This table is from the 1933 article 'The relative effects of paternal and
maternal age' in Down's syndrome by the geneticist Lionel Penrose.
The row totals at the right of the table contain the paternal-age-specific frequencies for the
'Normal' (N) and Down's children (D) separately.
Likewise, the columns totals at the bottom contain separate maternal-age-specific frequencies for the
'Normal' and Down's children.
However, the frequencies in the body of the table are the
sums
of the frequencies of
Normal and Down's cases.
The
CHALLENGE is to split each row-column-specific sum into the frequency of N and the frequency of D cases.
It is easy to split a few of the small (N + D) counts into their separate N and D components. e.g. N[18,18] = 1; D[18,18] = 0.
But for larger (N + D) counts closer to the centre of the table, the task of splitting them into N and D becomes progressively more difficult.
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Background
Down syndrome or Down's syndrome, also known as trisomy 21, is now known to be a genetic disorder
caused by the presence of all or part of a third copy of chromosome 21.
It is typically associated with physical growth delays, characteristic facial features,
and mild to moderate intellectual disability.
The article
The relative effects of paternal and maternal age in Down's syndrome
by Lionel Penrose, was published in the
Journal of Genetics, May 1933, Volume 27, Issue 2, pp 219-224. This was
before its genetic nature was known. Penrose was one of the first to establish that its frequency rate was a stronger function
of maternal than paternal age, and (in a separate article in 1934) of
maternal age than birth order
JH became aware of Penrose's work through the
Wellcome Library's recent digitization of
The Lionel Penrose papers. These papers also contain extensive correspondence
with statistician Ronald Fisher, a pioneer in statistical genetics.
Lionel Penrose was the father of mathematician
Roger Penrose,
chess Grandmaster Jonathan Penrose,
mathematician
Oliver Penrose
(who graciously provided JH with this
reconsideration of his father's 1933 work.
[It appears as the chapter 'A beautiful method of analysis': O. Penrose, pp 443-451
in "Fifty years of human genetics: A Festschrift and liber amicorum to celebrate the life and work of George Robert Fraser",
edited by Oliver Mayo and Carolyn Leach, ISBN 9781862547537, Wakefield Press, Adelaide, 2007]),
and geneticist
Shirley Victoria Hodgson (who graciously sent JH
a copy of her father's book "Clinical and Genetic Study of 1280 Cases of Mental Defect: Colchester Survey").
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