Correlation ratio
From Psychology Wiki
Community portal · Tasks to do · News · Help
Clinical · Educational · Ind&Org · Other fields · Professional · Transpersonal · World
Assessment |
Biopsychology |
Comparative |
Cognitive |
Developmental |
Language
Personality |
Philosophy |
Research Methods |
Social |
Statistics
Statistics: Scientific method · Research methods · Experimental design · Undergraduate statistics courses · Statistical tests · Game theory · Decision theory
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.
Suppose each observation is yxi where x indicates the category that observation is in and xi is the label of the particular observation. We will write nx for the number of observations in category x (not necessarily the same for different values of x) and
and 
then the correlation ratio η (eta) is defined so as to satisfy
which might be written as
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; if not then the correlation ratio will be larger in magnitude, though still no more than 1 in magnitude. It can therefore be used for judging non-linear relationships.
| This page uses content from the English-language version of Wikipedia. The original article was at Correlation ratio. The list of authors can be seen in the page history. As with Psychology Wiki, the text of Wikipedia is available under the GNU Free Documentation License. |
