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**Herman Otto Hartley** (born Hermann Otto Hirschfeld in Berlin, Germany; 1912–1980) was a German American statistician.^{[1]} He made significant contributions in many areas of statistics, mathematical programming, and optimization. He also founded Texas A&M University's Department of Statistics.

H.O. Hartley | |
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Born | Hermann Otto Hirschfeld April 13, 1912 Berlin, Germany |

Died | December 30, 1980 | (aged 68)

Alma mater | University of Berlin University of Cambridge University College London |

Known for | Pearson Hartley Biometrika Tables, Greenwood Hartley Guide to Tables in Mathematical Statistics, mathematical foundations for correspondence analysis, pioneer in the use of EM algorithm, F-max test, survey sampling, mathematical programming and optimization, estimation of variance components, analysis of incomplete data, stochastic PERT |

Awards | Wilks Memorial Award (1973) Fellow of Institute of Mathematical Statistics (1949) Fellow of American Statistical Association (1953) Elected Member of International Statistics Institute President, Eastern North American Region International Biometric Society (1959) President, American Statistical Association (1979) |

Scientific career | |

Fields | Statistics, mathematics |

Institutions | Harper Adams Agricultural College Scientific Computing Service University College London Iowa State University Texas A&M University Duke University |

Thesis | Calculus of Variations and Optimal Control (1934 and 1940)Statistical Distribution Functions |

Doctoral advisor | Adolf Hammerstein (in Berlin) John Wishart (in Cambridge) |

Doctoral students | George Box |

Hartley's earliest papers appeared under the name H.O. Hirschfeld. His father having been born in England, Hartley had dual nationality. He cleverly translated his German last name Hirschfeld (Hirsch = Hart, Feld = field = lea = ley) into English.^{[2]}

In 1934, at the age of 22, Hartley earned a Ph.D. in mathematics from the University of Berlin, followed by a Ph.D. in mathematical statistics from the University of Cambridge in 1940 and a Doctorate of Science in mathematical statistics from University College London in 1954.^{[3]} He began his independent academic career at UCL, where he met Egon Pearson, with whom he collaborated to produce the classic two-volume *Biometrika Tables for Statisticians,* and also developed Hartley's F-max test^{[4]} for equality of variances.

A one-year Visiting Research Professor in Statistics position at then-Iowa State College brought Hartley to the United States in 1953 and to the forefront of a major statistics program.^{[5]} The position was extended after that initial year to include nine more years, during which he became deeply involved in research and teaching. His early computational talent enabled him to play a prominent part in instituting computing both for scientific and administrative purposes at Iowa State, which for the first time had university-wide service in data processing and numerical analysis. He also was a remarkably active consultant on statistics to a wide variety of scientists on campus.

After a decade at Iowa State, Hartley came to Texas A&M University, where he was appointed in 1963 as a distinguished professor and founding director of the Institute of Statistics.^{[6]} He was tasked with leading the Graduate Institute of Statistics, which had been formed a year earlier with only a handful of faculty, two graduate students, and the lofty mandate of providing statistical research, consulting, and instruction for all of Texas A&M University. In the ensuing decade and a half, he built his initial faculty of four into a group of 16, directed more than 30 doctoral students, and attracted significant research funding.

Hartley was short in stature, and in giving lectures, he would often begin with an audience icebreaker, asking, "Can you hear me? Can you see me?" He brought many distinguished statisticians to Texas A&M during his tenure, including Pearson, a slight man of "considerable height" who towered above Hartley when standing side by side, earning him the classic introduction from Hartley: "Never were there two more appropriate statisticians to work on the concept of range statistics."^{[6]}

Hartley remained active at Texas A&M until 1979, when he accepted a full-time visiting professor position at Duke University while also serving as statistician with the National Testing Service in Durham, N.C., until his death on December 30, 1980.

Hartley was an elected fellow of the Institute of Mathematical Statistics (1949) and the American Statistical Association (1953)^{[7]} as well as an elected member of the International Statistical Institute (1954). He served as president of the Eastern North American Region of the Biometric Society (1959), which was the first region formed in the present-day International Biometric Society, and as president of the American Statistical Association (1979). During his lifetime, Hartley earned many accolades for his contributions to mathematics and statistics, including the ASA's 1973 Samuel S. Wilks Medal recognizing his national and international efforts in the field of statistics.

A prolific author, Hartley published nearly 100 papers (three-quarters of them during the final two decades of his career) in top-tiered journals until his mandatory retirement in 1977.

**Hartley's most well-known work includes:**

*Biometrika Tables for Statisticians*with E. Pearson in 1954 and 1972- The origination of the EM Algorithm methodology while at Iowa State in 1958.
^{[8]}Today it is one of the most widely used estimation methods. - Hartley’s F-max Test for equality of variances
^{[4]}

**He also made pioneering contributions to:**

- Politz-Simmons Estimator, which is a method for dealing with bias due to “not at home” entries in survey sampling.
- Hartley-Ross Estimator, which aims to estimate the mean of finite population of size N with the help of a known mean of a correlated variable. Unbiasedness proved and variance given.
- RHC Sampling Scheme, which estimates the population total using an unequal-probability sampling without replacement from a finite population
- Correspondence analysis, which is similar to principal component analysis but as applied to categorical data.

**Hartley's other research spanned a variety of ground-breaking topics, including:**

- Sample survey estimation and design
^{[9]} - Mathematical optimization
^{[10]}^{[11]} - Variance component estimation
^{[8]} - Stochastic PERT
^{[12]} - The development of designed experiments to estimate safe doses of carcinogenic agents

Through his passion for mathematics and statistics, amiable demeanor, and lively energy, Hartley won the hearts of his colleagues and students, who affectionately referred to him as HOH. Widely regarded as not only a brilliant academician, but also a warm and caring human being, Hartley was deeply committed to all phases of his profession, including education, research, and delivery of knowledge and advice to users of statistics.

Hartley's legacy at Texas A&M continues to unfold via the H.O. Hartley Award presented annually for the past 40 years to a statistics former student who best reflects Hartley's tradition of distinguished service to the discipline, the biannual Hartley Memorial Lecture Series also named in his honor, and the H.O. Hartley Chair in Statistics,^{[13]} established in July 2019 by his students and the Thomas W. Powell '62 Endowed Graduate Fellowship Fund.

**^**"ASA article by William B. Smith" (PDF). Archived (PDF) from the original on March 7, 2013.**^**David, H.A. "H.O. Hartley, 1912 - 1980".*International Statistical Review*.**50**(3): 327–330 – via JSTOR.**^**Herman Otto Hartley at the Mathematics Genealogy Project- ^
^{a}^{b}Hartley, H. O. (1950). "The Maximum F-Ratio as a Short-Cut Test for Heterogeneity of Variance".*Biometrika*.**37**(3/4): 308–312. doi:10.2307/2332383. ISSN 0006-3444. JSTOR 2332383. PMID 14801057. **^**Smith, W.B. (August 1981). "In Memoriam: Herman Otto Hartley (1912 - 1980)".*The American Statistician*.**35**(3): 142–143. doi:10.1080/00031305.1981.10479332. JSTOR 2683980 – via JSTOR.- ^
^{a}^{b}A. Agresti, X.-L. Meng (eds.) (2013).*Strength in Numbers: The Rising of Academic Statistics Departments in the U.S*. Springer. pp. 301–316.`{{cite book}}`

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has generic name (help) **^**"Election of New Fellows".*The American Statistician*.**8**(1): 17–18. February 1954. doi:10.1080/00031305.1954.10482018. JSTOR 2681662.- ^
^{a}^{b}Hartley, H. O.; Rao, J. N. K. (1967). "Maximum-Likelihood Estimation for the Mixed Analysis of Variance Model".*Biometrika*.**54**(1/2): 93–108. doi:10.2307/2333854. ISSN 0006-3444. JSTOR 2333854. PMID 6049561. **^**HARTLEY, H. O.; RAO, J. N. K. (1968). "A new estimation theory for sample surveys".*Biometrika*.**55**(3): 547–557. doi:10.1093/biomet/55.3.547. ISSN 0006-3444.**^**Hartley, H. O. (1961). "Nonlinear Programming by the Simplex Method".*Econometrica*.**29**(2): 223–237. doi:10.2307/1909291. ISSN 0012-9682. JSTOR 1909291.**^**Hartley, H. O.; Hocking, R. R. (1963). "Convex Programming by Tangential Approximation".*Management Science*.**9**(4): 600–612. doi:10.1287/mnsc.9.4.600. ISSN 0025-1909.**^**Hartley, H. O.; Wortham, A. W. (1966). "A Statistical Theory for PERT Critical Path Analysis".*Management Science*.**12**(10): B–469-B-481. doi:10.1287/mnsc.12.10.b469. ISSN 0025-1909.**^***Hartley Endowed Chair Award Ceremony - October 23, 2020*, archived from the original on 2021-12-12, retrieved 2021-06-04