Editing John Arbuthnot (section)

==Biography==
In his mid-life, Arbuthnot, complaining of the work of [[Edmund Curll]], among others, who commissioned and invented a biography as soon as an author died, said, "Biography is one of the new terrors of death," and so a biography of Arbuthnot is made difficult by his own reluctance to leave records. [[Alexander Pope]] noted to [[Joseph Spence (author)|Joseph Spence]] that Arbuthnot allowed his infant children to play with, and even burn, his writings. Throughout his professional life, Arbuthnot exhibited a strong humility and social conviviality, and his friends often complained that he did not take sufficient credit for his own work.

Arbuthnot was born in [[Arbuthnott|Arbuthnot]], [[Kincardineshire]], on the north-eastern coast of Scotland, son of Margaret (née Lammie) and Rev Alexander Arbuthnot, an [[Scottish Episcopal Church|Episcopalian]] priest. He may have graduated with an arts degree from [[Marischal College]] in 1685.<ref>{{Cite web|url=https://www.researchgate.net/publication/265207566|title=Scots in London in the Eighteenth Century|last=Nenadic|first=Stana}}</ref> Where Arbuthnot's brothers took part in [[Jacobitism|Jacobite]] causes in 1689, he remained with his father. These brothers included Robert, who fled after fighting for [[James II of England|King James VII]] in 1689 and became a banker in [[Rouen]] and half-brother George, who fled to France and became a wine merchant. However, when [[William III of England|William and Mary]] came to the throne and the Scottish and English parliaments required all ministers to swear allegiance to them as king and queen, Arbuthnot's father did not comply. As a [[Nonjuring schism|non-juror]], he was removed from his church, and John was there to take care of affairs when, in 1691, his father died.

[[File:John Arbuthnot.gif|thumb|left|Arbuthnot, from a painting by [[Godfrey Kneller]]]]
Arbuthnot went to [[London]] in 1691, where he is supposed to have supported himself by teaching mathematics (which had been his formal course of study). He lodged with William Pate, whom Swift knew and called a "''bel esprit''". He published ''Of the Laws of Chance'' in 1692, translated from [[Christiaan Huygens]]'s ''De ratiociniis in ludo aleae.'' This was the first work on probability published in English. The work, which applied the field of [[probability]] to common games, was a success, and Arbuthnot became the private tutor of one Edward Jeffreys, son of Jeffrey Jeffreys, an [[member of Parliament|MP]]. He remained Jeffreys's tutor when the latter attended [[University College, Oxford]] in 1694, and he there met the variety of scholars then teaching mathematics and medicine, including Dr [[John Radcliffe (English physician)|John Radcliffe]], [[Isaac Newton]], and [[Samuel Pepys]]. However, Arbuthnot lacked the money to be a full-time student and was already well educated, although informally. He went to the [[University of St Andrews]] and enrolled as a doctoral student in [[medicine]] on 11 September 1696. The ''very same day'' he defended seven theses on medicine and was awarded the doctorate.

He first wrote [[satire]] in 1697, when he answered Dr [[John Woodward (naturalist)|John Woodward]]'s ''An essay towards a natural history of the earth and terrestrial bodies, especially minerals...'' with ''An Examination of Dr Woodward's Account &c.'' He poked fun at the arrogance of the work and Woodward's misguided, [[Aristotle|Aristotelian]] insistence that what is theoretically attractive must be actually true. In 1701, Arbuthnot wrote another mathematical work, ''An essay on the usefulness of mathematical learning, in a letter from a gentleman in the city to his friend in Oxford.'' The work was moderately successful, and Arbuthnot praises mathematics as a method of freeing the mind from [[superstition]].

In 1702, he was at [[Epsom]] when [[Prince George of Denmark]], husband of [[Anne, Queen of Great Britain|Queen Anne]] fell ill. According to tradition, Arbuthnot treated the prince successfully. According to tradition again, this treatment earned him an invitation to court. Also around 1702, he married Margaret, whose maiden name is possibly Wemyss. Although there are no baptismal records, it seems that his first son, George (named in honour of the prince), was born in 1703. He was elected to be a Fellow of the [[Royal Society]] in 1704. Also thanks to the Queen's presence, he was made an MD at [[University of Cambridge|Cambridge University]] on 16 April 1705.

Arbuthnot was an amiable individual, and Swift said that the only fault an enemy could lay upon him was a slight waddle in his walk. His conviviality and his royal connections made him an important figure in the Royal Society. In 1705, Arbuthnot became physician extraordinary to Queen Anne, and at the same time was put on the board trying to publish the ''Historia coelestius.'' Newton and [[Edmund Halley]] wanted it published immediately, to support their work on orbits, while [[John Flamsteed]], the Royal Astronomer whose observations they were, wanted to keep the data secret until he had perfected it. The result was that Arbuthnot used his leverage as friend and physician to Prince George, whose money was paying for the publication, to force Flamsteed to allow it out, albeit with serious errors, in 1712. Also as a scholar, Arbuthnot took up an interest in antiquities and published ''Tables of Grecian, Roman, and Jewish measures, weights and coins; reduced to the English standard'' in 1705, 1707, 1709, and, expanded with a preface (which indicated that his second son, Charles, was born in 1705), in 1727 and 1747.

Although Arbuthnot was not a [[Jacobitism|Jacobite]] after the fashion of his brothers, he was a [[Tories (British political party)|Tory]], for national and familial reasons. Anne was advised (and many said controlled) by [[Sarah Churchill, Duchess of Marlborough]], who was a champion of [[British Whig Party|Whig]] causes. In 1706, the Duchess of Marlborough fell out with Anne—a [[Schism (religion)|schism]] which the Tories were pleased to encourage. The marriage of lady-in-waiting Abigail Hill to [[Samuel Masham]], which was the first overt sign of Anne's displeasure with Sarah Churchill, took place in Arbuthnot's apartments at [[St James's Palace]]. The reasons for the choice of apartment and the degree of involvement of Arbuthnot in either the love match or Anne's estrangement, are not clear. As a Scotsman, Arbuthnot served the crown by writing ''A sermon preach'd to the people at the Mercat Cross of Edinborough on the subject of the union. Ecclesiastes, Chapter 10, Verse 27.'' The work was designed to persuade Scots to accept the [[Acts of Union 1707|Act of Union]]. When the Act passed, Arbuthnot was made a fellow of the Royal College of Physicians of Edinburgh. He was also made a [[In ordinary|physician in ordinary]] to the Queen, which made him part of the [[Medical Household|royal household]].

Arbuthnot returned to mathematics in 1710 with ''An argument for Divine Providence, taken from the constant regularity observed in the births of both sexes'' (linked below) in the Royal Society's ''Philosophical Transactions.'' In this paper, Arbuthnot examined birth records in London for each of the 82 years from 1629 to 1710 and the [[human sex ratio]] at birth: in every year, the number of males born in London exceeded the number of females. If the probability of male and female birth were equal, the probability of the observed outcome would be 1/2<sup>82</sup>. This vanishingly small number led Arbuthnot to believe that this phenomenon was not due to chance, but to divine providence: "From whence it follows, that it is Art, not Chance, that governs." This paper was a landmark in the [[history of statistics]]; in modern terms he performed [[statistical hypothesis testing]], computing the [[p-value|''p''-value]] (via a [[sign test]]), interpreted it as [[statistical significance]], and rejected the [[null hypothesis]]. This is credited as "… the first use of significance tests …",<ref name="Bellhouse2001">{{Citation
|last=Bellhouse
|first=P.
|title=in Statisticians of the Centuries by 
|editor1=C.C. Heyde
|editor1-link=Chris Heyde
|editor2-link=Eugene Seneta
|editor2= E. Seneta
|year=2001
|publisher=Springer
|isbn=0-387-95329-9
|pages=39–42
|chapter=John Arbuthnot}}
</ref> the first example of reasoning about statistical significance and moral certainty,<ref name="Hald1998">{{Citation
|last=Hald
|first=Anders
|title=A History of Mathematical Statistics from 1750 to 1930
|year=1998
|publisher=Wiley
|pages=65
|chapter=Chapter 4. Chance or Design: Tests of Significance}}</ref> and "… perhaps the first published report of a [[nonparametric test]] …".<ref name="Conover1999">{{Citation
|last=Conover
|first=W.J.
|title=Practical Nonparametric Statistics
|edition=Third
|year=1999
|publisher=Wiley
|isbn=0-471-16068-7
|pages=157–176
|chapter=Chapter 3.4: The Sign Test
}}</ref>