Dear Dr. Wojtasiński,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript by Oct 11 2025 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org . When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

• A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
• A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
• An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols . Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols .

We look forward to receiving your revised manuscript.

Kind regards,

Andrea Schiavio

Academic Editor

PLOS ONE

Journal Requirements:

When submitting your revision, we need you to address these additional requirements.

1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at

https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and

https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf .

2. In the online submission form, you indicated that your data will be submitted to a repository upon acceptance.  We strongly recommend all authors deposit their data before acceptance, as the process can be lengthy and hold up publication timelines. Please note that, though access restrictions are acceptable now, your entire minimal  dataset will need to be made freely accessible if your manuscript is accepted for publication. This policy applies to all data except where public deposition would breach compliance with the protocol approved by your research ethics board. If you are unable to adhere to our open data policy, please kindly revise your statement to explain your reasoning and we will seek the editor's input on an exemption.

3. Thank you for stating the following in your manuscript:

“The study presented in the article was conducted as a component of a broader project that received approval and funding from Narodowe Centrum Nauki (grant no: 2024/08/X/HS6/00465).”

We note that you have provided additional information within the Acknowledgements Section that is not currently declared in your Funding Statement. Please note that funding information should not appear in the Acknowledgments section or other areas of your manuscript. We will only publish funding information present in the Funding Statement section of the online submission form.

Please remove any funding-related text from the manuscript and let us know how you would like to update your Funding Statement. Currently, your Funding Statement reads as follows:

“The study presented in the article was conducted as a component of a broader project funded by the Polish National Science Centre (Narodowe Centrum Nauki, NCN). The grant (no: 2024/08/X/HS6/00465) was awarded to M.W. under the MINIATURA 8 funding scheme.

Funder websites: 

https://www.ncn.gov.pl/en 

https://www.ncn.gov.pl/konkursy/wyniki/miniatura8

The funder had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.”

Please include your amended statements within your cover letter; we will change the online submission form on your behalf.

4. Your ethics statement should only appear in the Methods section of your manuscript. If your ethics statement is written in any section besides the Methods, please delete it from any other section.

5. Please remove your figures from within your manuscript file, leaving only the individual TIFF/EPS image files, uploaded separately. These will be automatically included in the reviewers’ PDF.

6. Please include captions for your Supporting Information files at the end of your manuscript, and update any in-text citations to match accordingly. Please see our Supporting Information guidelines for more information: http://journals.plos.org/plosone/s/supporting-information.

7. If the reviewer comments include a recommendation to cite specific previously published works, please review and evaluate these publications to determine whether they are relevant and should be cited. There is no requirement to cite these works unless the editor has indicated otherwise. 

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Partly

**********

2. Has the statistical analysis been performed appropriately and rigorously? -->?>

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

**********

3. Have the authors made all data underlying the findings in their manuscript fully available??>

The PLOS Data policy

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

**********

4. Is the manuscript presented in an intelligible fashion and written in standard English??>

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

**********

Reviewer #1: I sincerely thank the editor and the authors for giving me the opportunity to review this well-executed, theoretically grounded, and methodologically rigorous work. The article makes a significant contribution to the literature on flow measurement, especially regarding its assessment at the state level and the distinction from dispositional aspects. I particularly appreciate the clarity of the theoretical framework beginning at line 22, the critical discussion of competing models (lines 67–162), the justification for using the Psychological Flow Scale (PFS) (lines 299–322), and the thorough cultural and linguistic adaptation (lines 458–470). The experimental design is well-calibrated (lines 420–450), the sample is appropriate, and the data collection is enhanced by objective measures which, although not analyzed here, strengthen the overall structure. The use of Multilevel Confirmatory Factor Analysis (lines 541–620) is entirely appropriate and enables a model consistent with the dynamic, situational nature of the construct.

I now point out some recommended line-by-line changes. At line 102, I suggest reformulating “It also received approval from…” as “The study protocol was approved by…” for greater clarity and stylistic consistency. At line 194, I recommend reinforcing the critique of “perceived challenge-skill balance” with an added note emphasizing the debated and ambiguous nature of the construct in older models. At line 356, it should be clarified that physiological data were collected but are not discussed in the current article, to avoid creating unmet expectations. At line 402, the phrase “acceptable internal consistency” should be changed to “marginal internal consistency,” as α = .74 is near the lower psychometric threshold. At lines 406–407, it should be more clearly stated that the absorption subscale of the Flow Short Scale has extremely low reliability (α = .20) and therefore cannot be used independently or in separate analysis. At line 630, the term “item-by-person interactions (18%)” could be clarified with a brief explanatory note to assist less experienced readers. At line 698, replace “over-extraction” with “model overfitting” for greater terminological transparency. At lines 812–814, I suggest briefly explaining the TEFI index for readers unfamiliar with graph analysis methods. At line 890, I recommend encouraging the authors to reflect on why the correlation between trait and state flow is weak for the absorption dimension, suggesting possible misalignment between instruments or differences in metacognitive awareness. At line 989, I recommend adding a note on the limits of self-report measures, such as: “While self-reports are informative, they remain vulnerable to cognitive bias and demand characteristics.”

As for deletions, lines 368–370 repeat previously stated concepts and could be condensed. Lines 558–565 provide already known statistical details and may be compacted. Lines 1080–1082 in the conclusion are redundant and do not add new insights.

The data analysis is well conducted, with appropriate statistical models, excellent fit indices, and a clear distinction between intra- and inter-individual variability. The use of EGAnet further strengthens the empirical evidence for the three-factor structure of the PFS. The results align well with the theoretical framework and reinforce the convergent validity of the scale with other instruments like the FSS. However, the convergent validity with the GFPS scale shows only weak correlations, which should be interpreted more critically. The manuscript currently lacks an explicit section dedicated to the study’s limitations: I encourage the authors to add at least three key points in the final discussion. First, generalizability is limited because the study used a highly controlled lab task, which does not reflect the ecological richness of real-life flow experiences. Second, the sample is homogeneous in age, education, and handedness, limiting representativeness. Third, the exclusive use of self-report measures—though sophisticated—does not allow for triangulation of subjective flow with objective indicators. Even though physiological data were collected, the fact that they are not analyzed here constitutes a methodological limitation.

Finally, I propose that the authors include the following reference in the bibliography, which is important for reinforcing the attention to cross-cultural psychometric validation of self-report instruments:

Diotaiuti, P., Girelli, L., Mancone, S., Valente, G., Bellizzi, F., Misiti, F., & Cavicchiolo, E. (2022). Psychometric properties and measurement invariance across gender of the Italian version of the TEMPEST Self-Regulation Questionnaire for Eating adapted for young adults. Frontiers in Psychology, 13, 941784. https://doi.org/10.3389/fpsyg.2022.941784.

I suggest citing this work in the Method section, particularly in the paragraph discussing the cross-cultural adaptation process (around line 459), with the following sentence: “This adaptation process aligns with recent methodological recommendations for ensuring psychometric robustness and measurement invariance across populations (e.g., Diotaiuti et al., 2022).”

This citation would help position the work within a network of methodologically aligned studies, reinforcing the rigor of the adaptation procedure. I again thank the authors for the clarity and precision of their work and remain available for any further clarification

Reviewer #2: The study is well structured, original, and enriched with relevant statistical analyses. However, I find that the sample size too small to conduct an CFA (borderline) compared to current recommendations (≈200+). For this reason, I recommend that the authors provide the calculation of the sample size required for such an analysis and support their argument with references.

Reviewer #3: Wonderful success in developing a Polish translation of the PFS instrument! You have affirmed the original structure which suggests that the best model for the PFS is culturally viable. Considering that there might be cultural/linguistic differences, I would like to know if any content validity assessments of the statements were taken during the translation from English into Polish. For example, the PFS was developed from 60 initial items and expert reviewers reduced that pool to 36 items. Then a sample of lay-people were asked to review the meaning and relevance of the 36 items which resulted in a 28 item pool used for EFA. Given that the translated meaning of the items might carry different weight and interpretation, it would seem that only using the resulting items from the final model of the original PFS for the Polish item pool is shortsighted. Slightly different items from the content validated PFS items may have yielded better scores because they were interpretable to the polish sample in a clearer way (of course there is an infinite amount of items one could ask, however, the PFS provides the 28 item data set in their supplementary material). This is a limitation which should be acknowledged, as the main point of your submission is validating the conceptualisation of flow from Norsworthy et al's construct structure–which you do successfully statistically–in a way which supports the use of valid items for a Polish sample. By not evaluating content validity you do not know whether similar items would be better or clearer at conceptualising the construct for a Polish sample, which in turn might have improved your internal structure and correlational loading with the other measures. This is not a major limitation, given the internal structure was confirmed, but it is something to discuss given the purpose of your article.

There are discrepancies between the article and the R session concerning the reporting of participants. You report an initial sample of 151 which was reduced by 31 in the article (10 did not complete the experiment and 21 lacked within-person variability). First, the reduction of participants within the data (pfs_raw) only contains 140 participants. This suggests that 11 participants were cut prior to the analysis. Second, there doesn't seem to be a theoretical reason for why responses to the items need to have variability. By sight alone, I noticed that these 20 filtered participants did not egregiously report similar responses to all of the items but rather had similar responses to the same item across trials, and were different scores between items. This could mean that the response to the item was consistent throughout, possibly because the holistic experience of doing the experiment was the flow state. The lack of within-person variability for the 20 participants cannot be discounted unless there is considerable a priori reason why those responses are "incorrect" (potential clarification of variability in multilevel models: https://doi.org/10.1080/00273170701710072). Removing these participants for statistical convenience is not recommended as it misappropriates the way in which participants answered your instrument. Given that there is no strong theoretical reason to exclude the participants for within person variability, I'm of the opinion that the excluded participants should only be those who did not complete the full experiment. This allows you to do an interesting examination of the validity of the response process by looking at the convergent validity of the tracking procedure alongside the scores (e.g., https://doi.org/10.1038/s41598-020-61636-5; https://psycnet.apa.org/doi/10.1037/tps0000426). You could also examine the no-within-person-variability group and their general trait scores as compared to the participants with higher variability. Given that Multilevel modelling–in a longitudinal context–will produce residual variance of participants, it is more informative for the validation of your instrument to keep all of the participants and report what variance exists within this sample. Going back to the discrepancy, there should be 21 excluded from your analysis (within R) based on what you reported in the article, but from 140 it only reduces to 120 participants (pfs_wide_filtered) rather than to 119. This should be clarified within the article and the full preprocessing should be reported with the raw data–reflecting 151 initial participants.

I ran all of the analyses with the pfs_wide data set to review what might be lost if you were to include the within-person group (I commend you highly for such a clear presentation of analysis, both within the article and the supplementary material. The original analysis in R performed great!). Your multi-level reliability estimates stay the same (RkF = 1; RkR = .97; RkRn = .97). Generalisability to change decreases slightly (.88), reliability of single time-point improves (R1R = .65) and the within-person variability falls (Rcn = .67). Incorporating all of the participants who completed your experiment may require you to reevaluate the models you estimate but I ran each with the pfs_wide data just as you specified:

Model 1: χ²(24) = 108.86, p < .001; CFI = .988; TLI = .981; RMSEA = .067; SRMR = .031

Model 2: χ²(24) = 108.86, p < .001; CFI = .988; TLI = .981; RMSEA = .067; SRMR = .031 (no negative residual variance for reward ψ = .45, p = .067!!)

Model 3: χ²(48) = 348.46, p < .001; CFI = .981; TLI = .972; RMSEA = .047; SRMR within = .039; SRMR between = .036 (negative residual variance for item_2 ψ = -.019, p = .165)

Model 4: χ²(46) = 345.35, p < .001; CFI = .981; TLI = .971; RMSEA = .048; SRMR within = .039; SRMR between = .037

Model 5: (identical to model 4, some potential issues with estimation) χ²(46) = 345.35, p < .001; CFI = .981; TLI = .971; RMSEA = .048; SRMR within = .039; SRMR between = .037

A three cluster solution in the lower level and first order structure clearly retains with the EGA, using the rfs_wide data. Looking at the convergent validity (correlations) between both the FSS and GFPS produces marginal changes. I would like to see the sub-scales of the FSS present within table 1, this is commonly reported while presenting a convergent-validity correlation, so we can see differences (like those between the absorption scores). Reporting the pearson's r should follow some standard interpretation (e.g., Dancey, C. P., & Reidy, J., 2007) and it should be made clear when the coefficient is weakly or strongly loaded. As an aside, you could represent your models with MLM equations to bolster interpretability but this is not required for a general audience (e.g., https://doi.org/10.1016/j.jsp.2009.09.002).

I believe the setup for differentiating the state and trait components of flow for this scale development is handled well throughout the article. The acknowledgement (twice) that there are more discriminat and convergent validity indices coming makes me wish I could read that article in addition to this one. You could rewrite this acknowledgement in the conclusion to hypothesise why those measures would produce convergent and discriminat validity evidence. If there was one analysis I would like to see incorporated into this article it would be the continuous mouse movement performance. Looking into the performance change between trials would provide an additional piece of convergent validity evidence for the state argument for both the Polish PFS and FSS.

The article was written clearly and produced original research which replicated the internal structure of the PFS with a Polish sample. As someone not familiar with the literature of flow, I found your introduction a good catchup from what I knew already. One area which might need minor improvement is the methods section. Including all of the participants who completed the experiment would fix the problem of having to explain the demographics of the participant sample twice. It is also confusing to be presented with the results of the overall performance on the task before knowing what the task entails, this could instead be reported alongside the procedure or as a first analysis. The idea of performance skill is interesting but I wish I knew what the boundaries were (0-10; 0-100; 0-5). I found it confusing that even with the calibration of the task difficultly for each participant there were differences within the gender. Because you purposefully calibrated the difficulty, I interpret the analysis of performance skill as being a check of how well the difficulty was adjusted throughout the experiment. Was it that women exhibited lower skill or did the procedure challenge the female participants differently or were the calibration procedures not attempting to control for these differences? Explaining the rationale for that process of determining performance skill more would clarify what it was for and entailed.

Your presentation of the materials was very clear. The original PFS is a very competently developed instrument in terms of the validity and reliability tests that were undertaken, so you could explain the breadth of evidence they provide beyond just the Cronbach alpha scores, which will further support why you can be confident using this instrument for translation. Adding a link to the supplementary material (i.e., see Supplementary Material) for the translation material at the end of the methods section would also be very nice.

Utilising both traditional multilevel modelling and an exploratory hierEGA was a great check of the internal consistency of the structure. Grand that it was also a theoretically supported structure, highlight that connection and trajectory from the strong theory more! A big question for the article overall might be determining whether the original PFS and your experiment provide the falsifying tests necessary to support validity claims for state based flow (https://doi.org/10.1007/s11336-006-1447-6). This could be acknowledged to some degree to show that you examined the validity evidence necessary to support claims that the instrument properly captures the construct for your specified purpose, and more importantly (in your case) within a different socio-cultural understanding than the original developed instrument.

Specific editorial errors: In the section titled Flow Concept: Past and Current Understanding, cite the critics you refer to as pointing out definitional inconsistencies, remove 'by' before Norsworthy (i.e., led respectively by Peifer and Norsworthy), the em dashes in the paragraph detailing the third dimension of Norsworthy's framework need fixing, in the last paragraph you should change "Norsworthy et al.'s" to "Norsworthy and colleagues'". In section 2 Self Report Instruments for Flow Measurement, for the third paragraph change operationalized to operationalize. In section 3 Current Study, the last sentence of paragraph two should read "previous ESM research, allowing for more robust". In section 6. Discussion, I believe there is an added space in the first sentence "the Polish adaptation of the_PFS". Overall, I do not believe that it is necessary to label the sections with numerals. This could however be a stylistic choice.

I have suggested major revision because after adding the assumed no-variability participants to the analysis there could be potential issues with your models (although I did not see any from my simple re-analysis) which may have ramifications for the interpretation of your discussion. I also suggested adding the mouse tracking analysis as an additional piece of evidence to interpret convergent validity for state flow. Other conceptual points (content validity) also need consideration to position this article's contribution and limitations. The article is well written overall but the methods section could be rearranged to facilitate a clearer description of the task, the participants, and the procedure. - Connor Kirts

**********

what does this mean? ). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy

Reviewer #1: Yes:  Pierluigi Diotaiuti

Reviewer #2: No

Reviewer #3: Yes:  Connor Kirts

**********

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/ . PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org . Please note that Supporting Information files do not need this step.

The Flow Experience: Polish Adaptation and Validation of the Psychological Flow Scale (PFS)

PONE-D-25-32166R1

Dear Dr. Wojtasiński,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

An invoice will be generated when your article is formally accepted. Please note, if your institution has a publishing partnership with PLOS and your article meets the relevant criteria, all or part of your publication costs will be covered. Please make sure your user information is up-to-date by logging into Editorial Manager at Editorial Manager®  and clicking the ‘Update My Information' link at the top of the page. For questions related to billing, please contact billing support .

If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

Andrea Schiavio

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

Reviewer #2: All comments have been addressed

Reviewer #3: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions??>

Reviewer #2: Yes

Reviewer #3: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously? -->?>

Reviewer #2: Yes

Reviewer #3: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available??>

The PLOS Data policy

Reviewer #2: Yes

Reviewer #3: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English??>

Reviewer #2: Yes

Reviewer #3: Yes

**********

Reviewer #2: (No Response)

Reviewer #3: Thank you once again for the work you have put forth. Rereading the manuscript was a joy and I think the improvements have progressed the clarity and rigour further. The acknowledgement of the content validity processes and rephrasing of the approach of translation into Polish highlight the care that went into crafting this instrument. The choice to amend the exclusion of participants is also encouraging and I'm glad that my quick glance at the code for the analyses still support strong models after your rerun. Along that line, thank you for the inclusion of the preliminary mouse tracking convergent validity! Excited to see that the performance index is supporting that this self-report tool as a measure of flow states. Hopefully, this consideration helps as a through line argument–between this article and the next–as you investigate these indices further to build upon the validity evidence in your follow up paper!

**********

what does this mean? ). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy

Reviewer #2: Yes:  Amayra Tannoubi

Reviewer #3: Yes:  Connor Kirts

**********