A clinical research study was conducted comparing two different treatments for joint pain. The study was conducted on 100 participants who were randomly assigned to receive either treatment A (n=50) or treatment B (n=50). Before the participants received the experimental treatments they had their joint pain assessed using a visual analog scale instrument where the participant had to identify their level of joint pain (higher score on a scale from 0-100 means more pain).

After 6 weeks of treatment the participants were again asked to assess their joint pain using the visual analog scale.

Here are the results -

For treatment A the baseline joint pain was 85 and the follow-up joint pain was 70.

A paired t-test was performed on this data and showed that the 15 point improvement in joint pain was statistically significant with a p-value of 0.01 for this change.

For treatment B the baseline joint pain was 65 and the follow-up joint pain was 55.

A paired t-test was performed on this data and showed that the 10 point improvement in joint pain was not statistically significant with a p-value of 0.08 for this change.

In addition to the two paired t-tests, a direct comparison of the 6-week measures was made between groups (comparing the 70 in treatment A vs the 55 in treatment B) using a 2-sample t-test. This test was statistically significant (p=0.03).

Finally, a comparison of the changes in joint pain scores was made between the two treatments (15 point improvement for Treatment A vs 10 point improvement for Treatment B) using a two-sample t-test - and this test was found to be not statistically significant (p=0.09).

So in summary the results of the tests performed were as follows:

Paired t-test comparing change in joint pain in Trt A - 15 unit change, p=0.01,

Paired t-test comparing change in joint pain in Trt B - 10 unit change, p=0.08,

Two sample t-test comparing week 6 joint pain - Trt A (70) vs Trt B (55), p=0.03,

Two sample t-test comparing change in joint pain between groups (Trt A 15 point improvement vs Trt B 10 point improvement), p=0.09.

Researcher 1 claims Treatment A is better than Treatment B - as can be seen by the fact that the participants in Treatment A showed a significant improvement (15 units, p=0.01) in the paired t-test but participants in Treatment B did not (p=0.08).

Researcher 2 claims Treatment B is better than Treatment A because the 2-sample t-test comparing the 6 week measures showed that Treatment B had a significantly lower joint pain at 6 weeks than Treatment A (55 vs 70, p=0.03).

Researcher 3 claims that we cannot tell which treatment is better because the 2-sample t-test comparing the change in joint pain between groups was non-significant (15 vs 10 points, p=0.09).

Discuss how could all three of these conclusions come from the same study. Look at each Researcher's claim and determine whether there are any problems with their statements and if so describe what the problem(s) are.

Then indicate what you think is the correct interpretation of this study - this does not need to be one of the three researcher's claims - it can be your own interpretation based on the data shown above.