Within Group Variation Summing the variation within each group and

# Within group variation summing the variation within

• Rutgers University
• STATS 401
• Notes
• JaydipS
• 78
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Chap 12-41 Within-Group Variation Summing the variation within each group and then adding over all groups i k n SSW MSW T Mean Square Within = SSW/degrees of freedom 2 1 1 ) x x ( SSW i ij n j k i j
Chap 12-42 Within-Group Variation (continued) Group 1 Group 2 Group 3 Response, X 2 2 2 12 2 1 11 ) x x ( ... ) x x ( ) x x ( SSW k kn k 3 x 1 x 2 x
Chap 12-43 One-Way ANOVA Table Source of Variation df SS MS Between Samples SSB MSB = Within Samples n T - k SSW MSW = Total n T - 1 SST = SSB+SSW k - 1 MSB MSW F ratio k = number of populations n T = sum of the sample sizes from all populations df = degrees of freedom SSB k - 1 SSW n T - k F =
Chap 12-44 One-Factor ANOVA F Test Statistic Test statistic MSB is mean squares between variances MSW is mean squares within variances Degrees of freedom df 1 = k 1 (k = number of populations) df 2 = n T k (n T = sum of sample sizes from all populations) MSW MSB F H 0 : μ 1 = μ 2 = … = μ k H A : At least two population means are different
Chap 12-45 Interpreting One-Factor ANOVA F Statistic The F statistic is the ratio of the between estimate of variance and the within estimate of variance The ratio must always be positive df 1 = k -1 will typically be small df 2 = n T - k will typically be large The ratio should be close to 1 if H 0 : μ 1 = μ 2 = … = μ k is true The ratio will be larger than 1 if H 0 : μ 1 = μ 2 = … = μ k is false
Chap 12-46 Table 14.5 (p. 544) Percentage Points of ( F (v 1 , v 2 ) Distributions = 5