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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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.