"There is, then, in this analysis of variance no indication of any other than innate and heritable factors at work." (Sir Ronald A Fisher, "The Causes of Human Variability", Eugenics Review Vol. 10, 1918)
"The mean and variance are unambiguously determined by the distribution, but a distribution is, of course, not determined by its mean and variance: A number of different distributions have the same mean and the same variance." (Richard von Mises, "Probability, Statistics And Truth", 1928)
"However, perhaps the main point is that you are under no obligation to analyse variance into its parts if it does not come apart easily, and its unwillingness to do so naturally indicates that one’s line of approach is not very fruitful." (Sir Ronald A Fisher, [Letter to Lancelot Hogben] 1933)
"The analysis of variance is not a mathematical theorem, but rather a convenient method of arranging the arithmetic." (Sir Ronald A Fisher, Journal of the Royal Statistical Society Vol. 1, 1934)
"The statistics themselves prove nothing; nor are they at any time a substitute for logical thinking. There are […] many simple but not always obvious snags in the data to contend with. Variations in even the simplest of figures may conceal a compound of influences which have to be taken into account before any conclusions are drawn from the data." (Alfred R Ilersic, "Statistics", 1959)
"Pencil and paper for construction of distributions, scatter diagrams, and run-charts to compare small groups and to detect trends are more efficient methods of estimation than statistical inference that depends on variances and standard errors, as the simple techniques preserve the information in the original data." (William E Deming, "On Probability as Basis for Action" American Statistician Vol. 29 (4), 1975)
"A good estimator has to be more than just consistent. It also should be one whose variance is less than that of any other estimator. This property is called minimum variance. This means that if we run the experiment several times, the 'answers' we get will be closer to one another than 'answers' based on some other estimator." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)
"Two clouds of uncertainty may have the same center, but one may be much more dispersed than the other. We need a way of looking at the scatter about the center. We need a measure of the scatter. One such measure is the variance. We take each of the possible values of error and calculate the squared difference between that value and the center of the distribution. The mean of those squared differences is the variance." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)
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