Question 1

To investigate the effects of sleep deprivation on reaction time, a study was conducted. 50 volunteers were randomly allocated, 25 to a control group and 25 to the sleep deprivation group. The sleep deprivation group stayed awake all night. In the morning, all the volunteers attempted a task, where they had to press a button as quickly as possible, in response to a stimulus. The time from the stimulus to the response was recorded.

For the above study:

1. Identify the response variable.
2. Define an appropriate null and alternative hypothesis.
3. Describe a suitable analytical test to use to report on the required comparison.
4. Use JMP to calculate the power to detect a difference in response time of 100ms, assuming the standard deviation of response time is 120ms and the significance level is 5%. Include a screen shot of the calculation from JMP.
5. Comment on the value of power obtained in part d). Is that value obtained sufficient? If not, what sample size would be required to achieve sufficient power?

Question 2

A psychologist wished to evaluate the effect of exercise on depression. A total of 21 subjects were randomly selected and then assigned randomly to one of three groups: A) a control group – they were not told anything regarding exercise, and were given information to read on dealing with depression; B) a group of occasional walkers; C) a group of regular runners. A depression score was given to each subject at the end of the three month study. A higher depression score is indicative of more depressive symptoms.

The data are provided in depression-exercise.sav.

1. Is random assignment used in this study? Why is it important?
2. Provide a side by side box-plot for depression score based on exercise group. Comment on whether there appears to be a relationship.
3. i) State the appropriate null and alternative hypotheses for the given research question. Define all symbols and subscripts.
   ii) Report the value of the test statistic, associated degrees of freedom and the p-value. Include relevant SPSS output.
   iii) What are the assumptions underlying the test conducted. Comment on whether these assumptions have been met or not, including SPSS output (where needed) to support your comments.
4. Are post-hoc tests required? If yes, describe the results, if not, explain why not.
5. Provide an appropriate concluding statement with regard to the ANOVA as well as the post-hoc testing that summarises the findings of this research.
6. Explain one problem with the design described in terms of testing the effect of exercise on depression. How could the design be improved?
7. i) A difference of 5 points on the test score is considered to be clinically meaningful. Based on your sample data, calculate the power of the test to detect a difference of at least 5 points between the groups (using a significance level of 0.05). Discuss and explain the results including your calculation from JMP.

ii) What would be the number of observations required to achieve a power of 80%?

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Solution: The downloadable solution consists of 7 pages, 926 words and 5 charts.
Deliverable: Word Document