Maternity Unit Closures + A Dose of Hard Sums = You have got to be kidding me…

Today’s Telegraph is running a story (not yet on the web) that of the 21 Midwife-led Maternity units proposed for closure or already closed, only 4 are in Labour Constituencies. Of course, the opposition are crying "foul", but I thought "Let’s have a look at the hard sums to see how preposterous the claim is that the closures aren’t politically biased". Here we go. There are 57 Birth Centres and 21 have been shut down or are being shut down. Even though two-thirds of constituencies in the country are presently Labour, let’s assume for the sake of making a point that the Birth Centres are split 50/50 Labour / Non-Labour (28 Labour / 29 Non-Labour just to be overly generous to the Labour argument). Now, assume that we close just one unit, the chances of it being non-Labour is 29/57. That’s a little over 50%. Now, assuming that the first Birth Centre closed was Non-Labour, the chance that the second one that closes is also Non-Labour is 28/56 (which is exactly 50%). But more crucially, the chance that both of the first two to close are Non-Labour is 29/57 * 28/56, which comes out as 203/798 or a little over 25%. Now, extend that all the way to 21 closures, and assume only 4 are non-Labour. The sum to calculate the probability that all are non-Labour (assuming a random selection) is complicated, but it comes out as 0.0555% or approx 1 in 1,800. So to sum-up so far, 1 in 1,800 is the probability that if the centres had all been selected randomly at the most 4 Labour ones would have been picked. But let’s give the Labour Party the benefit of a bit more doubt. Let’s assume that 75% of the 57 Maternity Units are in non-Labour areas (43 non-Labour, 14 Labour). The result is now 34.3% or almost 1 in 3. Let me remind you what that means. If 75% of the Maternity Units were in non-Labour areas, the chances of upto 4 Labour ones being selected for closure is still 1 in 3. But for the sake of being uber-generous to Labour, let’s assume that almost 90% of all the Maternity Centres were in non-Labour areas (50 non-Labour, 7 Labour when rounding up given the benefit of the doubt to Labour). Only now does the probability of 4 or less closures being Labour get to 95%. Let’s be very clear then:

  • If 75% of the Maternity Wards had been in Non-Labour areas, the chances of a random selection picking 4 or less Labour ones out of 21 is only 1 in 3.
  • If 50 % had been in Non-Labour areas, the chances of 4 or less Labour ones being picked becomes 1 in 1,800.

No political bias in the selection of Maternity Wards? You have got to be kidding me… Anybody got the exact distribution of Labour / Non-Labour constituencies for these Maternity Units? If so I’ll do the exact calculations…

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