Consider the following data from a repeated-measures design. You want to use a repeated-measures t test to
Question:
Consider the following data from a repeated-measures design. You want to use a repeated-measures t test to test the null hypothesis H: DD= 0 (the null hypothesis states that the mean difference for the general population is zero). The data consist of five observations, each with two measurements, A and B, taken before and after a treatment. Assume the population of the differences in these measurements are normally distributed.Complete the following table by calculating the differences and the squared differences:
| Observation | A | B | Difference Score | Squared Difference Score |
|---|---|---|---|---|
| (D = B - A) | (D) | |||
| 1 | 1 | 3 | ||
| 2 | 3 | 4 | ||
| 3 | 5 | 7 | ||
| 4 | 4 | 4 | ||
| 5 | 8 | 9 |
The mean difference score is MDD= .
For a repeated-measures t test, you need to calculate the t statistic, which requires you to calculate s and sMDMD.What is the estimated standard deviation of the difference scores?
| s | = | / | = | 2.80 / | = |
What is the estimated standard error of the mean difference scores? (Note: For best results, retain at least six decimal places from your calculation of s.)
| sMDMD | = | s / | = |
What is the t statistic for the repeated-measures t test to test the null hypothesis H: DD= 0?
| t | = | MDD- / | = | 3.21 |
t Distribution
Degrees of Freedom = 7
-4.0-3.0-2.0-1.00.01.02.03.04.0t.2500.5000.2500-0.7110.711
You conduct a two-tailed test at = .05. To use the Distributions tool to find the critical values, you first need to set the degrees of freedom in the tool. The degrees of freedom are .
The critical values (the values for t scores that separate the tails from the main body of the distribution, forming the critical region) are .
Finally, since the t statistic in the critical region, you the null hypothesis.
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