Callahan ( 2009 ) demonstrated that tai chi can...

Callahan ( 2009 ) demonstrated that tai chi can significantly reduce symptoms for individuals with arthritis. Participants were 18 years old or older with doctordiagnosed arthritis. Self-reports of pain and stiffness were measured at the beginning of an eight-week tai chi course and again at the end. Suppose that the data produced an average decrease in pain and stiffness of $M_{D}=8.5$ points with a standard deviation of 21.5 for a sample of $n=40$ participants. a. Use a two-tailed test with $\alpha=.05$ to determine whether the tai chi had a significant effect on pain and stiffness. b. Compute Cohen's $d$ to measure the size of the treatment effect.

Callahan ( 2009 ) demonstrated that tai chi can significantly reduce symptoms for individuals with arthritis. Participants were 18 years old or older with doctordiagnosed arthritis. Self-reports of pain and stiffness were measured at the beginning of an eight-week tai chi course and again at the end. Suppose that the data produced an average decrease in pain and stiffness of $M_{D}=8.5$ points with a standard deviation of 21.5 for
a sample of $n=40$ participants.
a. Use a two-tailed test with $\alpha=.05$ to determine whether the tai chi had a significant effect on pain and stiffness.
b. Compute Cohen's $d$ to measure the size of the treatment effect.

Key Concepts

Hypothesis Testing

Hypothesis testing involves formulating a null hypothesis, which usually states that there is no effect or no difference, and an alternative hypothesis, which posits that an effect is present. In statistical studies, researchers use sample data to determine whether to reject the null hypothesis in favor of the alternative, employing tests such as the t-test under a prespecified significance level.

Paired Samples t-test

The paired samples t-test is used when the same subjects are measured twice, such as before and after an intervention. This test compares the mean difference of the paired observations to determine if there is a statistically significant change, taking into account the variability of the differences within the paired data.

Significance Level (alpha)

The significance level, often set at 0.05, defines the threshold for rejecting the null hypothesis. It represents the probability of committing a Type I error, which is rejecting the null hypothesis when it is actually true. Choosing a significance level helps determine the statistical rigor of the test.

Cohen's d Effect Size

Cohen's d is a standardized measure that quantifies the size of the treatment effect by expressing the difference between two means in units of standard deviation. It offers an important complement to p-values by providing an indication of the practical significance of the results, beyond merely testing if an effect exists.

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