Sex stats – size matters and a problem of approximation

Saturday morning. Test Match Special on the radio. Browsing the web.

My eye is caught by a BMJ press release (newsroom page) on holiday sex stats (pdf).

There are lots of percentages. The BMJ has helpfully interpreted those in words – something I strongly recommend in my training workshops.

Two interpretations have caught my eye:

BMJ-men-women BMJ-61.5-almost-two-thirds

In the first, almost 58.5% is described as over half, ie over 50%. True – but over half is a big range! And 58.5% is a long way over half.

In the second, 61.5% is described as almost two thirds. Two thirds as a percentage is 66.7% (to one decimal place).

The difference between 61.5% and 58.5% is just 3 percentage points. They are closer to each other than they are to the 66.7% and 50% to which they are respectively compared. Two thirds and one half differ by a whopping 16.7 percentage points.

Both 58.5% and 61.5% are 1.5 percentage points away from 60% aka three fifths.

So 61.5% could be described as “a little over three fifths”, and 58.5% could be described as “a little under three fifths”.

Does this matter?

Yes. When we convert percentages to words it makes it easier for others to understand, and to remember. A politician might glaze over at 61.5% and 58.%, but be comfortable with “almost two thirds” and “over half”.

A problem comes when approximations in words – easily recalled and reported onwards – get turned back to numbers. Things get lost in translation.

Let’s use our BMJ numbers: what if a debate becomes one of two thirds versus one half – of 66.7% to 50%. Not of 61.5% and 58.5%. How would any decisions be affected?

Alternatively, what if the words used had been “a little over three fifths” and “a little under three fifths”? Would recalling both as three fifths – a difference of zero percentage points – be less problematic than the 16.7 percentage point gap?

In the end, size matters. And so does approximate size. Choose your words carefully!


If you need to…

● make sense of the numbers, data and statistics you work with daily

● have greater impact with the data you collect and the surveys you commission

● develop confidence talking and writing about the numbers that matter

… I can help with training and consultancy.

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