The peril of percentages

According to the Mail Online reporting in 2012:

Nearly a third of Americans – 27% – now get news from smartphone and tablet apps such as Mail Online’s, according to a new study by the Pew Research Center.

Whenever, I’ve given a talk or run a workshop on communicating with statistics and numbers people tell me that percentages are the things that most confuse them.

So the good thing about the Mail’s news article is that they chose to use words to describe the percentage figure and then gave the figure.

But was this the best choice of words?

Let’s have a look at some basic fractions in terms of percentages…

One half 50.00%
One third 33.33%
One quarter 25.00%
One fifth 20.00%
One sixth 16.67%

We want to use an easily understood fraction to describe in words what 27% is, or thereabouts.

Mail Online suggests it is ‘nearly a third’. But how near? Well subtracting 27 from 33.33 gives us 6.33. So one third is 6.33 percentage points bigger than 27%.

(NB it’s 6.33 percentage points, not 6.33 percent, bigger. I’ll blog about the difference soon.)

Was there another choice?

Well, looking at the table above 27% comes between 25% and 33.33%. In other words, 27% is between one quarter and one third.

And the difference between 27% and one quarter is 2 percentage points. That’s quite bit smaller than the difference between 27% and one third.

So, in this case, I’d say that Mail Online would have been better to compare to one quarter rather than to one third and reword to “Just over a quarter of Americans – 27% – now get news…”.

You may be thinking that this is a pedantic point but it’s not. Newspapers – and their online equivalents – are often referenced by all sorts of people (politicians, for example) to make a case. And, quite often, people naturally abbreviate what they remember reading. So, it’s not hard to see how ‘nearly a third’ goes to ‘a third’.

If money is involved this sort of ‘statistical inflation’ really matters.

How would you feel if you got a 27% increase in pay? Pretty good, I’m sure.

But what if your employer boasted that this was a one-third increase. Just a little annoyed?

So, using words is good. But which words?

Well, the simplest thing to do is to express a percentage figure as “in a hundred”, or “out of a hundred”, or similar phrases. After all, percent or per cent is simply per one hundred.

So, 27% is 27 in every hundred.

But by using fractions we can make things easier still for people to understand.

This is why I’m developing a percentages-to-words guide. It’s draft at the moment and very much based on what I might say. Others might say something different and I’d love to hear suggestions. Also, do check my sums. I may have a maths degree but, to be honest, I managed to trip myself up a few times when putting this together – percentages are pesky!

And if you’d like some training on working with percentages for you and your team, do get in touch.

This could be as part of a full or half day workshop on numbers and stats in communications. Or a special focus on percentages in a lunchtime informal seminar.

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