As both a stats-junkie and a former charity trustee, I’ve been intrigued by the claims about charitable spending made by an organisation calling itself The True and Fair Foundation.
Among the bold assertions made in the Foundation’s report, A Hornet’s Nest: A Review of Charitable Spending By UK Charities (pdf), is “1,020 charities, with a combined income of £6bn in their latest reported accounts on the Charity Commission’s website, spent 50% or less on their charitable activities”.
The NCVO, among others, has pointed out the weaknesses in the claims.
What immediately stood out for me was this table in the Foundation’s report (screengrab below):
At the bottom is “Average 43%”. Now, anything with a percentage and an average always make me alert. They are two of the statistical measures that trip people up.
It looks like the report’s authors have simply added the individual percentage spends and divided by 17.
Now, any average is meant to summarise the data – in basic terms to show what is typical.
Is 43% typical?
No. Of the 17 charities just 6 have a percentage lower than 43%. Nearly twice as many (11) are higher.
In slightly technical terms, this is what happens when an arithmetic mean is taken of a skewed distribution.
Say you and 20 of your friends are at a party. It’s quite likely that your salaries are not too different. And then Bill Gates walks in – he got your wildcard invitation and has actually come along. If you took the arithmetic mean of your collective incomes, you’re all bazillionaires!
A better average in this case would be the median – the income in the middle, so half of incomes are below and half are above. Bill coming to your party won’t shift this much.
It works the same for the charity table above. The halfway point is Age UK at 48%. Not much higher than 43%, you might say, but bear in mind that the calculation used for the Lloyd’s Register is disputed by them, as are figures for others.
A visualisation helps. In this case, a good bog-standard bar chart like the one below.
In red is the True and Fair Foundation “average”. In yellow, is the median (Age UK). That 43% figure is looking decidedly odd and it would make me cautious about accepting other figures within the report at face value.
For ‘A Hornet’s Nest”, it looks like the sting in that tale* is more than average!
*For the avoidance of doubt, the use of ‘tale’ not ‘tail’ is deliberate!