Solver ... Hypothesis Testing for Two or more Samples

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20160524173607anova_stat_file.xls
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ANOVA

Analysis of Variance
Group A Group B Group C Group D Group E SUMMARY 18.60
18.5 26.3 20.6 25.4 12.48 Groups Count Sum Average Variance
24 25.3 25.2 19.9 14.96 Group A 25 389.170 15.567 11.968 230.2098137778 287.236944 287.236944 Group A 17.023 14.111 15.567
17.2 24 20.8 22.6 17.44 Group B 20 369.700 18.485 21.215 0.2706688889 403.0815 403.0815 Group B 20.113 16.857 18.485
19.9 21.2 24.7 17.5 17.5 Group C 15 373.350 24.890 4.543 593.2099266667 63.599 63.599 Group C 26.770 23.010 24.890
18 24.5 22.9 20.4 19.9 Group D 10 180.600 18.060 16.343 2.9304177778 147.088 147.088 Group D 20.363 15.757 18.060
17.99 21.95 24.07 17.44 Group E 5 82.280 16.456 7.991 23.0122755556 31.96592 31.96592 Group E 17.626 15.286 16.456
17.48 21.18 24.48 16.2 3.650775581
16.97 20.41 24.89 14.96 ANOVA
16.46 19.64 25.3 13.72 Source of Variation SS df MS F F crit
15.95 18.87 25.71 12.48 Treatment 849.633 4 212.408 15.937 2.503
15.44 18.1 26.12 Error 932.971 70 13.328
14.93 17.33 26.53
14.42 16.56 26.94 Total 1782.604 74
13.91 15.79 27.35
13.4 15.02 27.76 Null hypothesis: m1 = m2 = m3 = m4 = m5
12.89 14.25 Alternate hypothesis: Not all the means are equal
12.38 13.48 Significance level: 0.05
11.87 12.71 p-Value 0.0000
11.36 11.94 Decision: Reject the null hypothesis
10.85 11.17
10.34 Mean Differences Post-Hoc Tests
9.83 Difference Lower Upper Difference in
17.2 Comparison of Means Conf. Limit Conf. Limit Treatment Means???
19.9 Group A to Group B 2.918 0.734 5.103 ***Means are different***
18 Group A to Group C 9.323 6.945 11.701 ***Means are different***
Group B to Group C 6.405 3.918 8.892 ***Means are different***
Group A to Group D 2.493 -0.231 5.218 - no difference -
Group B to Group D 0.425 -2.395 3.245 - no difference -
Group C to Group D 6.830 3.857 9.803 ***Means are different***
Group A to Group E 0.889 -2.678 4.456 - no difference -
Group B to Group E 2.029 -1.612 5.670 - no difference -
Group C to Group E 8.434 4.674 12.194 ***Means are different***
Group D to Group E 1.604 -2.384 5.592 - no difference -
©2007 DrJimMirabella.com
&C&A
Also referred to as ALPHA. This is your tolerance for error; it is the probability of incorrectly rejecting the null hypothesis.
If the decision is to REJECT THE NULL HYPOTHESIS, then the results of the Post-Hoc test determine where the specific differences lie. Otherwise, ignore this section.
If the confidence interval does not contain the ZERO, the means are concluded to be different.
A p-value is the probability of making a type 1 error if you reject the null hypothesis. In other words, it is the probability you would be making a mistake to reject the null.

Graph

Group A Group A Group A
Group B Group B Group B
Group C Group C Group C
Group D Group D Group D
Group E Group E Group E
Confidence Intervals of Groups
17.0230484611
14.1105515389
15.5668
20.1131352756
16.8568647244
18.485
26.7700086793
23.0099913207
24.89
20.3625309881
15.7574690119
18.06
17.6264250185
15.2855749815
16.456