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{{Short description|English statistician and economist}}
{{EngvarB|date=April 2014}}
{{Infobox scientist
|name              = Arthur Lyon Bowley
|image             = Arthur Lyon Bowley in 1950.jpg
|image_size        =
|caption           = Bowley in 1950
|birth_date        = 6 November 1869
|birth_place       = [[Bristol]], England
|death_date        = {{death-date and age|21 January 1957|6 November 1869}}
|death_place       = [[Surrey]], England
|residence         =
|citizenship       =
|nationality       = British
|field             = Statistics, Economics
|work_institutions = [[London School of Economics]] [[University College London]]
|alma_mater        = [[University of Cambridge]]
|doctoral_advisor  =
|doctoral_students =
|known_for         = [[Bowley's law]]
|author_abbrev_bot =
|author_abbrev_zoo =
|prizes            = [[Commander of the Order of the British Empire|CBE]] {{small |(1937)}} [[Guy Medal]] {{small|(silver, 1895) (Gold, 1935)}}
|spouse            = Julia Hilliam
|children          = 3
}}

''' Sir Arthur Lyon Bowley''', [[Fellow of the British Academy|FBA]] (6 November 1869 – 21 January 1957) was an English statistician and economist<ref name=Times_obituary>{{Cite newspaper The Times |title= Sir Arthur Bowley |date= 23 January 1957 |page= 12 |issue= 53746}}</ref><ref>{{cite journal|title=Bowley, Arthur Lyon|journal=Who's Who|year=1907|volume= 59|page=196|url=https://books.google.com/books?id=yEcuAAAAYAAJ&pg=PA196}}</ref> who worked on economic statistics and pioneered the use of sampling techniques in social surveys.

==Early life==
Bowley's father, James William Lyon Bowley, was a minister in the [[Church of England]]. He died at the age of 40 when Arthur was one, leaving Arthur's mother as mother or stepmother to seven children. Arthur was educated at [[Christ's Hospital]], and won a scholarship to [[Trinity College, Cambridge]] to study mathematics.<ref name="ReferenceA">{{acad|id=BWLY887AL|name=Bowley, Arthur Lyon}}</ref> He graduated as Tenth [[Wrangler (University of Cambridge)|Wrangler]].<ref name="ReferenceA"/>

At Cambridge Bowley had a short course of study with the economist [[Alfred Marshall]] who had also been a Cambridge wrangler.{{clarify|date=August 2014}} Under Marshall's influence Bowley became an economic statistician. His ''Account of England's Foreign Trade'' won the [[Cobden Essay Prize]] and was published as a book. Marshall watched over Bowley's career, recommending him for jobs and offering him advice. Most notoriously Marshall told him the ''Elements of Statistics'' contained "too much mathematics."<ref>{{harvtxt|Darnell|1981}}, p.&nbsp;141.</ref>

==Academic career==
After leaving Cambridge Bowley taught mathematics at [[St. John's School, Leatherhead|St John's School]] in [[Leatherhead]] from 1893 to 1899. Meanwhile, he was publishing in economic statistics; his first article for the journal of the [[Royal Statistical Society]]) appeared in 1895.<ref name=Times_obituary/> In that year the [[London School of Economics]] opened. Bowley was appointed as a part-time lecturer and he would be connected with the School until he retired in 1936. He can be considered one of the School's intellectual fathers. However, he continued to teach elsewhere; for more than a decade he taught at University College, Reading (now the [[University of Reading]]). He was the [[William Newmarch|Newmarch]] lecturer at [[University College London]] (1897–98 and 1927–28). At the LSE he became [[Reader (academic rank)|Reader]] in 1908, and Professor in 1915. In 1919, he was appointed to a newly established [[Chair of Statistics]], probably the first of its kind in Britain. In Bowley's time, however, the LSE statistics group was very small: Margaret Hogg arrived in 1919 and left for the United States in 1925,<ref>{{cite journal |last=Hurlin |first=Ralph |year=1935 |title=Margaret Hope Hogg |journal=[[Journal of the American Statistical Association]] |volume=30|issue=192|pages=751–754|doi=10.1080/01621459.1935.10503303 }}</ref> [[E. C. Rhodes]] arrived in 1924<ref>{{cite journal |last=Grebenik |first=E. |year=1965 |title=Edmund Cecil Rhodes, 1892–1964 (obituary) |journal=[[Journal of the Royal Statistical Society]] |series=Series A |volume=128 |issue=4 |pages=615–616 |jstor=2343496 }}</ref> and [[R. G. D. Allen]] in 1928.<ref>{{citation|url=http://www.oxfordreference.com/view/10.1093/acref/9780199541454.001.0001/acref-9780199541454-e-1790 |contribution=Allen, Sir Roy George Douglas (1906–83)|author=Graham Upton and Ian Cook|edition=2nd|title=A Dictionary of Statistics|publisher=Oxford University Press|year=2008|isbn=978-0-19-954145-4 }}.</ref> Bowley's students included Ronald George,<ref>{{cite journal |last=Benjamin |first=Bernard |year=1970 |title=R. F. George (obituary) |journal=[[Journal of the Royal Statistical Society]] |series=Series A |volume=133 |issue=1 |pages=128–129}}</ref> Lewis Connor<ref>{{cite journal |last=Morrell |first=A. J. H. |year=1965 |title=L. R. Connor(obituary) |journal=[[Journal of the Royal Statistical Society]] |series=Series A |volume=128 |issue=1 |pages=162}}</ref> and [[Winifred Mackenzie]], first recipient of the [[Frances Wood (statistician)|Frances Wood]] memorial prize.<ref>{{cite journal| last1 = Taylor| first1 = Ursula Winifred| last2 =Aldrich | first2 = John| title=Winifred Mackenzie: Statistician, missionary, mother| journal= Significance| year= 2022 | volume= 19 | issue=5 | pages= 35–37| doi = 10.1111/1740-9713.01689| s2cid = 252533061}}</ref> As a post-graduate student [[Josiah Stamp]] worked "nominally" under Bowley's supervision.<ref>{{cite journal |last=Bowley |first=A. L. |year=1941 |title=Lord Stamp (obituary) |journal=[[Journal of the Royal Statistical Society]]|volume=104 |issue=2 |pages=193–196}}</ref>

Bowley produced a stream of studies of British economic statistics, beginning in the 1890s with work on trade and on wages and income. His 1900 publication ''Wages in the United Kingdom in the Nineteenth Century'' was created using the unpaid assistance of [[Edith Marvin]] when she was a researcher at the [[London School of Economics]].<ref>{{Cite ODNB|title=Marvin [née Deverell], Edith Mary (1872–1958), inspector of schools|url=https://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-48586|access-date=2020-10-29|year=2004|language=en|doi=10.1093/ref:odnb/48586|last1=Gordon|first1=Peter}}</ref> Proceeding to studies of [[national income]] in the 1920s and&nbsp;–30s. Especially noteworthy was his collaboration with [[Josiah Stamp, 1st Baron Stamp|Josiah Stamp]] on a comparison of the UK national income in 1911 and 1924. (Official national income statistics date only from the Second World War.) From around 1910 Bowley worked on social statistics as well. In aim, the work was a continuation of such surveys of social conditions as [[Rt Hon Charles Booth|Charles Booth's]] "Life and Labour of the People in London" (1889–1903) and [[Benjamin Seebohm Rowntree|Seebohm Rowntree's]] "Poverty, A Study of Town Life" (1901). The methodological innovation was the use of sampling techniques. Bowley gave a detailed exposition of his approach to sampling in a 62-page paper published in 1926. The culmination of Bowley's work on social surveys was the monumental ''New Survey of London Life and Labour.'' Even in the 1930s his research could take a new direction, as when he collaborated with his junior colleague [[R. G. D. Allen]] on an econometric study of family expenditure.<ref>{{harvtxt|Darnell|1981}}, p.&nbsp;159: "Bowley's major contribution to econometrics was the path-breaking text ''Family Expenditure'' (1935) which he wrote in collaboration with R. G. D. Allen".</ref> He retired in 1936 but served as acting Director of the Oxford University Institute of Statistics during the Second World War.

==Books==
Bowley's "Elements of Statistics"<ref>{{cite journal|author=Sanger, C. P.|title=Review: ''Elements of Statistics'' by A. L. Bowley|journal=The Economic Journal|date=June 1901|volume=11|issue=42|pages=193–197|doi=10.2307/2957149|jstor=2957149|s2cid=190139505 |url=https://zenodo.org/record/1449665}}</ref> is generally regarded as the first English-language [[statistics text-book]] {{By whom|date=December 2017}}. It described the techniques of descriptive statistics that would be useful for economists and social sciences, and in the early editions contained little statistical theory.

In statistical theory Bowley was not an innovator but drew on the writings of [[Karl Pearson]], [[Udny Yule]] and [[Francis Ysidro Edgeworth|F. Y. Edgeworth]]. In the 1930s, Bowley informed [[Ronald Fisher|Fisher]] that "Professor Edgeworth had written a great deal on a kindred subject" and slapping Neyman down with "I am not at all sure that the 'confidence' [in confidence interval] is not a 'confidence trick.'"<ref>{{harvtxt|Darnell|1981}}, p.&nbsp;165.</ref>

Bowley's teaching presaged several of the [[Exploratory data analysis|EDA]] ideas later popularised by [[John Tukey]], including [[stemplot]]s, decile [[boxplot]]s, the [[seven-figure summary]] and [[trimean]].{{citation needed|date=August 2013}}

Bowley's '"The Mathematical Groundwork of Economics'"<ref>{{cite journal|author=Edgeworth, F. Y.|title=Review: ''The Mathematical Groundwork of Economics'' by A. L. Bowley|journal=The Economic Journal|date=Sep 1924|volume=34|issue=135|pages=430–434|doi=10.2307/2222651|jstor=2222651|url=http://www.byterfly.eu/islandora/object/librib:719073/datastream/PDF/content/librib_719073.pdf}}</ref><ref>{{cite journal|author=Persons, W. M.|title=Review: ''The Mathematical Groundwork of Economics'' by A. L. Bowley|journal=Bull. Amer. Math. Soc.|year=1925|volume=31|issue=8|pages=469–470|url=https://www.ams.org/journals/bull/1925-31-08/S0002-9904-1925-04111-7/S0002-9904-1925-04111-7.pdf|doi=10.1090/s0002-9904-1925-04111-7}}</ref> was a notable attempt to provide the practising economist with the main ideas and techniques of mathematical economics; it was the first book in English of its kind. One of its successes was to bring the [[Edgeworth box]] to the attention of economists generally. Bowley was so successful that this is often referred to as the "Edgeworth-Bowley box". He also introduced the concept of [[conjectural variation]] into the theory of oligopoly in this book.

==Honours==
Bowley received many honours. In 1922, he became [[Fellow of the British Academy]], was appointed a [[Commander of the British Empire|CBE]] in 1937 <ref>{{London Gazette |date=11 May 1937 |supp=y |issue=34396 |pages=3073–3106 }}</ref> and knighted in 1950. He served on the council of the [[Royal Economic Society]] and was president of the [[Econometric Society]] 1938–9. The [[Royal Statistical Society]] awarded him its [[Guy Medal]] in Gold in 1935 and he served as its president 1938–40.<ref>{{cite web|url=http://www.rss.org.uk/site/cms/contentviewarticle.asp?article=486 |title=Royal Statistical Society Presidents |publisher=Royal Statistical Society |access-date=6 August 2010 |archive-url=https://web.archive.org/web/20120317044817/http://www.rss.org.uk/site/cms/contentviewarticle.asp?article=486 |archive-date=17 March 2012 |df=dmy }}</ref>

==Personal life==
According to Allen and George, "In personality Bowley was somewhat shy and retiring. He did not readily make friends and his close friendship with [[Edwin Cannan]] over many years was an almost unique experience." They recall an anecdote about an occasion when Bowley and Cannan were cycling with [[Francis Edgeworth]]. When Edgeworth wanted to discuss a mathematical question Cannan said, "Bowley, let us go a little faster, Edgeworth cannot talk mathematics at more than eight miles an hour."{{citation needed|date=August 2013}}

Bowley married Julia Hilliam in 1904 and the couple had three daughters.<ref name=Times_obituary/> His daughter, [[Marian Bowley]], also had an academic career in economics.<ref>{{citation|title=Seasons of a Scholar: Some Personal Reflections of an International Business Economist|first=John H.|last=Dunning|publisher=Edward Elgar Publishing|year=2009|isbn=9781848444973|page=58|url=https://books.google.com/books?id=kneQxADTuS0C&pg=PA58|quote=Marian Bowley was as rigorous and demanding a scholar as I imagine her father – Sir Arthur Bowley, the father of economic statistics and Professor of Economics at University College Reading between 1907 and 1919 – must have been.}}</ref>

==Bowley's law==
Bowley formulated [[Bowley's law]], which says that the proportion of [[GNP]] from labour is constant.

==Main publications of A. L. Bowley==
* [https://archive.org/details/accountofengland00bowl ''A Short Account of England's Foreign Trade in the Nineteenth Century''], 1893.
* ''Wages and Income in the United Kingdom Since 1860'', 1900.
* [http://catalog.hathitrust.org/Record/006554956 ''Elements of Statistics''], 1901. (4th edition in 1920)
* [https://archive.org/details/cu31924013702950 ''An Elementary Manual of Statistics''], 1910.
* [https://archive.org/details/livelihoodpovert00bowluoft ''Livelihood and Poverty: a study in the economic conditions of working-class households''], with A.R. Bennett-Hurst, 1915.
* ''The Division of the Product of Industry'', 1919
* ''The Mathematical Groundwork of Economics'', 1924.
* [https://archive.org/details/in.ernet.dli.2015.216222 ''Has Poverty Diminished? ''], with M.Hogg, 1925.
* Measurement of Precision attained in Sampling, ''Bulletin de l'Institut International de Statistique,''(1926) 22, Suppl. to Book 1, 1–62. [http://gallica.bnf.fr/ark:/12148/bpt6k61602s Gallica (after p. 451)]
* ''The National Income 1924'' with [[Josiah Stamp, 1st Baron Stamp|J. Stamp]], 1927.
* Bilateral Monopoly, 1928, ''Economic Journal. ''
* ''F. Y. Edgeworth's Contributions to Mathematical Statistics'', 1928.
* ''New Survey of London Life and Labour'', 1930–35.
* ''Family Expenditure'' with R.G.D. Allen, 1935.
* ''Three Studies in National Income'', 1939.

==Discussions==
*{{cite journal | last1 = Allen | first1 = R.D.G. | author-link = Sir Roy Allen | author-link2 = George R. F. | last2 = George | first2 = R. F. | year = 1957 | title = Obituary of Professor Sir Arthur Bowley | journal = [[Journal of the Royal Statistical Society, Series A]] | volume = 102 | pages = 236–241 }}
* [[W F Maunder]] and Sir Arthur Lyon Bowley (1869–1957) in '' Studies in the History of Statistics Probability,'' (ed. E S Pearson and M G Kendall) 1970. London: Griffin.
*{{citation|last=Darnell|first=A.|contribution=A.L. Bowley, 1969-1957|pages=140–174|title=Pioneers of Modern Economics in Britain|editor1-first=D. P.|editor1-last=O'Brien|editor2-first=J. R.|editor2-last=Presley|year=1981|location=London|publisher=Macmillan|url=https://books.google.com/books?id=8DZiFD1oNwwC&pg=PA140|isbn=9780333231753}}.
* Bowley, Arthur Lyon, pp.&nbsp;277–9 in ''Leading Personalities in Statistical Sciences from the Seventeenth Century to the Present, '' (ed. [[Norman Lloyd Johnson|N. L. Johnson]] and [[Samuel Kotz|S. Kotz)]] 1997. New York: Wiley. Originally published in ''Encyclopedia of Statistical Science. ''

==See also==
*[[Stem-and-leaf display]] attributed to Bowley's work

==References==
{{Reflist}}

==External links==
{{wikisource|works=or}}
*[https://web.archive.org/web/20060213233326/http://www.statistics.gov.uk/downloads/horizons/H32_web.pdf Horizons March 2005: Stats in History—Arthurian Legend]
*[https://archive.today/20121223085643/http://archives.lse.ac.uk/Record.aspx?src=CalmView.Catalog&id=COLL+MISC+0772 Bowley Papers at the LSE Archives]
*[https://web.archive.org/web/20050228230810/http://cepa.newschool.edu/het/profiles/bowley.htm New School: Arthur Lyon Bowley]

The New School entry has a photograph. There is another at
*[http://www.york.ac.uk/depts/maths/histstat/people/bowley.gif Bowley] on the [http://www.york.ac.uk/depts/maths/histstat/people/welcome.htm Portraits of Statisticians] page.

In the 4th edition of the ''Elements'' (1920) Bowley gave a lot more space to statistical theory. The following excerpt illustrates his approach
*[http://www.york.ac.uk/depts/maths/histstat/bowley.pdf Bowley's Pearsonian approach to chi-squared] on the [http://www.york.ac.uk/depts/maths/histstat/lifework.htm Life and Work of Statisticians] page.
This was written just before Bowley got involved in the controversy between Fisher and Pearson on chi-squared. In the fifth edition (1926) Bowley added a reference to his own contribution.

For Bowley's contribution to sampling theory put in historical perspective see
*[https://web.archive.org/web/20000919054016/http://lib.stat.cmu.edu/~fienberg/DonnerReports/FirstCensus.pdf Part D: A Review of Statistical Sampling from Laplace to Neyman]
*{{NPG name}}

{{Guy Medal}}
{{Royal Statistical Society presidents}}
{{Presidents of the Econometric Society}}
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{{DEFAULTSORT:Bowley, Arthur Lyon}}
[[Category:1869 births]]
[[Category:1957 deaths]]
[[Category:Scientists from Bristol]]
[[Category:People educated at Christ's Hospital]]
[[Category:Alumni of Trinity College, Cambridge]]
[[Category:English economists]]
[[Category:English statisticians]]
[[Category:Commanders of the Order of the British Empire]]
[[Category:Knights Bachelor]]
[[Category:Academics of the London School of Economics]]
[[Category:Fellows of the Econometric Society]]
[[Category:Presidents of the Econometric Society]]
[[Category:Presidents of the Royal Statistical Society]]