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. To create the following data, we kept the same sample means that appeared in problem 8 but increased the SS values within each sample.
a. Calculate the sample variance for each of the three samples. Describe how these sample variances compare with those from problem 8.
b. 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 problem 8?
c. Use an ANOVA with = .05 to determine whether there are any significant differences among the three treatment means. (Does your answer agree with your prediction in part b?)
To find: The sample variances.
To compare: The sample variances with sample variances of problem 8.
The data shows the values of independent-measures of the three treatment conditions.
Let k represents the numbers of treatments. Then,
For treatment 1
Let is the sample variance for treatment 1. Then,
Thus, the sample variance for treatment 1 is 2.67.
For treatment 2:
Let is the sample variance for treatment 2
To explain: The outcome of the analysis.
To test: Whether there are significant difference between there treatments means.
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