The Stage 2 manuscript follows almost all of the preregistered steps and reports the outcomes in a well-justified manner, with no unwarranted changes from the Stage 1 manuscript.

However, I believe there is one notable deviation from the preregistered protocol that is not properly addressed. Specifically, while the authors originally stated that they would apply a Welch adjustment to account for variance inequalities (page 17 in Stage 1 Manuscript), the final analyses use HC3 robust standard errors instead (described on page 19 in Stage 2 Manuscript and applied on page 23). Although HC3 can be a suitable alternative, the authors should adhere to their preregistered plan by reporting the Welch-adjusted results as the primary analysis, exactly as specified. The HC3-based analysis can then be presented as an exploratory robustness check. This approach would fully honor the original preregistration and simultaneously demonstrate the robustness of the findings through additional analyses. 

 Dear authors, 
 
Thank you for your Stage 2 Registered Report. I appreciate the thorough execution of your study and your careful interpretation of the findings, but I am not completely happy with how you have engaged with my suggestios in the last round of reviews if I am honest. I therefore have a few more comments regarding your handling of the Bayesian analysis and its integration into the results and discussion sections. These primarily relate to the interpretation of Bayes factors, the specificity of your reference to Hoijtink et al. (2019b), and the implications of your statistical choices. Just a note about comparing between stage 1 ad 2, I think you remained methodologically consistent with the Stage 1 plan, but that the interpretation of results and discussion of limitations could have been more thorough and that's what I am focusing on the most here as it also comes back to some of the original comments I made.

First, you removed the problematic statement about "values greater than 1 supporting the corresponding hypothesis," which I think is good, though now you simply state that Bayes factors will be interpreted contextually following Hoijtink without actually explaining why you avoid thresholds. I find this problematic. While you’re avoiding the mistake of implying that BF10 > 1 always provides meaningful evidence, I think you still need to explain why you reject fixed thresholds entirely rather than (e.g.) highlighting BF10 > 3 as moderate evidence which is (largely) accepted practice. Obviously, we can deviate from what's typically done, but whatever choices are made must be motivated sufficiently, especially when it comes to 

Second, you still refer to Hoijtink et al. (2019b) as a guide for interpreting your Bayesian analysis, and still fail to properly specify which aspects of that extensive work you are following. While you now mention using a Cauchy prior and pooling across imputations, you dont clarify (for example) whether you are incorporating posterior probabilities as an alternative or supplement to Bayes factors. A sentence specifying exactly how you apply Hoijtink’s framework would strengthen this section, and will better satisfy the concern I originally had for the stage 1 RR.

In the results, you performed a Bayesian analysis but did not fully integrate it into the interpretation (in my opinion). You state that a BF10 of approximately 24,757 supports a non-null effect, while BF10 ≈ 0.103 supports the null, but do not really discuss the practical implications of these findings which I think is quite an oversight. Given that the first Bayes factor is extraordinarily large, you could have reflected on whether this indicates strong evidence for a backfire effect rather than just a failure of BTS. A discussion of how the Bayesian results fit into your broader conclusions is what I suggest here – I think it would be an addition that would really make your findings more informative.

Another issue concerns your decision to preregister a one-tailed test – the main result would have been statistically significant had you preregistered a two-tailed test rather than a one-tailed test, but you don’t acknowledge this as a potential limitation. Since you used a one-tailed test, you implicitly assumed a directional effect in advance – that is not an ideal choice when testing an intervention that could plausibly backfire, I would argue. Some reflection on whether this decision was appropriate and/or how it may have influenced your conclusions would add some value to the discussion.

Finally, while your discussion on the possible backfire effect is interesting, you don’t consider whether a different analytical approach (e.g., mixture models or priors that allow for unexpected effects) might provide additional insights. Instead, you speculate about the reasons for the observed pattern without critically evaluating whether your chosen statistical framework was well-suited to detecting and interpreting such an effect. I think this point needs some attention in the write-up. 

In general, I judge this to be a strong and well-executed stage 2, and I appreciate the effort that went into conducting and reporting it. My comments are intended to help clarify your Bayesian analysis and strengthen the discussion of your findings - I hope my tone doesn’t come across as negative in any way. I look forward to seeing your revisions! 
 
I sign all of my reviews, 
Dr. Sarahanne M. Field