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To compute ANOVA (Analysis of Variance) for the given data, we will follow step-by-step calculations using parametric statistics, focusing on understanding variability between groups and within groups. Step 1: Organize the data We have three groups with 10 scores each: * Group A: 34, 32, 23, 66, 44, 44, 33, 23, 43, 33 * Group B: 26, 34, 23, 13, 34, 76, 43, 35, 57, 34 * Group C: 28, 56, 54, 33, 56, 54, 23, 25, 54, 34 Step 2: Compute the group means and the overall mean * Mean of Group A: $$ \bar{X}_A = \frac{34+32+23+66+44+44+33+23+43+33}{10} = \frac{375}{10} = 37.5 $$ * Mean of Group B: $$ \bar{X}_B = \frac{26+34+23+13+34+76+43+35+57+34}{10} = \frac{375}{10} = 37.5 $$ * Mean of Group C: $$ \bar{X}_C = \frac{28+56+54+33+56+54+23+25+54+34}{10} = \frac{417}{10} = 41.7 $$ * Overall mean ($\bar{X}_{\text{total}}$): $$ \bar{X}_{T} = \frac{375 + 375 + 417}{30} = \frac{1167}{30} \approx 38.9 $$ Step 3: Compute the Sum of Squares Between Groups (SSB) $$ SSB = n \sum (\bar{X}_i - \bar{X}_T)^2 ___ _______ _______ ___ _________ _________ _____ ______ ___.
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