Introduction to Mathematical Statistics

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R. G. Adams, 1918 - Mathematical statistics - 150 pages

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Page 65 - ... probably the exception rather than the rule among political and economic values, and even where the distribution appears normal .(without any strong a priori reason) caution must be exercised in measuring degrees of reliability by means of the probable error formula. Yet to quote one authority : " It can be shown mathematically that even when the form of distribution is distinctly non-normal the ordinary rules for finding the probable deviations hold with an approximation close enough for practical...
Page 149 - The Application of the Method of Multiple Correlation to the Estimation of Post-Censal Population," Journal of the Royal Statistical Society, 74 (May, 1911), 575-620.
Page 76 - The correlation ratio is obtained by the formula , = °mv ' "i where <rmv is the standard deviation of the weighted means of the y arrays about the mean of the population. 2m, the square root of the mean square deviation of the means of the arrays from the regression line, is derived by the formula due to PEARSON (1905).
Page 65 - That is, a deviation greater than about three times the standard deviation must significantly indicate that the measurement is not that of an individual taken from the same material ; it does not belong to the same distribution but to another distribution which has some conditions different from the first.
Page 73 - Two characteristics are said to be correlated -when there is a tendency for the changes in the value of one to depend on the changes in the value of the other.
Page 150 - On the Theory of Consistence of Logical Class Frequencies and its Geometrical Representations", Phil.
Page 80 - ... are expressed in terms of money which has cheapened and consequently, at least to some extent, caused both wages and general prices to increase. When money is becoming cheaper both wages and prices tend in general to rise together; when money is becoming dearer both wages and prices tend in general to fall together.
Page 147 - Contributions to the mathematical theory of evolution. I. On the dissection of asymmetrical frequency curves. Phil. Trans.
Page 70 - The columns and rows are spoken of as arrays ; the columns as y-arrays of type x and the rows as x-arrays of type y.
Page 106 - But the sum of the squares of two quantities is always greater than twice their products and hence each term on the left is greater than the corresponding term on the right, thus proving the theorem.

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