2. Describe what is measured by the estimated standard error in the bottom of the independent-measures t statistic.
4. Describe the homogeneity of variance assumption and explain why it is important for the independent measures t test.
6. One sample has SS = 70 and a second sample has SS = 42.
a. If n = 8 for both samples, find each of the sample variances, and calculate the pooled variance. Because the samples are the same size, you should find that the pooled variance is exactly halfway between the two sample variances.
b. Now assume that n = 8 for the first sample and n = 4 for the second. Again, calculate the two sample variances and the pooled variance. You should find that the pooled variance is closer to the variance for the larger sample.
8. Two separate samples, each with n _ 12 individuals, receive two different treatments. After treatment, the first sample has SS = 1740 and the second has SS = 1560.
a. Find the pooled variance for the two samples.
b. Compute the estimated standard error for the sample mean difference.
c. If the sample mean difference is 8 points, is this enough to reject the null hypothesis and conclude that there is a significant difference for a two-tailed test at the .05 level?
d. If the sample mean difference is 12 points, is this enough to indicate a significant difference for a two-tailed test at the .05 level?
e. Calculate the percentage of variance accounted for (r2) to measure the effect size for an 8-point mean difference and for a 12-point mean difference.
10. For each of the following, assume that the two samples are selected from populations with equal means and calculate how much difference should be expected, on average, between the two sample means.
a. Each sample has n = 5 scores with s2 = 38 for the first sample and s2 = 42 for the second. (Note: Because the two samples are the same size, the pooled variance is equal to the average of the two sample variances.)
b. Each sample has n = 20 scores with s2 = 38 for the first sample and s2 = 42 for the second.
c. In part b, the two samples are bigger than in part a, but the variances are unchanged. How does sample size affect the size of the standard error for the sample mean difference?