On Sat, 14 Dec 2013 06:46:49 -0800 (PST), oercim <email@example.com> wrote:
>Hello, I have a comment for ANOVA. However, I cant find its relation with usual logic of ANOVA. Lets we have a variance s1= which is variance of whole data. Lets s2 be the avarage of variance of each groups(within). So If the means are equal, total s1 must be very close to s2. As the means gets far, the total vaiance will be larger according to s2. I mean, If the means are equal s1/s2=~1, If the means are not close, s1/s2>1. However, I cant find a relation with this logic and ythe usual between- within logic. Do I think something wrong? Thanks a lot.
I suspect that you are being confused by terminology - sometimes "variance" is used to describe an average, and sometimes it is a total. For what you are asking, I think you are wrong in referring to "s2 [as] the average of variance of each groups (within)".
"Analysis of sums of squares" is a less ambiguous way to describe ANOVA.
The simple and famous ANOVA relationship is TotalSS= WithinSS + BetweenSS.
The TotalSS is the sum of the WithinSS of the separate groups, plus the BetweenSS.
When group means are (near) equal, the BetweenSS is (near) zero.