Definition
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
- and
where is the mean of the category x and is the mean of the whole population. The correlation ratio η (eta) is defined as to satisfy
which can be written as
i.e. the weighted variance of the category means divided by the variance of all samples.
It is worth noting that if the relationship between values of and values of is linear (which is certainly true when there are only two possibilities for x) this will give the same result as the square of the correlation coefficient, otherwise the correlation ratio will be larger in magnitude. It can therefore be used for judging non-linear relationships.
Read more about this topic: Correlation Ratio
Famous quotes containing the word definition:
“It is very hard to give a just definition of love. The most we can say of it is this: that in the soul, it is a desire to rule; in the spirit, it is a sympathy; and in the body, it is but a hidden and subtle desire to possess—after many mysteries—what one loves.”
—François, Duc De La Rochefoucauld (1613–1680)
“According to our social pyramid, all men who feel displaced racially, culturally, and/or because of economic hardships will turn on those whom they feel they can order and humiliate, usually women, children, and animals—just as they have been ordered and humiliated by those privileged few who are in power. However, this definition does not explain why there are privileged men who behave this way toward women.”
—Ana Castillo (b. 1953)
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)