It’s a fact of life that there are usually lots of different ways of looking at anything.  For instance, a famous one is whether this glass is “half full” or “half empty”:

You’ll come across a lot of statistics in your everyday life – here are a few examples:

·         Statistics about who’s the most popular politician

·         Statistics about how long you’re likely to live

·         Statistics about whether travel by plane is safer than travel by car

·         Statistics about how hard it is to win the lottery

Now, smart but dishonest people can use statistics to prove just about anything, if they bend the rules and use some dodgy techniques.  For instance, a group of people supporting not allowing people to drive until they’re 25 might do a survey just after a young driver had been involved in a horrific accident.  With the memory of this accident fresh in most people’s minds, the group would have a much better chance of getting a lot of “yes I think the driving age should be raised” answers.  They could also only survey old people to help bend the statistics even more in their favour.

The easiest way to warp the results of a statistical survey is to have a sample that isn’t representative of the general population.  For instance, asking only old people whether a new skate park should be built in a local suburb is an example of a bad sample – you’re not getting a representative opinion of what the entire population thinks (both young and old people).

Use too small a sample

Now, if you don’t have time to form a bad, misrepresentative sample, you can always resort to having a really, really small sample.  You can prove anything with a small sample.  For instance, about 85 to 90% of the human population is right handed, so most people are right handed, although I’m sure you would know at least a few left handers yourself.  Say you wanted to prove some ridiculous statement like, “all humans are right handed.”  What you could do is take a survey of 5 people only, and ask them whether they are left or right handed.  There would be a reasonable chance that all would be right handed.

If this was the case, you might then make some far fetched statement like “All people are right handed”.  Because your sample size is so small, there would be no way you could justifiably make this sort of statement.  If you surveyed another 5 people, you could just as easily get 1 or 2 people who are left handed, which would prove your statement wrong immediately.  So, the sample size has to be big enough.

Repeated small samples

Really, really dodgy people will do repeated small sample surveys until they get the results they want.  For instance, if they were trying to prove all people were right handed, they’d keep doing samples of 5 until they got one where everyone was right handed.  They’d then use that sample as ‘conclusive proof’ (haha) that all people were right handed, and conveniently neglect to mention the other samples where not everyone was right handed.  This is bad, bad, bad maths.