The Art of Statistics: Learning from Data

by David Spiegelhalter

He found there had been more males than females baptized in every year, with an overall sex ratio of 107, varying between 101 and 116 over the period. But Arbuthnot wanted to claim a more general law, and so argued that if there were really no difference in the underlying rates of boys and girls being born, then each year there would be a 50:50 chance that more boys than girls were born, or more girls than boys, just like flipping a coin. But to get an excess of boys in every year would then be like flipping a fair coin 82 times in a row, and getting heads every time. The probability of this happening is 1/282, which is a very small number indeed, with 24 zeros after the decimal place. If we observed this in a real experiment, we would confidently claim that the coin was not fair. Similarly Arbuthnot concluded that some force was at work that produced more boys, which he thought must be to counter the greater mortality of males: ‘To repair that Loss, provident Nature, by the Disposal of its wise Creator, brings forth more Males than Females; and that in almost a constant proportion.’1 Figure 10.1 The sex ratio (number of boys per 100 girls) for London baptisms between 1629 and 1710, published by John Arbuthnot in 1710. The dashed line represents an equal number of boys and girls; the curve is fitted to the empirical data. In all years there were more baptized boys than girls. Arbuthnot’s data have been subject to repeated analysis, and although there may be counting errors...

More males than females, 21 to 20 ratio