Surgery vs. placebo for the knee pain: Refer to Example 10. Is Arthroscopic Surgery Better than Placebo? Here we show MINITAB output comparing mean knee pain scores for the placebo (group 1) to debridement arthroscopic surgery (group 2).
a) State and interpret the result of the confidence interval.
b) State all steps and interpret the results of the significance test.
c) Based on the confidence interval and test m would you conclude that the arthroscopic surgery works better than the placebo? Explain.
To answer these questions, we need access to the specific data and output from the study mentioned, Example 10. Without the actual data and output, we cannot provide an accurate interpretation. However, I can guide you on how to interpret the results if you have the necessary information.
a) Confidence Interval:
To interpret the result of a confidence interval, you will need the confidence level specified in the output. Typically, confidence intervals are reported as a range with an associated confidence level. For example, a 95% confidence interval means that we are 95% confident that the true population parameter lies within that interval.
Interpretation:
If the confidence interval for the difference in mean knee pain scores between the placebo group and the arthroscopic surgery group does not include zero, it suggests that there is a significant difference between the two groups at the given confidence level. If zero is included in the confidence interval, it implies that the difference in means is not statistically significant.
b) Significance Test:
To perform a significance test, we need to know the null hypothesis and the alternative hypothesis, as well as the p-value.
Steps to conduct a significance test:
1. Formulate the null hypothesis (H0) and the alternative hypothesis (Ha). In this case, the null hypothesis might be that there is no difference in mean knee pain scores between the placebo group and the surgery group, while the alternative hypothesis is that there is a difference.
2. Determine the appropriate test statistic, such as a t-test or z-test, depending on the sample size and assumptions.
3. Calculate the p-value associated with the test statistic.
4. Compare the p-value to the significance level (usually denoted by alpha) to make a decision. If the p-value is lower than the significance level, we reject the null hypothesis in favor of the alternative hypothesis.
Interpretation:
If the p-value is less than the significance level, it suggests that the observed difference in mean knee pain scores between the two groups is statistically significant. Rejecting the null hypothesis indicates that there is evidence to support a difference between the two groups.
c) Conclusion:
To determine whether arthroscopic surgery works better than the placebo, we need to consider both the confidence interval and the significance test results.
If the confidence interval does not include zero and the significance test indicates a statistically significant difference, it suggests that arthroscopic surgery is more effective than the placebo. Conversely, if the confidence interval includes zero and the significance test is not statistically significant, it suggests that there is no evidence to support the claim that arthroscopic surgery works better than the placebo.
Remember that the interpretation of results should always be done cautiously and in context with the specific study and its limitations. It is always best to consult the actual study or consult with a professional statistician for a comprehensive analysis.