How to Lie with Statistics summary

Knowing what we know now, how can we avoid biased samples without having to count “all the beans”?

One way is to employ a strategy called stratified random sampling:

Imagine you’re looking to buy a new house and you run across a real estate agent eager to move you into his neighborhood. Hoping to entice you, he tells you that the average income in that neighborhood is $100,000 per year. A year later, he comes back to you saying that the average income is only $20,000 per year, even though wages stayed the same and nobody moved in or out of the neighborhood. So what happened? Is he a liar?

Not precisely: he just used statistics to his advantage. His trick was to use different kinds of “averages” to change your perception.

In the first blink, we learned that our sample has to be large enough to be considered good statistical evidence.

Because if a sample is too small, it’s not “statistically significant.” To get an idea of why that is, ask yourself what the probability is of getting heads in a coin toss? 50 percent, right? Now, find a coin and toss it ten times. How often did it come up heads? Five times? It’s possible, but unlikely.

Have you ever heard something that was just too good to be true? The same thing can happen when we’re talking about statistics. Luckily, in statistics, you have an easy way to find out whether someone is trying to dupe you: just find the standard error.

No measurement can be perfectly accurate because, as we’ve seen, it’s extremely difficult to “count all the beans” or create a perfect sample. We have to take into account the standard error, or the average imprecision of how our data was measured.

What do you do if you want to convince someone of something, but you just don’t have the proof? One way is to simply demonstrate something else as being true and then pretend it’s the same thing.

This method, which statisticians sometimes call the semi-attached figure, is among the most common deceptions in statistics.

Not all statistical errors hide a malicious intent. Some errors result from simple misunderstandings, such as the post-hoc fallacy, which says that we often assume causal relationships between two things simply because they occur at the same time.

However, just because two things happen simultaneously doesn’t mean that’s the case. In fact, when A and B happen together, we can’t necessarily know whether A causes B or whether it was the other way around.

By now, you should understand the basics of how to lie with statistics. But these “lies” are not always born of ill motives, and many statistical errors can be caused unintentionally by simple incompetence.

That said, it’s still worth noting that most of these errors inflate and sensationalize statistics and their meanings rather than deflate and level them. So what can you do to defend yourself against bad statistics?