researcher wants to know if a treatment significantly changes the wellbeing of someone with depression. The average person with depression scores a 7.2 on a wellbeing scale with a SD of 1.4 points. The researcher administers the treatment to 25 clients for a month and finds their wellbeing at the end to be 7.7. Assume an alpha level of .05. How do we interpret this effect size? Would we reject the null hypothesis if the test was nondirectional(two-tailed)? Would we reject the null hypothesis if the alpha level was .01 (directional/one-tailed)?
A researcher wants to know if a treatment significantly changes the wellbeing of someone with depression. The average person with depression scores a 7.2 on a wellbeing scale with a SD of 1.4 points. The researcher administers the treatment to 25 clients for a month and finds their wellbeing at the end to be 7.7. Assume an alpha level of .05.
- How do we interpret this effect size?
- Would we reject the null hypothesis if the test was nondirectional(two-tailed)?
- Would we reject the null hypothesis if the alpha level was .01 (directional/one-tailed)?
The effect size can be interpreted as the magnitude of the change in wellbeing due to the treatment. In this case, the mean wellbeing score increased from 7.2 to 7.7 after the treatment, indicating an improvement in wellbeing. The effect size is the difference in means, which is . This suggests that the treatment has a positive effect on wellbeing.
To determine whether we would reject the null hypothesis, we can perform a hypothesis test. Let's consider both the two-tailed (nondirectional) and one-tailed (directional) scenarios:
1. Two-Tailed Test:
- Null Hypothesis (): The treatment has no effect on wellbeing ().
- Alternative Hypothesis (): The treatment has an effect on wellbeing ().
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