Question

What does it mean to partition variation?

Answer 1

Generally we know that, Variance is used to represent the numbers in given set how far lie to be apart.

That means it calculated the sum of squared deviations and overall mean

So, parition of variation process under deals with sum of squares (SS).

Partitioning your data into fixed and random components of variation . Making the effort to collect additional data when it is warranted can save a lot of time and effort trying to model variation as if it were random. trying to find a surrogate for those variables can be a reasonable alternative.

In the ANOVA setting,the parition of variance works as follows,

the observed variance in a particular variable is partitioned into components attributable to different sources of variation. ...ANOVA is useful for testing three or more group means for statistical significance.