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When women act forcefully, research suggests, men are more likely to react badly. Another executive spent 30 years in Fortune companies, rising to the C-suite, the pool from which the next chief executive may be chosen. She described her experience in detail but insisted on anonymity because she has a settlement agreement with the company and remains friendly with her former boss. She gained a reputation for finding growth where others had not, often doubling the revenue of her divisions.

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She was seen as a possible successor to the chief executive, but she said she was unprepared for corporate politics at the very top. But the next rungs of the ladder depend not only on results but also on prevailing in an environment where everyone is competing for a chance at the top job. You just walked into the gym. You whip the ball, and if it happens to knock somebody on the head, so what?


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Her turning point came when she was outmaneuvered by male colleagues during a corporate reorganization. Believing she was not going to rise further, she asked for an exit package. Looking back, she is convinced that being a woman hurt her. All of the guys had missed their numbers more. She drew an unwelcome conclusion.

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I truly believe that. Such experiences resonate even with women who did rise to the top job. It actually does work for most of your career. Sally Blount, dean of the Kellogg School of Management at Northwestern and the only woman to lead a top 10 business school, noted that data predicts that half or more of the women who earn an M. The reasons range from family conflicts to placing less inherent value on position or money. That accounts in part for the low number of women who do reach the very top job, because fewer remain in the pipeline.

Yet even those women who stay and reach the C-suite are more likely than men to be overlooked, Ms. Blount said.

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The parallels with politics are striking. Research in both fields, including some conducted after Mrs. In a Korn Ferry survey in April of male and female senior executives, 43 percent said they thought that continued bias against women as chief executives was the primary reason more women did not make it to the top in their own companies — and 33 percent thought women in their firms were not given sufficient opportunities to become leaders.

At DuPont, Ms.

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Kullman said, she found that men were being promoted within two years, women in three. The Lean In survey shows a pervasive sense among women that they face structural disadvantages: They are less likely than men to believe they will be able to participate in meetings, receive challenging assignments or find their contributions valued. The bleakest perceptions are from minority women; only 29 percent of black women think the best opportunities at their companies go to the most deserving employees, compared with 47 percent of white women.

Some men see the competition in zero-sum terms. One corporate recruiter described a conversation with a male client seeking an additional board post. Yet many women work in companies with public commitments to diversity and clear policies against discrimination, with many men who sincerely believe they want women to advance. That makes many of the subtler ways women encounter bias more pernicious than blatant discrimination, a Harvard Business Review meta-analysis found. Gerri Elliott, a former senior executive at Juniper Networks who said she did not personally encounter bias , recounts a story related by a colleague: A presenter asked a group of men and women whether anyone had expertise in breast-feeding.

A man raised his hand. He had watched his wife for three months. But she and other women describe a culture in which men sometimes feel hesitant to give women honest but harsh feedback, which can be necessary for them to ascend, because they fear women may react emotionally. Dina Dublon, who retired in as chief financial officer of JPMorgan Chase, said male colleagues sometimes told her they were reluctant to have dinner or drinks with female subordinates — important bonding activities in the corporate world — because it might be seen as flirtatious.

The challenge for women is how to enter into the intangible but crucial circle of male camaraderie. It is narrow-minded and ineffective, but human. The widespread concern in business circles about the slow progress of women to the top has spawned a virtual cottage industry of recent initiatives, from Paradigm for Parity , of which Ms.

Kullman is a co-chairwoman, to x25, a Rockefeller Foundation initiative aiming for female chief executives in the Fortune by That number now stands at 32 — an all-time high and spurt from last year, when there were Assuming that these samples were representative of France, Laplace produced his estimate for the entire population.

The method of least squares , which was used to minimize errors in data measurement , was published independently by Adrien-Marie Legendre , Robert Adrain , and Carl Friedrich Gauss Gauss had used the method in his famous prediction of the location of the dwarf planet Ceres. The observations that Gauss based his calculations on were made by the Italian monk Piazzi.

The method of least squares was preceded by the use a median regression slope. This method minimizing the sum of the absolute deviances. A method of estimating this slope was invented by Roger Joseph Boscovich in which he applied to astronomy. The term probable error der wahrscheinliche Fehler - the median deviation from the mean - was introduced in by the German astronomer Frederik Wilhelm Bessel. Other contributors to the theory of errors were Ellis , De Morgan , Glaisher , and Giovanni Schiaparelli In the 19th century authors on statistical theory included Laplace, S.

Gustav Theodor Fechner used the median Centralwerth in sociological and psychological phenomena. Francis Galton used the English term median for the first time in having earlier used the terms middle-most value in and the medium in Adolphe Quetelet — , another important founder of statistics, introduced the notion of the "average man" l'homme moyen as a means of understanding complex social phenomena such as crime rates , marriage rates , and suicide rates.

The first tests of the normal distribution were invented by the German statistician Wilhelm Lexis in the s. The only data sets available to him that he was able to show were normally distributed were birth rates. Although the origins of statistical theory lie in the 18th-century advances in probability, the modern field of statistics only emerged in the lateth and earlyth century in three stages. The first wave, at the turn of the century, was led by the work of Francis Galton and Karl Pearson , who transformed statistics into a rigorous mathematical discipline used for analysis, not just in science, but in industry and politics as well.

The second wave of the s and 20s was initiated by William Sealy Gosset , and reached its culmination in the insights of Ronald Fisher.

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This involved the development of better design of experiments models, hypothesis testing and techniques for use with small data samples. The final wave, which mainly saw the refinement and expansion of earlier developments, emerged from the collaborative work between Egon Pearson and Jerzy Neyman in the s. The first statistical bodies were established in the early 19th century.

The Royal Statistical Society was founded in and Florence Nightingale , its first female member, pioneered the application of statistical analysis to health problems for the furtherance of epidemiological understanding and public health practice. However, the methods then used would not be considered as modern statistics today. The Oxford scholar Francis Ysidro Edgeworth 's book, Metretike: or The Method of Measuring Probability and Utility dealt with probability as the basis of inductive reasoning, and his later works focused on the 'philosophy of chance'.

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Although statistical surveys of social conditions had started with Charles Booth 's "Life and Labour of the People in London" and Seebohm Rowntree 's "Poverty, A Study of Town Life" , Bowley's, key innovation consisted of the use of random sampling techniques. Francis Galton is credited as one of the principal founders of statistical theory.

His contributions to the field included introducing the concepts of standard deviation , correlation , regression and the application of these methods to the study of the variety of human characteristics - height, weight, eyelash length among others. He found that many of these could be fitted to a normal curve distribution. Galton submitted a paper to Nature in on the usefulness of the median. The actual weight was pounds: the median guess was The guesses were markedly non-normally distributed.

Galton's publication of Natural Inheritance in sparked the interest of a brilliant mathematician, Karl Pearson , [29] then working at University College London , and he went on to found the discipline of mathematical statistics. His work grew to encompass the fields of biology , epidemiology , anthropometry, medicine and social history.

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In , with Walter Weldon , founder of biometry , and Galton, he founded the journal Biometrika as the first journal of mathematical statistics and biometry. His work, and that of Galton's, underpins many of the 'classical' statistical methods which are in common use today, including the Correlation coefficient , defined as a product-moment; [31] the method of moments for the fitting of distributions to samples; Pearson's system of continuous curves that forms the basis of the now conventional continuous probability distributions; Chi distance a precursor and special case of the Mahalanobis distance [32] and P-value , defined as the probability measure of the complement of the ball with the hypothesized value as center point and chi distance as radius.

He also founded the statistical hypothesis testing theory , [32] Pearson's chi-squared test and principal component analysis. The second wave of mathematical statistics was pioneered by Ronald Fisher who wrote two textbooks, Statistical Methods for Research Workers , published in and The Design of Experiments in , that were to define the academic discipline in universities around the world. He also systematized previous results, putting them on a firm mathematical footing. In his seminal paper The Correlation between Relatives on the Supposition of Mendelian Inheritance , the first use to use the statistical term, variance.

In , at Rothamsted Experimental Station he started a major study of the extensive collections of data recorded over many years. This resulted in a series of reports under the general title Studies in Crop Variation. In he published The Genetical Theory of Natural Selection where he applied statistics to evolution.

Over the next seven years, he pioneered the principles of the design of experiments see below and elaborated his studies of analysis of variance.


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    • He furthered his studies of the statistics of small samples. Perhaps even more important, he began his systematic approach of the analysis of real data as the springboard for the development of new statistical methods. He developed computational algorithms for analyzing data from his balanced experimental designs. In , this work resulted in the publication of his first book, Statistical Methods for Research Workers. In , this book was followed by The Design of Experiments , which was also widely used. In addition to analysis of variance, Fisher named and promoted the method of maximum likelihood estimation.

    Fisher also originated the concepts of sufficiency , ancillary statistics , Fisher's linear discriminator and Fisher information. His article On a distribution yielding the error functions of several well known statistics presented Pearson's chi-squared test and William Sealy Gosset 's t in the same framework as the Gaussian distribution , and his own parameter in the analysis of variance Fisher's z-distribution more commonly used decades later in the form of the F distribution.