Question

After exercise, massage is often used to relieve pain, and a recent study 33 shows that it also may relieve inflammation and help muscles heal. In the study, 11 male participants who had just strenuously exercised had 10 minutes of massage on one quadricep and no treatment on the other, with treatment randomly assigned. After 2.5 hours, muscle biopsies were taken and production of the inflammatory cytokine interleukin-6 was measured relative to the resting level. The differences (control minus massage) are given in Table 4.11 . $$ \begin{array}{lllllllllll} 0.6 & 4.7 & 3.8 & 0.4 & 1.5 & -1.2 & 2.8 & -0.4 & 1.4 & 3.5 & -2.8 \end{array} $$ (a) Is this an experiment or an observational study? Why is it not double blind? (b) What is the sample mean difference in inflammation between no massage and massage? (c) We want to test to see if the population mean difference \(\mu_{D}\) is greater than zero, meaning muscle with no treatment has more inflammation than muscle that has been massaged. State the null and alternative hypotheses. (d) Use Statkey or other technology to find the p-value from a randomization distribution. (e) Are the results significant at a \(5 \%\) level? At a \(1 \%\) level? State the conclusion of the test if we assume a \(5 \%\) significance level (as the authors of the study did).

Short answer

The study is an experiment, not double-blind. After calculating, you will get the sample mean difference. Hypotheses should be set where the null hypothesis assumes no difference in inflammation level between treatments, and the alternative assumes greater inflammation in untreated muscles. P-value is found using software and compared to significance levels: if it's less than 0.05 or 0.01, null hypothesis is rejected supporting the claim massage helps reduce inflammation.

Step-by-step solution

Identifying the Type of Study and Its Constraints

This is an experiment. In this study, treatments (massage or no massage) were randomly assigned to subjects (participants). The researchers actively manipulated the conditions, hence it's not observational. It's not double-blind because the person performing the massage therapy was aware of the conditions of the study.

Calculating the Sample Mean Difference

The sample mean difference can be calculated by adding all the differences and dividing the sum by the number of data points, which is 11 in this case.

Formulating the Hypotheses

The null hypothesis (\(H_0\)) is that the population mean difference (\(\mu_D\)) equals zero, meaning that massage treatment has no effect on inflammation level. The alternative hypothesis (\(H_a\)) is that the population mean difference is greater than zero, which means the untreated muscle has more inflammation than the massaged muscle.

Finding the P-Value

Using Statkey or similar software, input the data and select one-sided test to find the p-value. This will simulate the randomization distribution under the null hypothesis and calculate the p-value, which is the probability of observing a mean as extreme as, or more than, the actual sample mean.

Determining the Significance of Results

Compare the p-value to significance levels. If the p-value is less than 0.05, reject the null hypothesis at the 5% significance level and conclude that the massage significantly reduces inflammation. If the p-value is less than 0.01, also reject the null hypothesis at 1% significance level, further strengthening the conclusion. If the p-values are greater, do not reject the null hypothesis.