Statistical Outliers: of Baldness and Long Gestations

At what point is a human gestation period ‘impossibly’ long. This was the question a British court had to consider in the 1949 appeal to the 1948 judgement in Hadlum vs Hadlum.

Ms Hadlum had a gestation period of 349 days, taking into account when Mr Hadlum went off to the war. The average human gestation is 40 weeks or 280 days, although new research shows an average of 268 days or 38 weeks, varying by +- 37 days http://www.sciencedaily.com/releases/2013/08/130806203327.htm

The widely used statistical definition of an outlier was given by Douglas Hawkins in 1980, ‘an observation which deviates so much from other observations as to cause suspicions that it was generated by a different mechanism’. (Hawkins DM, 1980, Identification of outliers. Chapman & Hall).

Hmn! The court upheld the 1948 finding that such a long gestation was possible, and so Ms Hadlum had not been ‘unfaithful’ to Mr Hadlum, cause for divorce back in those dark days. In the 1951 case of Preston-Jones vs Preston-Jones, however, the court found a gestation period of 360 days to be the limit. The judge concluded that ‘If a line has to be drawn I think it should be drawn so as to allow an ample and generous margin’.

Statisticians have established guidelines for ‘outliers’, that are lines in the sand, if not in concrete.

But speaking of sand, at what point do grains of sand form a heap of sand?

How many hairs constitutes the threshold distinguishing between bald and not bald?

(philosophers call this is the Sorites or ‘heap’ paradox).

The world ‘forgot’ how to make concrete from about 500-1300 AD, but was there a day when we could still make concrete, and a day in which we couldn’t? Something to think about on a Sunday afternoon!

2014 Excel implementation of some simple outlier detection techniques, by John Foreman http://au.wiley.com/WileyCDA/WileyTitle/productCd-111866146X.html

References on the above legal cases

1978 Statistics journal: http://www.jstor.org/discover/10.2307/2347159?uid=2&uid=4&sid=21103476515283

1953 Medical journal: http://link.springer.com/article/10.1007/BF02949756