Government Maths – The Great Educational Balls up -Part 8 (or maybe 27)

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OK, the following was released after a Freedom of Information request.

5. Known to social care[1]
25 of the 90 LAs asked responded (28% response rate).
• Based on the data we have from the 25 LAs, the average (median) proportion of EHE children per LA known to social care is approximately 7%. We estimate there are approximately 3% of children (5-16 years) known to social care [in] maintained schools. [2]
• Within the 25 LAs for which we have data, there were 477 registered home educated children who were currently known to social care.
• On average (median) 7 children per LA are known to social care.
• Extrapolating to the national level (150 LAs), this means around 1350 home educated children are known to social care in some capacity (6.75%).
> [1] Known to social care includes Section 17, 37 or 47 enquiries.
> [2] Using 2005 data (the latest available), these are approximate figures and include disabled children.

This was supplied in response to a query for “…in relation to the statement (by Graham Badman) reported in the media that "Children educated at home are twice as likely to be on social services registers for being at risk of abuse as the rest of the
population" - 'full details of the statistical evidence on which Mr
Badman bases this assertion' .

Let’s get the obvious one dealt with first. 150 X 7 = 1050 not 1350.

Some more points (I’m sure I’ll miss many others)

- These “statistics” relate to children “known to social care” not “at risk of abuse”.

- Median? You really want to use a median here? I haven’t studied much by way of statistics but I smell a rat. And multiplying up to extrapolate an overall proportion? Let’s try that for some sample figures.

Lets say numbers reported were thus from a sample of 7 “LA” responses:

0 0 0 7 7 7 8

Median value, (the middle one) = 7

So if we take that median and extrapolate a number of children across all LAs we have 7 X 7 = 49. So therefore across all the LAa we have extrapolated there are 49 children known to social care. But hold on, if we add them up there are only 29! We just added 20 new cases through our dodgy maths. But imagine if we instead extrapolated from that sample of 7 up to all the LAs in the country. We couldn’t check because we don’t have data from them all. Could the same mistake possibly be made? Raed the quoted stats above again. Trust them?

- What about population size? The assumption has been made that these LAs are representative of the population of all LAs. Is this likely?

- Could there be sample bias? Maybe LAs who feel there is an issue are more likely to respond. Those with no cases don’t bother.

I could go on. But others have done it much better here.

So, do you trust the maths on which Mr Badman has been basing his opinions? Opinions which have been publicised in the press and informed his review, which looks set to lead to far reaching legislation. Nice to know it’s all based on sound stats <cough>.