On some properties of normal distributions, univariate and bivariate, based on sums of squares of frequencies
成果类型：
Article
署名作者：
Yule, GU
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
发表日期：
1938
页码：
110
关键词：
摘要：
If the distribution of a normal variate has standard deviation [sigma] and the total integral [image] ydx is N1, y2 has also a o normal distribution with standard deviation [image]and integral [image]. This suggests that, if N2 is the sum of squares of class frequencies, a good estimate for [sigma] might be [image],N1 being of course the sum of class frequencies. [sigma] and [sigma]e are compared for several series of statistics; their agreement is an inadequate test for normality. An example indicates that increased coarseness of grouping causes an increase in [sigma]e comparable to that of [sigma] without Sheppard''s correction, [image] which Yule called the Concentration, indicates the extent to which frequency is piled on to a few intervals. For a strictly normal distribution the standard error of [sigma]e is about one-ninth more than that of [sigma]. Deviation from normality markedly changes this fraction. Similar considerations for bivariate distributions lead to the equation [image] This suggests using K as an estimate for the coefficient of contingency, where [image],N2N2[image] being the sums of squares of frequencies for [chi]1 and [chi]2 respectively, and N2[image] the sum of squares of frequencies for both variates. This suggestion turns out to have little value.