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Ch 16 - ANOVA

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Unformatted text preview: variances are similar 2 x3 6.80 (descriptively best) s 3 2.56 Step 2: Calculate the overall sample mean (based on all N n1 n2 ... n k observations): x 7.3 8.2 8.5 5.2 8.095 OR 19 x 5(8.22) 7(9.30) 7(6.80) 8.095 19 Step 3: Calculate the sum of squares between groups: SS Groups groups ni xi x 2 = 5(8.22 – 8.095)2 + 7(9.30 – 8.095)2 + 7(6.80 – 8.095)2 = 21.98 Step 4: Calculate the sum of squares within groups (due to error): SSE groups ni 1si2 = (5-1)(2.74) + (7-1)(2.61) + (7-1)(2.56) = 41.98 Step 5: OPTIONAL: Calculate the total sum of squares: No Thank You! 176 Step 6: Fill in the ANOVA table: Source Groups Sum of Squares DF Mean Square 21.98 k-1 = 2 Error (Within) 41.98 21.98/2=10.99 10.99/2.62 = 4.2 N-k = 16 41.98/16=2.62 Total 63.96 N-1 = 18 Here are the results from SPSS: ANOVA RESPONSE Between Groups Within Groups Total Sum of Squares 21.981 41.988 63.969 df 2 16 18 F Both estimate the common popul variance but MSE is an unbiased estimator. Mean Square 10.991 2.624 F 4.188 Sig. .034 Within = ERROR One of the assumptions in ANOVA is that the population standard deviations are all equal. Using the data, give an estimate of this common population standard deviation. s 2 MSE 2.62 so s p MSE 2.62 1.62 p Give the observed test statistic value. F = 4.2 What is the distribution of the test statistic if the three drugs are equally effective in terms of the mean response? An F distribution with 2 and 16 df What is the corresponding p‐value for assessing if the three drugs are equally effective in terms of the mean response? The p‐value is 0.034 At the 5% level, what is your conclusion? We reject H0 and conclude that the three drugs do not appear to be equally effective in terms of the mean response. 177 We Rejected H0 in ANOVA: What is next? Multiple Comparisons The term multiple comparisons is used when two or more comparisons are made to examine the specific pattern of differences among means. The most commonly analyzed set of multiple comparisons is the...
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