Example
Suppose there is a distribution of test scores in three topics (categories):
- Algebra: 45, 70, 29, 15 and 21 (5 scores)
- Geometry: 40, 20, 30 and 42 (4 scores)
- Statistics: 65, 95, 80, 70, 85 and 73 (6 scores).
Then the subject averages are 36, 33 and 78, with an overall average of 52.
The sums of squares of the differences from the subject averages are 1952 for Algebra, 308 for Geometry and 600 for Statistics, adding to 2860, while the overall sum of squares of the differences from the overall average is 9640. The difference of 6780 between these is also the weighted sum of the square of the differences between the subject averages and the overall average:
This gives
suggesting that most of the overall dispersion is a result of differences between topics, rather than within topics. Taking the square root
Observe that for the overall sample dispersion is purely due to dispersion among the categories and not at all due to dispersion within the individual categories. For a quick comprehension simply imagine all Algebra, Geometry, and Statistics scores being the same respectively, e.g. 5 times 36, 4 times 33, 6 times 78.
The limit refers to the case without dispersion in the categories contributing to the overall dispersion. The trivial requirement for this extreme is that all category means are the same.
Read more about this topic: Correlation Ratio
Famous quotes containing the word example:
“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
—Marcel Proust (1871–1922)