Dissembling some of Badman’s stats (again)

By guest blogger Bruce Stafford : )

This note is based on a quick look at the statistics contained in the latest (that is, the third) survey of local authorities conducted for the Review of Elective Home Education in England.

Is it a representative sample?

A key issue with the previous two surveys was a total lack of clarity about whether they were representative of all local authorities or not.  This is important because if the sample was biased the resulting estimates would not be valid.  Notwithstanding various Freedom of Information requests the representativeness of the previous two surveys continues to be unknown.

Given this context, and hence doubts about the legitimacy of earlier Review claims, it might be expected that at the third attempt details would be given about the representativeness of this latest survey; if for no other reason as a courtesy to allay the fears of the home educating community.  However, the findings from the survey, submitted to the Select Committee, simply assert that it was a representative sample (para. 5). 

Whilst the response rate was 49 per cent (74 out of 150 local authorities responded), that nearly half replied does not make the sample representative – because the half that did not reply might be very different from those that did.  More evidence is required to demonstrate that the sample is representative.

Indeed, there are reasons to believe that the sample tends to over-represent those local authorities with a larger proportion of the child population.  This would make the sample problematic if either the home educated population was evenly spread across the population, or if it were over-represented in local authorities with smaller child populations, that is, in more rural areas.

Badman states that the mid-2008 population estimate for the 74 local authorities was 4,303,700.  The same mid-year population estimates show that the number aged 5 to 16 years was 7,201,400.[1]  This means that the 74 local authorities covered 60 per cent (4.5m/7.2m = 59.6%) of children of school age.  Or the 76 local authorities that did not respond had a smaller child population (40 per cent).  So are home educated families more likely to live in larger (in terms of population) local authorities, presumably urban and metropolitan areas?  If not, there is a hint here that the sample is not as representative as claimed.

So it appears that we have gone full circle, or is it that we never left the starting point?  The onus, once again, is on Badman to conclusively demonstrate that his sample is representative.

Estimating the size of the home education community

Badman’s report estimated that there were 20,000 home educated children.  This third survey reveals that the 74 local authorities know of 11,700 home educated children.  As their child population is given as 4,303,700 then 0.27 per cent are home educated (11,700/4.3m).  Applying this proportion to the total number of children (7,201,400 * 0.272) gives 19,577.7, which rounding up gives 20,000.

The note implies that this is the estimate for England.  However, as the original Review acknowledged many home educated children are not known to local authorities – his estimate is only based on those known to local authorities – and so is an underestimate.

If local authorities only knew about 1 in 2 home educated children the (rounded) estimate would be 39,200, if one in three it would 58,700 and if only one in four it would be 78,300.  As we do not the number of home educated children these local authorities do not know about the correct course of action, as home educators have previously pointed out to the review team, should be to present a range for the estimated number of home educated children.  Rather than categorically state that the estimate is 20,000 it would be prudent to say the number is unknown, but may lie between 20,000 and say 78,300.

---

[1] To get these estimates you have to download a zip file from http://www.statistics.gov.uk/statbase/Product.asp?vlnk=15106, the data by age for England is given in Table 4.