Statistics

Caught two minutes of Tonight with Trevor McDonald last night, talking about one year on from the change in licensing laws, one statement talking about ambulance responses grabbed my attention

Between the hours of [x] and [y] incidents have decreased by 2%, but between [y] and [z] have increased by 40%

I thought about knocking out a quick quip, but upon thinking about it I believe it requires a longer explanation.

We all know the quote

Lies, damned lies, and statistics

It's good, it keeps us on our toes, and it's wrong; statistics can't lie they're just numbers. If the data is collected without bias and the formulas applied to it then it simply can't lie, but how we interpret it and how it's presented can certainly mislead.

Imagine two people - one against the licensing laws, and one for them. The person against would use the 2% and 40% saying

Ah yes it might have decreased by 2% then, but it's increased by 40% there

and smile, smugly satisfied that he's proven his case. However let's look at his figures -

We're not given any more information, although later comments suggest that the x-y hourly incidents were greater then the y-z ones, so we're going to have to make them up. Watch carefully, I've nothing up my sleeves and my hands never leave my wrists.

Let's assume that there were 100 incidents between the hours of x and y. These have decreased by 2% to 98, a difference of -2. Let's then assume that there were 5 incidents between y and z. These have increased by 40% to 7, a difference of +2

Well will you look at that, overall there's been no difference at all. Now you might think - "That's unfair, you started off with two widely differing amounts" Okay, but think about it. You haven't been told what the real figures are, so why couldn't they be like this?

Okay in the interests of 'fairness' let's start with 100 for both incidents.
x-y: 100+2%=102
y-z: 100+40%=140
Overall increase of 38

So what about the person who's for the laws, what can they say? Well instead of splitting up the figures x-y and y-z let's look at the entire x-z range instead
Initial x-z figures = 100+100 = 200
Current x-z figures = 98+140=238
Percentage increase = 19%
So he can say

Ah but overall the increase has only been 19%, which is not huge and was expected in the first year.

Confused? We have two different people saying two apparently different things which are really both exactly the same.

Try this common tool used in presenting accounting figures - you earn £100/day and get a 10% pay increase, shortly after the firm gets into trouble and you're asked to take a 10% pay cut. Fine you'll just be back to where you started from; won't you?

£100+10%=£110
£110-10%=£99

Oops!

It's not just percentages; it works with figures too. I might say that youth related incidents have increased by 250 in only a year. Terrible until you're told that you started off with 5000; a petty increase of just 5%

So next time you hear someone, or you read a big shocking headline, quoting percentages or figures; remember to look at the data behind those quotes, if it's not presented there's probably a good reason why not.