ANOVA Group A 18.5 24 17.2 19.9 18 17.99 17.48 16.97 16.46 15.95 15.44 14.93 14.42 13.91 13.4 12.89 12.38 11.87 11.36 10.85 10.34 9.83 17.2 19.9 18 Group B 26.3 25.3 24 21.2 24.5 21.95 21.18 20.41 19.64 18.87 18.1 17.33 16.56 15.79 15.02 14.25 13.48 12.71 11.94 11.17 Group C 20.6 25.2 20.8 24.7 22.9 24.07 24.48 24.89 25.3 25.71 26.12 26.53 26.94 27.35 27.76 Group D 25.4 19.9 22.6 17.5 20.4 17.44 16.2 14.96 13.72 12.48 Group E 12.48 14.96 17.44 17.5 19.9 SUMMARY Groups Group A Group B Group C Group D Group E Count 25 20 15 10 5 Sum 389.170 369.700 373.350 180.600 82.280 Average 15.567 18.485 24.890 18.060 16.456 Variance 11.968 21.215 4.543 16.343 7.991 ANOVA Source of Variation Treatment Error SS 849.633 932.971 df 4 70 MS 212.408 13.328 F 15.937 Total 1782.604 74 Upper Conf. Limit 5.103 11.701 8.892 5.218 3.245 9.803 4.456 5.670 12.194 5.592 Difference in Treatment Means??? ***Means are different*** ***Means are different*** ***Means are different*** - no difference - no difference ***Means are different*** - no difference - no difference ***Means are different*** - no difference - Null hypothesis: Alternate hypothesis: Significance level: p-Value Decision: m1 = m1 = m1 = m1 = m1 Not all the means are equal 0.05 0.0000 Reject the null hypothesis Mean Differences Post-Hoc Tests Difference Comparison of Means Group A to Group B 2.918 Group A to Group C 9.323 Group B to Group C 6.405 Group A to Group D 2.493 Group B to Group D 0.425 Group C to Group D 6.830 Group A to Group E 0.889 Group B to Group E 2.029 Group C to Group E 8.434 Group D to Group E 1.604 Lower Conf. Limit 0.734 6.945 3.918 -0.231 -2.395 3.857 -2.678 -1.612 4.674 -2.384 F crit 2.503 Confidence Intervals of Groups 30.000 25.000 20.000 15.000 10.000 5.000 0.000 Group A Group B Group C Group D Group E \fMean - INDEP Two Sample Hypothesis Test for the Mean (Independent Samples) Level of Significance 0.05 Sample Mean Sample Size Sample Standard Deviation Group 1 100 30 10 Standard Error (Computed) Test Statistic (Computed) 1.99 -2.51 Two-Tailed Test H1: (m1 <> m1) Group 2 105 40 5 Lower Crit Value Upper Crit Value p-Value Decision -1.9600 1.9600 0.0143 Reject the null hypothesis Upper-Tail Test (m1 > m1 OR m1 < m1) n/a 1.6449 0.9929 Do not reject the null hypothesis H1: Lower-Tail Test (m1 < m1 OR m1 > m1) -1.6449 n/a 0.0071 Reject the null hypothesis H1: If you REJECT the null hypothesis, conclude that H1 is true. If you DO NOT REJECT the null hypothesis, there is insufficient evidence to conclude that H1 is true. NEVER conclude that the null hypothesis is true (i.e., we CANNOT ACCEPT the null). Mean - INDEP (raw data) Two Sample Hypothesis Test for the Mean (Independent Samples) Group 1 2 4 9 3 2 Group 2 3 7 5 8 4 3 Level of Significance 0.05 Sample Mean Sample Size Sample Standard Deviation Group 1 4.000 5 2.915 Standard Error (Computed) Test Statistic (Computed) 1.51 -0.66 Two-Tailed Test H1: (m1 <> m1) Group 2 5.000 6 2.098 Lower Crit Value Upper Crit Value p-Value Decision -2.2622 2.2622 0.5245 Do not reject the null hypothesis Upper-Tail Test (m1 > m1 OR m1 < m1) n/a 1.8331 0.7392 Do not reject the null hypothesis H1: Lower-Tail Test (m1 < m1 OR m1 > m1) -1.8331 n/a 0.2608 Do not reject the null hypothesis H1: If you REJECT the null hypothesis, conclude that H1 is true. If you DO NOT REJECT the null hypothesis, there is insufficient evidence to conclude that H1 is true. NEVER conclude that the null hypothesis is true (i.e., we CANNOT ACCEPT the null). 2007 DrJimMirabella.com Mean - PAIRED Two Sample Hypothesis Test for the Mean (Paired Samples) Item 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Condition 1 135 110 131 142 105 130 131 110 125 149 Condition 2 128 105 119 140 98 123 127 115 122 145 Level of Significance 0.05 Standard Error (Computed) Test Statistic (Computed) 4.40 3.30 H 1: Two-Tailed Test (m d <> 1), (m1 <> m1) H1: Upper-Tail Test (md > 1), (m1 > m1 OR m1 < m1) H1: Lower-Tail Test (md < 1), (m1 < m1 OR m1 > m1) Lower Crit Value Upper Crit Value p-Value Decision -2.2622 2.2622 0.0092 Reject the null hypothesis n/a 1.8331 0.0046 Reject the null hypothesis -1.8331 n/a 0.9954 Do not reject the null hypothesis If you REJECT the null hypothesis, conclude that H1 is true. If you DO NOT REJECT the null hypothesis, there is insufficient evidence to conclude that H1 is true. NEVER conclude that the null hypothesis is true (i.e., we CANNOT ACCEPT the null). 2007 DrJimMirabella.com Proportion Two Sample Hypothesis Test for the Proportion Level of Significance 0.05 Number of Successes Sample Size Group 1 60 100 Group 2 140 200 Proportion (Computed) 0.60 0.70 Z Test Statistic (Computed) -1.73 Lower Crit Value Upper Crit Value p-Value Decision Two-Tailed Test H1: (P1 <> P2) -1.9600 1.9600 0.0833 Do not reject the null hypothesis Upper-Tail Test H1: (P1 > P2 or P2 < P1) n/a 1.6449 0.9584 Do not reject the null hypothesis Lower-Tail Test H1: (P1 < P2 or P2 > P1) -1.6449 n/a 0.0416 Reject the null hypothesis If you REJECT the null hypothesis, conclude that H1 is true. If you DO NOT REJECT the null hypothesis, there is insufficient evidence to conclude that H1 is true. NEVER conclude that the null hypothesis is true (i.e., we CANNOT ACCEPT the null). 2007 DrJimMirabella.com