ANOVA Types of Variation

Variation between Groups Weighted sum of variances between sample mean and overall mean Large  factor affects system Small  likely from same data set SSGroups=n 1 (x 1 -x) 2 +n 2 (x 2 -x) 2 +…+n k (x k -x) 2 Used in numerator of F-statistic Degrees of freedom= k-1

Variation within Groups Weighted sum of variances between data values and sample mean of each group Small  high precision SSE= (n 1 -1)s 1 2 +(n 2 -1)s 2 2 +…+(n k -1)s k 2 Used in denominator of F-statistic Degrees of freedom= N-k

Total Variation Total sum of squares Sum of variation between groups and within groups SSTotal= Σ values (x ij -x bar ) 2 Degrees of freedom= (k-1)+(N-k)=N-1

F-statistic Variation among sample means divided by the natural variation within groups Numerator is determined from SSGroups – MSGroups= SSGroups/(k-1) Denominator is determined from SSE – MSE= SSE/(N-k) Tests null hypothesis