ANOVA Within-Group Variation
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An ANOVA Within-Group Variation is a statistical measure that measures the variance due to the differences within individual samples.
- Example(s):
- Counter-Example(s):
- See: Grand Mean, Population, F-test Statistic, Decision Rule.
References
2021
- (James, 2021) ⇒ https://people.richland.edu/james/lecture/m170/ch13-1wy.html Retrieved:2021-09-19.
- QUOTE: The variation due to differences within individual samples, denoted SS(W) for Sum of Squares Within groups. Each sample is considered independently, no interaction between samples is involved. The degrees of freedom is equal to the sum of the individual degrees of freedom for each sample. Since each sample has degrees of freedom equal to one less than their sample sizes, and there are $k$ samples, the total degrees of freedom is $k$ less than the total sample size: $df = N - k$.
The variance due to the differences within individual samples is denoted MS(W) for Mean Square Within groups. This is the within group variation divided by its degrees of freedom. It is also denoted by $s_w^2$. It is the weighted average of the variances (weighted with the degrees of freedom).
- QUOTE: The variation due to differences within individual samples, denoted SS(W) for Sum of Squares Within groups. Each sample is considered independently, no interaction between samples is involved. The degrees of freedom is equal to the sum of the individual degrees of freedom for each sample. Since each sample has degrees of freedom equal to one less than their sample sizes, and there are $k$ samples, the total degrees of freedom is $k$ less than the total sample size: $df = N - k$.