On the selection of endogenous and exogenous signals

Alerting is one of the three components of attention which involves the eliciting and maintenance of arousal. A seminal study by Posner et al. (Posner MI, Klein R, Summers J, Buggie S. 1973 Mem. Cognit. 1, 2–12 (doi:10.3758/BF03198062)) focused on how changing the interval between an alerting signal and a target would impact the speed and accuracy of responding. Participants indicated whether targets were presented on the left or right side of the fixation point. Auditory warning signals were played at various intervals prior to the target to alert participants and prepare them to make a response. Reaction times revealed a robust, U-shaped, preparation function. Importantly, a clear speed-accuracy trade-off (SAT) was observed. In the current experiment, we replicated the methodological components of this seminal study while implementing a novel auditory warning signal (Lawrence MA, Klein RM. 2013 J. Exp. Psychol. General 142, 560 (doi:10.1037/a0029023)) that was either purely endogenous (change in quality without a change in intensity; analogous to isoluminant colour change in vision) or a combination of endogenous and exogenous (change in both quality and intensity). We expected to replicate the U-shaped preparation function and SAT observed by Posner and colleagues. Based on Lawrence and Klein's findings we also expected the SAT to be more robust with the intense signal in comparison to the isointense signal.


5)
On the 9th page, line 3, the authors state that the target presentation followed the</i> end of the auditory signal by 100/250/850ms. However, these are SOA times (stimulus <i>onset asynchrony), and the reason for the change in SOA compared to the original study was to ensure that the time between the end of the auditory signal and the onset of the target was in fact identical to the previous study. Therefore, I strongly suspect that the authors actually mean to say that the time between the start of the auditory signal and the onset of the target was 100/250/850ms. Please revise this section and ensure all descriptions of stimulus timing are correct.
6) It is not clear why the SOA time needed to be increased simply because the auditory signal length increased; there is nothing special about the time between the end of the auditory signal and the start of the target onset; participants can begin to respond to the auditory stimulus as soon as it is perceived, which is why stimulus onset asynchrony is considered a more important metric. In my opinion, it would be better to keep the original SOA times unchanged.
7) The use of past and future tense throughout the methods section is inconsistent, e.g., "participants will be run…" vs. "participants completed four blocks…". Please ensure you comply with the publication guidelines and keep the writing to past tense at this stage. 8) Finally, there are a very large number of writing errors and typos (e.g., the word "stimuli" is used for singular, when it should only be used for plural; "stimulus" is the singular term), as well as formatting errors (e.g., 5th page contains a sentence in a different typeface). These errors appear throughout, but are especially severe in the Figure legend of Figure 3. The authors should carefully review all sections of the manuscript to ensure no spelling or grammatical errors.
Provided the authors substantially reduce their grammatical/spelling errors, and add some additional clarifications in their introduction (particularly regarding the SOA variations relative to the original Posner study), I will be happy to accept this manuscript for publication in principle.
1, Based on the definition of different alerting signals in Lawrence and Klein (2013), and the logic behind the current study, I would like to see a fully design, i.e., 2 (Contingency: yes vs. no) * 2 (Intensity: change vs. no-change) * 4 (SOAs: 0, 50, 200, and 800 ms) * 2 (Compatibility: yes vs. no). I believed that, only in this way, the authors could compare endogenous (0Δ dB and C) and exogenous signals (+Δ dB and NC). Otherwise, as described in the paper that there was no NC condition, we could only examine the difference between endogenous signal (0Δ dB and C) and both endogenous and exogenous signal (+Δ dB and C).
2, As illustrated in Figure 1, 200 ms is the peak for RT, and 100 ms is the peak for accuracy. I think it is valuable to involve both in.
Minor points 1, See p. 9. In the main text, the authors mentioned Figure 1 and 1a, but I cannot find them in On behalf of the Editors, I am pleased to inform you that your Stage 1 Replication RSOS-190134 entitled "On the Endogenous and Exogenous Selection of Signals" deemed suitable for inprinciple acceptance in Royal Society Open Science subject to minor revision in accordance with the referee and editor suggestions. Please find their comments at the end of this email.
The reviewers and handling editors have recommended publication, but also suggest some minor revisions to your manuscript. Therefore, I invite you to respond to the comments and revise your manuscript.
To revise your manuscript, log into https://mc.manuscriptcentral.com/rsos and enter your Author Centre, where you will find your manuscript title listed under "Manuscripts with Decisions". Under "Actions," click on "Create a Revision." You will be unable to make your revisions on the originally submitted version of the manuscript. Instead, revise your manuscript and upload a new version through your Author Centre.
When submitting your revised manuscript, you will be able to respond to the comments made by the referees and upload a file "Response to Referees" in the "File Upload" step. You can use this to document any changes you make to the original manuscript. In order to expedite the processing of the revised manuscript, please be as specific as possible in your response to the referees. Three expert reviewers have appraised the manuscript. As you will see, all find merit in this replication study but also note a number of areas in the rationale and methods requiring greater clarity and justification, including most notably the sample size and mapping between the hypotheses and analyses. In revising the manuscript, please attend carefully to every point raised in the reviews.
Reviewers' comments to Author: Reviewer: 1 Comments to the Author(s) My main concerns relate to the power and analysis pipeline 1. There is no discussion of how or why a sample of 24 participants was selected. I has expected to see a an apriori power calculation based on effects previously observed in the literature used to justify the sample size 2. The analysis doesn't seem to address the hypothesis 2, which is " comparing performance in the high-intensity signal condition to the no-intensity signal condition to see if there are differences in the relationship between RT and ER, as predicted by Lawrence and Klein (2013)". The 2x2 anova described in the analysis section does not include a hgh v low intensity factor, so the these conditions are not statistically compared. It seems to me that a 2x2x2 omnibus anova would be more appropriate to address hypothesis 2 Reviewer: 2 Comments to the Author(s) This study implements implements a relatively recent auditory stimulus technique, which accounts for differences between exogenous and endogenous alerting, and applies it to a wellestablished paradigm with the intention of replicating the results originally obtained from this paradigm, as well as determining the independent influence of endogenous and exogenous alerting on this established pattern of results.
Generally, the motivations of this study are well structured and clearly laid out, and without a doubt demonstrate the importance of carrying out this research. Most importantly, the description of the upcoming methods and analyses are put forward in a transparent fashion, though there are some discrepancies in the description of stimuli and procedures; hopefully these are due simply to errors in writing. Overall, several issues will need to be addressed before I can recommend this manuscript for publication in principle. These issues are laid out below: 1) When describing Lawrence & Klein's (2013) methodology, the description of the concept of "contingency" is lacking in clarification. Since I have read this paper myself, I understand that contingency in this case means that the order of presentation of signal and target was predictable and alternating. Nowhere in your manuscript is this clarified, and readers may be confused and potentially assume that you are referring to the identity or the location of the signal with respect to the target. Also, clarifying the actual procedure of Lawrence & Klein's experiment will help readers to understand that their task was qualitatively different, and to appreciate the motivation for the current study.
2) The figures you have uploaded are extremely low in DPI quality, to the extent that they are difficult to read. Please increase the DPI substantially before re-uploading.
3) On the 7th page (counting from the first page of the introduction), on line 17, the authors refer to " Figure 1", but are in fact referring to Figure 3. 4) On the 8th page, line 31/32, the authors state that the auditory signal was 50ms. However, in the footnote on the same page, they state that this signal was increased to 100ms. Please ensure this is consistent and correct. 5) On the 9th page, line 3, the authors state that the target presentation followed the</i> end of the auditory signal by 100/250/850ms. However, these are SOA times (stimulus <i>onset asynchrony), and the reason for the change in SOA compared to the original study was to ensure that the time between the end of the auditory signal and the onset of the target was in fact identical to the previous study. Therefore, I strongly suspect that the authors actually mean to say that the time between the start of the auditory signal and the onset of the target was 100/250/850ms. Please revise this section and ensure all descriptions of stimulus timing are correct.
6) It is not clear why the SOA time needed to be increased simply because the auditory signal length increased; there is nothing special about the time between the end of the auditory signal and the start of the target onset; participants can begin to respond to the auditory stimulus as soon as it is perceived, which is why stimulus onset asynchrony is considered a more important metric. In my opinion, it would be better to keep the original SOA times unchanged.
7) The use of past and future tense throughout the methods section is inconsistent, e.g., "participants will be run…" vs. "participants completed four blocks…". Please ensure you comply with the publication guidelines and keep the writing to past tense at this stage. 8) Finally, there are a very large number of writing errors and typos (e.g., the word "stimuli" is used for singular, when it should only be used for plural; "stimulus" is the singular term), as well as formatting errors (e.g., 5th page contains a sentence in a different typeface). These errors appear throughout, but are especially severe in the Figure legend of Figure 3. The authors should carefully review all sections of the manuscript to ensure no spelling or grammatical errors.
Provided the authors substantially reduce their grammatical/spelling errors, and add some additional clarifications in their introduction (particularly regarding the SOA variations relative to the original Posner study), I will be happy to accept this manuscript for publication in principle.

Reviewer: 3
Comments to the Author(s) This study was designed to replicate the seminal study by Posner et al, 1973, with both endogenous and exogenous signals adopted in Lawrence and Klein, 2013. The authors, in doing this way, tried to explore the difference on speed-accuracy tradeoff between endogenous and exogenous signals. The logic behind this study is very straightforward. This kind of comparison between endogenous and exogenous signals would have broad audiences in the field of attention. It also has strong general interesting. I only have some suggestions on the experimental design that might help improving the paper and make it more accessible to a wider audience.
1, Based on the definition of different alerting signals in Lawrence and Klein (2013), and the logic behind the current study, I would like to see a fully design, i.e., 2 (Contingency: yes vs. no) * 2 (Intensity: change vs. no-change) * 4 (SOAs: 0, 50, 200, and 800 ms) * 2 (Compatibility: yes vs. no). I believed that, only in this way, the authors could compare endogenous (0Δ dB and C) and exogenous signals (+Δ dB and NC). Otherwise, as described in the paper that there was no NC condition, we could only examine the difference between endogenous signal (0Δ dB and C) and both endogenous and exogenous signal (+Δ dB and C). Figure 1, 200 ms is the peak for RT, and 100 ms is the peak for accuracy. I think it is valuable to involve both in.

2, As illustrated in
Minor points 1, See p. 9. In the main text, the authors mentioned Figure 1 and 1a, but I cannot find them in On behalf of the Editor, I am pleased to inform you that your Manuscript RSOS-190134.R1 entitled "On the Endogenous and Exogenous Selection of Signals" has been accepted in principle for publication in Royal Society Open Science.
You may now progress to Stage 2 and complete the study as approved.
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Following completion of your study, we invite you to resubmit your paper for peer review as a Stage 2 Replication. Please note that your manuscript can still be rejected for publication at Stage 2 if the Editors consider any of the following conditions to be met: • The Introduction and methods deviated from the approved Stage 1 submission (required). • The authors' conclusions were not considered justified given the data.
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Once again, thank you for submitting your manuscript to Royal Society Open Science and I look forward to receiving your Stage 2 submission. If you have any questions at all, please do not hesitate to get in touch. We look forward to hearing from you shortly with the anticipated submission date for your stage two manuscript.  (2013) shown in fig 5 a bit hard to follow. As i understand it, L&K show faster RT but (slightly) reduced accuracy for a combined cue, whereas as the current study shows faster RT and improved accuracy. However, this pattern is also observed in the 'no signal' trials. There is some reference to participants having different mental states in the two studies. Is the idea that something about the design of the current study means that participants are better in the combined condition, irrespective of the presence of an alerting signal, and this is the cause of the inconsistency with L&K?
Final paragraph, 2nd sentence reads "This reinforces the theory that alerting increases response speed without improving the quality of information processed about the stimulus of interest, and instead is consistent with the suggestion that alerting changes the point at which information is consulted to generate a decision." This is a bit confusing and the 1st & 2nd part of the sentence seem to be offering similar interpretations of the data, but the 'and instead' connector suggests the data are consistent with one interpretation but not the other Review form: Reviewer 2

Do you have any ethical concerns with this paper? No
Have you any concerns about statistical analyses in this paper? No

Recommendation? Accept with minor revision
Comments to the Author(s) Thank you for your Stage 2 Submission; it was a pleasure to go through your results. Overall I am satisfied that this submission fulfills all the relevant criteria. Nonetheless, I do have some small points that would need to be addressed, or at the very least considered. Assuming that point 4 is addressed, I would be happy to accept this without further review (although I would prefer to see points 1 and 3 addressed as well). 1) Page 11, lines 42/43: The authors report a cut-off for trial exclusion as including "a respectable number of trials that fall within that bin". What is meant by respectable? Was there an objective threshold for this?
2) Page 11, line 36 to page 12, line 27 ("Data Processing" section): This binning method is in a way refreshing, as most studies just use 'default' threshold of around 200 and 1800. However, I am not convinced that using changes in accuracy from bin to bin is a logically sound method for trial exclusion. For slow responses, the accuracy (84%) is still very high, suggesting a large proportion of correct responses that are unlikely to be due to chance. The relative decrease in accuracy here may be related to factors that also increase the RT, e.g., participants were less sure of the correct response so took slightly longer, and were slightly less likely to be correct. In this case, their correct responses may still be meaningful. For both slow and anticipatory responses, the number of trials drops significantly, and this alone could be used to achieve the same outcomes. Given this, I see no reason why simply removing RTs that deviate above a threshold (e.g., +/-2.5 SDs from the mean) would not be equally or more effective, instead of using arbitrary bins. This is ultimately a small point, since not many trials were rejected overall, but the logic of using accuracy changes and binning in this way should be carefully considered.
3) Page 14, lines 42/43: Do the authors have any specific considerations regarding the differences in equipment from 45 years ago, with particular regard to how they may have influenced response times? 4) Figure 1: The colours for compatible and incompatible are reversed in the graph, relative to the figure legend. I suggest reversing the colours in the graph, as compatible is more intuitively associated with green, in which case the figure legend text is correct. Please ensure that the lines and the graph-legend "Cue Type" are changed.

Recommendation?
Accept as is On behalf of the Editor, I am pleased to inform you that your Stage 2 Replication submission RSOS-190134.R2 entitled "On the Endogenous and Exogenous Selection of Signals" has been accepted for publication in Royal Society Open Science subject to minor revision in accordance with the referee suggestions. Please find the referees' comments at the end of this email.
The reviewers and Subject Editor have recommended publication, but also suggest some minor revisions to your manuscript. Therefore, I invite you to respond to the comments and revise your manuscript.
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Kind regards, Andrew Dunn
Royal Society Open Science openscience@royalsociety.org on behalf of Professor Chris Chambers (Registered Reports Editor, Royal Society Open Science) openscience@royalsociety.org Associate Editor Comments to Author (Professor Chris Chambers): The Stage 2 manuscript was returned to the three original reviewers who assessed it at Stage 1. All are positive about the submission, noting that the Stage 1 primary criteria are met, but Reviewers 1 and 2 ask for clarification of the interpretation and Reviewer 1 queries the precision and validiity of the data processing procedures. Once these minor issues are addressed, full acceptance should be forthcoming without requiring further in-depth review.

Reviewer: 1
Comments to the Author(s) Minor: I found the explanation for the discrepancy between the current results and those of Lawrence & Klein (2013) shown in fig 5 a bit hard to follow. As i understand it, L&K show faster RT but (slightly) reduced accuracy for a combined cue, whereas as the current study shows faster RT and improved accuracy. However, this pattern is also observed in the 'no signal' trials. There is some reference to participants having different mental states in the two studies. Is the idea that something about the design of the current study means that participants are better in the combined condition, irrespective of the presence of an alerting signal, and this is the cause of the inconsistency with L&K?
Final paragraph, 2nd sentence reads "This reinforces the theory that alerting increases response speed without improving the quality of information processed about the stimulus of interest, and instead is consistent with the suggestion that alerting changes the point at which information is consulted to generate a decision." This is a bit confusing and the 1st & 2nd part of the sentence seem to be offering similar interpretations of the data, but the 'and instead' connector suggests the data are consistent with one interpretation but not the other Reviewer: 2 Comments to the Author(s) Thank you for your Stage 2 Submission; it was a pleasure to go through your results. Overall I am satisfied that this submission fulfills all the relevant criteria. Nonetheless, I do have some small points that would need to be addressed, or at the very least considered. Assuming that point 4 is addressed, I would be happy to accept this without further review (although I would prefer to see points 1 and 3 addressed as well). 1) Page 11, lines 42/43: The authors report a cut-off for trial exclusion as including "a respectable number of trials that fall within that bin". What is meant by respectable? Was there an objective threshold for this?
2) Page 11, line 36 to page 12, line 27 ("Data Processing" section): This binning method is in a way refreshing, as most studies just use 'default' threshold of around 200 and 1800. However, I am not convinced that using changes in accuracy from bin to bin is a logically sound method for trial exclusion. For slow responses, the accuracy (84%) is still very high, suggesting a large proportion of correct responses that are unlikely to be due to chance. The relative decrease in accuracy here may be related to factors that also increase the RT, e.g., participants were less sure of the correct response so took slightly longer, and were slightly less likely to be correct. In this case, their correct responses may still be meaningful. For both slow and anticipatory responses, the number of trials drops significantly, and this alone could be used to achieve the same outcomes. Given this, I see no reason why simply removing RTs that deviate above a threshold (e.g., +/-2.5 SDs from the mean) would not be equally or more effective, instead of using arbitrary bins. This is ultimately a small point, since not many trials were rejected overall, but the logic of using accuracy changes and binning in this way should be carefully considered.
3) Page 14, lines 42/43: Do the authors have any specific considerations regarding the differences in equipment from 45 years ago, with particular regard to how they may have influenced response times? 4) Figure 1: The colours for compatible and incompatible are reversed in the graph, relative to the figure legend. I suggest reversing the colours in the graph, as compatible is more intuitively associated with green, in which case the figure legend text is correct. Please ensure that the lines and the graph-legend "Cue Type" are changed.
Reviewers' comments to Author: Reviewer: 3 It is a pleasure to accept your Stage 2 Replication entitled "On the Endogenous and Exogenous Selection of Signals" in its current form for publication in Royal Society Open Science.
Thank you for your fine contribution. On behalf of the Editors of Royal Society Open Science, we look forward to your continued contributions to the Journal. Thank you for your response. We were delighted to hear that you thought this manuscript was suitable for in-principal acceptance. We have addressed reviewer comments in-line below, and believe we are returning an improved version of our original submission because of the feedback. Reviewer comments are italicized, while our responses are bolded. 2. The analysis doesn't seem to address the hypothesis 2, which is " comparing performance in the highintensity signal condition to the no-intensity signal condition to see if there are differences in the relationship between RT and ER, as predicted by Lawrence and Klein (2013)".
The 2x2 anova described in the analysis section does not include a hgh v low intensity factor, so the these conditions are not statistically compared. It seems to me that a 2x2x2 omnibus anova would be more appropriate to address hypothesis 2.

Appendix A
We originally proposed two 4 (foreperiod) x 2 (compatibility) ANOVAs to address our hypotheses, but it is evident that a 4 (foreperiod) x 2 (compatibility) x 2 (intensity) omnibus ANOVA would be more appropriate. Thank you for this suggestion.

Comments to the Author(s)
This study implements implements a relatively recent auditory stimulus technique, which accounts for differences between exogenous and endogenous alerting, and applies it to a well-established paradigm with the intention of replicating the results originally obtained from this paradigm, as well as determining the independent influence of endogenous and exogenous alerting on this established pattern of results.
Generally, the motivations of this study are well structured and clearly laid out, and without a doubt demonstrate the importance of carrying out this research. Most importantly, the description of the upcoming methods and analyses are put forward in a transparent fashion, though there are some discrepancies in the description of stimuli and procedures; hopefully these are due simply to errors in writing. Overall, several issues will need to be addressed before I can recommend this manuscript for publication in principle. These issues are laid out below: 1) When describing Lawrence & Klein's (2013) methodology, the description of the concept of "contingency" is lacking in clarification. Since I have read this paper myself, I understand that contingency in this case means that the order of presentation of signal and target was predictable and alternating. Nowhere in your manuscript is this clarified, and readers may be confused and potentially assume that you are referring to the identity or the location of the signal with respect to the target. Also, clarifying the actual procedure of Lawrence & Klein's experiment will help readers to understand that their task was qualitatively different, and to appreciate the motivation for the current study.
We have made our explanation of these methods clearer, as we agree that they are complex and important to understand.
2) The figures you have uploaded are extremely low in DPI quality, to the extent that they are difficult to read. Please increase the DPI substantially before re-uploading.
We have fixed our figures so they are now vector format.
3) On the 7th page (counting from the first page of the introduction), on line 17, the authors refer to " Figure 1", but are in fact referring to Figure 3.

Thank you for pointing this out.
4) On the 8th page, line 31/32, the authors state that the auditory signal was 50ms. However, in the footnote on the same page, they state that this signal was increased to 100ms. Please ensure this is consistent and correct.
This has been addressed.

5)
On the 9th page, line 3, the authors state that the target presentation followed the end of the auditory signal by 100/250/850ms. However, these are SOA times (stimulus onset asynchrony), and the reason for the change in SOA compared to the original study was to ensure that the time between the <i>end</i> of the auditory signal and the onset of the target was in fact identical to the previous study. Therefore, I strongly suspect that the authors actually mean to say that the time between the <i>start</i> of the auditory signal and the onset of the target was 100/250/850ms. Please revise this section and ensure all descriptions of stimulus timing are correct.
This has been clarified.
6) It is not clear why the SOA time needed to be increased simply because the auditory signal length increased; there is nothing special about the time between the end of the auditory signal and the start of the target onset; participants can begin to respond to the auditory stimulus as soon as it is perceived, which is why stimulus onset asynchrony is considered a more important metric. In my opinion, it would be better to keep the original SOA times unchanged.
When designing this replication, we elected to use a subset of the six SOAs to obtain more data perparticipant in each condition. The no-signal condition was required, so this left five other options.
We wanted to observe the U-function from the original study, so we elected to choose the shortest (50ms), middle (200ms), and longest (800ms) SOAs. Because our signal was 100ms instead of the original 50ms, we were required to double the time length of the 50ms SOA condition to ensure that the signal did not overlap with the presentation of the target. Then, to keep equal distance between the three signal SOAs, we elected to add 50ms onto the other two SOAs, resulting in our proposed 100ms, 250ms, and 850ms SOAs. This has been elaborated in footnote three.
7) The use of past and future tense throughout the methods section is inconsistent, e.g., "participants will be run…" vs. "participants completed four blocks…". Please ensure you comply with the publication guidelines and keep the writing to past tense at this stage.
This has been fixed.

8) Finally
, there are a very large number of writing errors and typos (e.g., the word "stimuli" is used for singular, when it should only be used for plural; "stimulus" is the singular term), as well as formatting errors (e.g., 5th page contains a sentence in a different typeface). These errors appear throughout, but are especially severe in the Figure legend of Figure 3. The authors should carefully review all sections of the manuscript to ensure no spelling or grammatical errors.
Provided the authors substantially reduce their grammatical/spelling errors, and add some additional clarifications in their introduction (particularly regarding the SOA variations relative to the original Posner study), I will be happy to accept this manuscript for publication in principle.
The article was searched for these errors and were corrected accordingly.

Comments to the Author(s)
This study was designed to replicate the seminal study by Posner et al, 1973, with both endogenous and exogenous signals adopted in Lawrence and Klein, 2013. The authors, in doing this way, tried to explore the difference on speed-accuracy tradeoff between endogenous and exogenous signals.
The logic behind this study is very straightforward. This kind of comparison between endogenous and exogenous signals would have broad audiences in the field of attention. It also has strong general interesting. I only have some suggestions on the experimental design that might help improving the paper and make it more accessible to a wider audience.
1, Based on the definition of different alerting signals in Lawrence and Klein (2013), and the logic behind the current study, I would like to see a fully design, i.e., 2 (Contingency: yes vs. no) * 2 (Intensity: change vs. no-change) * 4 (SOAs: 0, 50, 200, and 800 ms) * 2 (Compatibility: yes vs. no). I believed that, only in this way, the authors could compare endogenous (0Δ dB and C) and exogenous signals (+Δ dB and NC).
Otherwise, as described in the paper that there was no NC condition, we could only examine the difference between endogenous signal (0Δ dB and C) and both endogenous and exogenous signal (+Δ dB and C).
We appreciate these suggestions. Where we are only interested in conditions in which the signals are informative of the presentation of a target, we will stick to our original design that compares the combined signaling condition to the purely endogenous condition. This allows us to replicate the methods of the original study (combined signal) and compare this to a novel condition (purely endogenous). Additionally, based on these comments, we improved the clarity of our definition of the combined signal condition. Figure 1, 200 ms is the peak for RT, and 100 ms is the peak for accuracy. I think it is valuable to involve both in.

2, As illustrated in
We have expanded upon our footnote justifying the subset of the original studies 'foreperiods'. We wanted to still be able to observe the U-shaped functions, but also wanted to reduce the number of conditions so that each participant contributed more data to each combination. 100 and 200 were close enough in interval that we just chose one of the two.

Minor points
1, See p. 9. In the main text, the authors mentioned Figure 1 and 1a, but I cannot find them in Figure 1.