Correlation ratio

In statistics, the correlation ratio is a measure of the relationship between the statistical dispersion within individual categories and the dispersion across the whole population or sample. The measure is defined as the ratio of two standard deviations representing these types of variation. The context here is the same as that of the intraclass correlation coefficient, whose value is the square of the correlation ratio.As a descriptive statistic the utility of the correlation ratio is extremely limited. It will be noticed that the number of degrees of freedom in the numerator of η 2 {displaystyle eta ^{2}} depends on the number of the arraysAgain, a long-established method such as the use of the correlation ratio is passed over in a few words without adequate description, which is perhaps hardly fair to the student who is given no opportunity of judging its scope for himself. In statistics, the correlation ratio is a measure of the relationship between the statistical dispersion within individual categories and the dispersion across the whole population or sample. The measure is defined as the ratio of two standard deviations representing these types of variation. The context here is the same as that of the intraclass correlation coefficient, whose value is the square of the correlation ratio. Suppose each observation is yxi where x indicates the category that observation is in and i is the label of the particular observation. Let nx be the number of observations in category x and where y ¯ x {displaystyle {overline {y}}_{x}} is the mean of the category x and y ¯ {displaystyle {overline {y}}} is the mean of the whole population. The correlation ratio η (eta) is defined as to satisfy