The variability hypothesis, also known as the greater male variability hypothesis, states that males display greater variability in traits than females do. It has often been discussed in relation to cognitive ability, where it has been observed that human males are more likely than females to have very high or very low intelligence. The sex-difference in the variability of intelligence has been discussed since at least Charles Darwin. Sex-differences in variability are present in many abilities and traits - including physical, psychological and genetic ones. It is not only found in humans but in other sexually-selected species as well.
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Later that century the character of the variability hypothesis was altered to coincide better with Charles Darwin's emphasis on the importance of variation from the average for the evolutionary process. Following Darwin, the variability hypothesis was instead put forward as man's greater variability compared to women, and its application was soon extended to sex differences in mental abilities. Thus, men were thought to vary greatly in their abilities, while women were assumed to be basically the same in their abilities. The greater number of men at both ends of the intellectual spectrum (as patients in institutions and as great intellectual achievers) was taken as evidence of man's greater innate variability.
In the early twentieth century, the variability hypothesis flourished in sociological, psychological, medical and educational literature. The hypothesis received support not from empirical evidence, but rather from "armchair dogma" about innate female inferiority. Among the proponents of the variability hypothesis at this time were psychologists G. Stanley Hall, Edward Lee Thorndike, and James McKeen Cattell. One logical conclusion drawn from the variability hypothesis was that since women were not expected to exhibit above-average intelligence, it was unreasonable to expect eminence from them. This led Thorndike and Hall to suggest the adoption of curricula aimed at preparing women for their future roles as mothers and wives. The only significant critic of the variability hypothesis was Karl Pearson, a British psychologist who had studied variability in 1897 and found no sex differences. Pearson's research was the only published scientific investigation of the variability hypothesis prior to the work of American psychologist Leta Hollingworth.
Leta Hollingworth's studies
Hollingworth's position at the Clearing House for Mental Defectives allowed her the opportunity to refute the variability hypothesis. By examining the case records of 1,000 patients, Hollingworth determined that, although men outnumbered women in the clearing house, the ratio of men to women decreased with age. Hollingworth explained this to be the result of men facing greater societal expectations than women. Consequently, deficiencies in men were often detected at an earlier age, while similar deficiencies in women might not be detected because less was expected of them. Therefore, deficiencies in women would be required to be more pronounced than those in men in order to be detected at similar ages.
Hollingworth also attacked the variability hypothesis theoretically, criticizing the underlying logic of the hypothesis.  Hollingworth argued that the variability hypothesis was flawed because: (1) it had not been empirically established that men were more anatomically variable than women, (2) even if greater anatomical variability in men were established this would not necessarily mean that men were also more variable in mental traits, (3) even if it were established that men were more variable in mental traits this would not automatically mean that men were innately more variable, (4) variability is not significant in and of itself, but rather depends on what the variability consists of, and (5) that any possible differences in variability between men and women must also be understood with reference to the fact that women lack the opportunity to achieve eminence because of their prescribed societal and cultural roles. Additionally, the argument that great variability automatically meant greater range was criticized by Hollingworth.[how?]
In an attempt to examine the validity of the variability hypothesis, while avoiding intervening social and cultural factors, Hollingworth gathered data on birth weight and length of 1,000 male and 1,000 female neonates. This research found virtually no difference in the variability of male and female infants, and it was concluded that if variability "favoured" any sex it was the female sex. Additionally, along with the anthropologist Robert Lowie, Hollingworth published a review of literature from anatomical, physiological, and cross-cultural studies, in which no objective evidence was found to support the idea of innate female inferiority.
Hollingworth's doctoral dissertation also dealt with the psychology of women. Entitled "Functional periodicity: An experimental study of the mental and motor abilities of women during menstruation", it found no evidence of changes in performance associated with phases of the menstrual cycle, refuting a common belief of the time. Hollingworth's graduate supervisor was E. L. Thorndike, himself a supporter of the variability hypothesis.
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The results seem to vary based on the type of problem, but some recent studies have found that the variability hypothesis is true for parts of IQ tests, with more men falling at the extremes of the spectrum. In general different studies show different results; for example, males are more variable in mathematical and spatial abilities, but in some others the women are more variable.
Recent studies shows that greater male variability in mathematics persists in the U.S., although the ratio of boys to girls at the top end of the distribution is reversed in some specific immigrant groups. A 2007 meta-analysis found that males are more variable on most measures of quantitative and visuospatial ability. A 2014 review found that males tend to have higher variance on mathematical and verbal abilities but females tend to have higher variance on fear and emotionality; however, the differences in variance are small and the causes remain unknown. A 2005 meta-analyses found greater female variability on the advanced progressive matrices, and no difference in variability on the standard progressive matrices. A 2010 meta-analysis of 242 studies found that males have an 8% greater variance in mathematical abilities than females. A 2017 literature review by Sean Stevens for the Heterodox Academy found that males do tend to be more variable than females on a variety of measures of intelligence and personality and that gender-egalitarian countries demonstrate the greatest differences. Theodore P. Hill proposed an evolutionary origin of variability.
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