly_shows_how_stats_fool_juries.html


Okay, you ask, how will scams use statistics to fool you? The answer is... by giving you some numbers that *seems* to make sense to you... if you don't look closely.

MLM's "income disclosure statements" are well known to massage numbers. Here's one from FHTM:

The numbers look somewhat impressive, until you realize that ~95% of all affiliates earn less than $3000 A YEAR, and that's NOT including their own out-of-pocket expenses (printing brochures, business cards, flyers, etc.), time spent, miles driven, and such. You have to be in for more than 3 years to earn a decent income, according to this IDS.  Also, note how they switched from "per month" for 4 columns, then suddenly swapped to "annualized" (per year).

Here's one that disguised the information by only mentioning 25% of the people, and pretend that's 100%. If you don't read the stuff line by line, you'd have missed that.

Basically, beware when a table of figures was shown. The data is likely massaged and/or tweaked to show it in the best possible light, which may not be the "full truth".

Related articles

• Bad Argument: Apophenia and Patternicity
• How to deal with people who disagree: 4 types you need to know
• Bad Argument: Retrospective Falsification
• Cognitive Bias: Attribute Substitution