MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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For the preceding problem you should find that there are significant differences among the three treatments. One reason for the significance is that the sample variances are relatively small. The following data have the same sample means that appeared in the preceding question, but the SS values within each sample are doubled.
I | II | III | |
n = 6 | n = 6 | n = 6 | N = 18 |
M = 1 | M = 2 | M = 6 | G = 54 |
SS = 120 | SS = 130 | SS = 80 | ∑X² = 576 |
Calculate the sample variance for each of the three samples.
I | II | III |
s² = 24.00 | s² = 26.00 | s² = 16.00 |
These values aremuch larger than the variances in the previous question (12.00, 13.00, and 8.00).
Predict how the increase in sample variance should influence the outcome of the analysis. That is, how will the F-ratio for these data compare with the value obtained in the previous problem?
Larger sample variances shoulddecrease the F-ratio.
Use an ANOVA with α = .05 to determine whether there are any significant differences among the three treatment means.
Source
|
SS
|
df
|
MS
|
F
|
Fcriticalcritical
|
---|---|---|---|---|---|
Between treatments | 84 | ||||
Within treatments | 330 | ||||
Total | 414 |
F Distribution
Numerator Degrees of Freedom = 6
Denominator Degrees of Freedom = 16
0.01.02.03.04.05.06.07.08.09.010.011.012.0F
Conclusion:
Fail to reject the null hypothesis; there are no significant differences among the three treatments.
Reject the null hypothesis; there are no significant differences among the three treatments.
Fail to reject the null hypothesis; there are significant differences among the three treatments.
Reject the null hypothesis; there are significant differences among the three treatments.
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