ANOVA (Analysis of Variance)
ANOVA allows us to compare more than two means.
In case 1, we want to know if the differences in sample means can plausibly be
attributed to true differences in μ , 1 ,2and μ . 3
Case 2 could be a sample from the same population used in case 1. If true, we are
trying to protect against odd samples like in case 1.
We call this analysis of variance since we wish to analyze the variability in the data to
see how much can be attributed to differences in the μ’s and how much is due to
individual variability in each individual parameter.
So we have two forms of variability
Variability between populations – indicates true differences in μ
Variability within populations
H 0 μ 1 μ =2… = μ k
H A At least one μ diifers (at least two are different)
Each of the k populations have normal distribution.
σ 1 σ =2… = σ k
Each of the samples are selected independently.
Observations in each sample are selected independently.
ANOVA test based on SSM and SSE
SSM also called SSBetween, measures disparity between sample means
SSM = n ( 1 x 1 - x ) + n (2 x 2 - x ) + … + n (k xk + x )2 x