Tolerance intervals Q

#1
Hi there, these minitab questions are really troubling me. I have attempted them below.

In a double-blind placebo-controlled randomised trial of the effect of a Herbal Remedy on the nasal/respiratory condition known as Rhinitis, a measure of severity of the Rhinitis was taken one week before and one month after treatment. The primary question of interest is to determine whether or not the Herbal Remedy improves Rhinitis’ patients more than any such improvement on the Placebo in the population in question. Use the relevant output below to answer the following questions.

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1. Use the relevant interval estimate and p-value to answer the primary question of interest.
The relevant interval estimate is from the ‘’Two-Sample T-Test and CI: Improvement, Group’’. The difference between the mean improvements between the Herbal and Placebo group is 9.35, which is significant. Since the 95% CI for the difference in the improvements doesn’t contain zero, it can be concluded that the Herbal group does significantly improve in severity on average from the placebo group. The p-value is also less than 0.05, therefore we can reject the null hypothesis.

2. Provide an interpretation of the Tolerance Intervals provided:
The improvements in both Herbal and Placebo treatment groups are not significant as their tolerance intervals contain zero.

3. Does an analysis based on the simple differences in severity look justified? Explain why or why not:
No it does not look justified as based on the numerical and graphical summaries there was an improvement but these improvements are not statistically significant based on their tolerance intervals.
 

Miner

TS Contributor
#2
Is this a homework assignment? Did you perform the analysis, or are you being asked to interpret the analysis?

I ask, because a 2-sample t-test is not appropriate for this type of data, and the data are obviously not paired by test subject, so you cannot use a paired t-test either. I would have analyzed it using regression with a categorical predictor (Placebo/herbal) then determined whether the categorical predictor was significant.

I am also surprised to see tolerance intervals used outside of industrial statistics.
 

Miner

TS Contributor
#4
  1. Your response to the first question is correct.
  2. For the second question, remember that tolerance intervals reflect the variation of individual subjects. They are not the same as a confidence interval and cannot be interpreted as such (i.e., interval including zero). Tolerance intervals just show the distribution of the improvement.
  3. Same comment on tolerance intervals. An analysis of the means alone would not show a difference due to the spread. Analyzing the differences is a higher powered approach, but is still not the best. A better approach would be the one I described in an earlier post.
 
#5
  1. Your response to the first question is correct.
  2. For the second question, remember that tolerance intervals reflect the variation of individual subjects. They are not the same as a confidence interval and cannot be interpreted as such (i.e., interval including zero). Tolerance intervals just show the distribution of the improvement.
  3. Same comment on tolerance intervals. An analysis of the means alone would not show a difference due to the spread. Analyzing the differences is a higher powered approach, but is still not the best. A better approach would be the one I described in an earlier post.
Thank you, much appreciated.