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Randomization Test – Comparing Two Proportions
(adapted from Example 5.1: Dolphin Therapy)
Swimming with dolphins can certainly be fun, but is it also therapeutic for patients suffering from
clinical depression? To investigate this possibility, researchers recruited 30 subjects aged 1865 with a clinical diagnosis of mild to moderate depression. Subjects were required to
discontinue use of any antidepressant drugs or psychotherapy four weeks prior to the
experiment, and throughout the experiment. These 30 subjects went to an island off the coast
of Honduras, where they were randomly assigned to one of two treatment groups. Both groups
engaged in the same amount of swimming and snorkeling each day, but one group (the animal
care program) did so in the presence of bottlenose dolphins and the other group (outdoor nature
program) did not. At the end of two weeks, each subjects’ level of depression was evaluated,
as it had been at the beginning of the study (Antonioli and Reveley, 2005). The response
variable is defined as whether or not the subject achieved substantial reduction (improvement)
of their depression.
1. Why did the researchers include a comparison group in this study? Why didn’t they just see
how many patients showed substantial improvement when given the dolphin therapy?
The null hypothesis for this study should basically say that there is no association between
swimming with dolphins and treatment of depression while the alternative should state that there
is an association. We are going to write our hypotheses in terms of probabilities.
Null: The probability a subject will show improvement in their depression symptoms is the
same between those that swim with dolphins and those that don’t.
Alternative: The probability a subject will show improvement in their depression symptoms
is greater for those that swim with dolphins compared to those that don’t.
The results that the researchers found are shown in the following table:
Dolphin therapy Control group Total
Showed substantial improvement
10
3
13
Did not show substantial improvement
5
12
17
Total
15
15
30
2. Identify which of the variables in this study is explanatory and which is response.
3. A useful first step begin to see whether the data appear to support the claim that dolphin
therapy is effective is to calculate the conditional proportion that improved in each group.
Calculate these conditional proportions. Did the dolphin therapy group have a higher
conditional proportion that showed substantial improvement than the control group?
June 27, 2014
MAA PREP workshop
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