In this Stage 1 Registered Report submission, Alley et al. propose to test for measurement non-equivalence between online and student samples across ManyLabs samples, including student samples, MTurk samples and a sample from Project Implicit. The analysis to decide which scales to include for equivalence testing has already been performed, and this is appropriately outlined in the level of bias control section of the RR. I was able to fully reproduce the inclusion analysis from the provided code.

Overall, I consider this to be a well thought-out and very well written submission that will be widely read, and it is great that the authors have chosen to submit this as a RR. The code annotation, in particular, was very clear - which is appreciated. The research question is valid and there is a strong rationale for testing measurement equivalence between convenience samples. While I am not an expert in testing measurement equivalence, the analysis pipeline was clear and, combined with the annotated code, there is sufficient methodological detail to closely replicate the proposed study procedures and to prevent undisclosed flexibility in the procedures and analyses. I could not find the individual analysis code mentioned in the paper (pg. 15 “Code for the following analyses can be found in the supplementary materials. A separate R file for each measure, and the files are named for the measure analyzed) but this may be a placeholder for when each individual analysis has been performed, and I consider the “Planned Analysis Code” to sufficiently outline the analysis pipeline for all measures, which I was able to fully reproduce.

Below I list minor comments and questions for the authors, but I am confident this is a scientifically valid, thorough and very valuable submission that I look forward to reading once it is complete.

General:

Throughout the report, there was not much discussion of the power of the planned analyses to detect measurement inequivalence. This may be a moot point as the sample sizes in the current project are quite large, and the exact analyses to be conducted are contingent on the hierarchical analysis plan. However, it would be a good addition to have a power curve to make explicit the range of effect sizes that would be detected in a “typical” analysis, and their theoretical meaning – although to some extent this is already achieved in the sensitivity analysis, which is great.

Ordered minor comments

Page 6: This contains a very clear and accessible description of measurement equivalence. Please provide a more explicit formal definition also be provided after the first sentence, with any appropriate references.

Page 8: “It would also be ideal for replication researchers to test for ME between original and replication studies (Fabrigar & Wegener, 2016), but this is difficult in practice: for the most part, the original studies that are replicated do not have publicly available data.” Presumably the small sample size of many original studies would also mean it would be difficult to detect meaningful measurement invariance between samples.

Page 9: If the authors want a reference on between-platform differences in participant responses: Peer, E., Rothschild, D., Gordon, A., Evernden, Z., & Damer, E. (2022). Data quality of platforms and panels for online behavioral research. Behavior Research Methods, 54(4), 1643-1662.

Page 9/10: “While mean differences on a measure of a construct do not necessarily indicate non-equivalence, any of these differences in sample characteristics could potentially contribute to non-equivalent measurement.” Could this be unpacked? If there are substantial differences in some sample characteristics, is absolute equivalence plausible, or would you expect some non-equivalence but perhaps with very small effect sizes?

Page 11: RQ2, it could be made explicit here that this will be tested by looking at effects sizes as well as significance.

Page 12: “which is useful more broadly than just replication research” – good justification, if anything you are unselling the importance of these research questions for interpreting the results of any experiments!

Page 12: “which requires a series of preliminary analyses to determine if the data satisfy assumptions”. It would be useful to list all of the assumptions here.

Page 13: “Type I error rates for equivalence tests may be inflated when the baseline model is misspecified”. For accessibility, could an example of model misspecification increasing Type 1 error rates be given here, even if hypothetical?

Page 17: The authors may be more aware of this than I am and this may be a non-issue, but some concerns have been raised about using scaled χ2-difference tests to compare nested models (see http://www.statmodel.com/chidiff.shtml)

Results: The proposed data presentation looks appropriate, and thank-you to the authors for including these.

Finally, I don’t think this is necessary to address in the current project, but I thought about this several times while reading the manuscript: While the focus is on detecting measurement inequivalence between samples, there is some ambiguity about what the authors consider the sample to be – is it the experimental units (individual participants) only, the experimental units plus the setting (participants + online/location), are the experimenters included too? Replications vary across experimental units, treatments, measurements and settings (Machery, E. [2020]. What is a replication?. Philosophy of Science, 87(4), 545-567), and so it might be worth considering the degree to which measurement invariance could be introduced from other sources, e.g. different experimenters, that would not normally be associated with the sample, but nevertheless would differ between them.  

Best of luck with the project!

Benjamin Farrar