I am satified with the changes the authors made and have no further comments.

The authors have addressed all of my previous questions and suggestions.

I thank the reviewers for addressing my concerns.

The motivation for studying the link between perception and memory is now much more clear in the introduction section.

I appreciate the authors acknowledge that recruiting sufficient relatives of synaesthetes may be difficult, and I agree to the strategy to continue recruitment until sufficient families with sufficient relatives have been included in the study. 

Related to the point raised by R1 about the power to detect differences between synaesthetes and relatives, and given hypothesis 4 about expecting weaker effects for relatives, would the authors consider including even more relatives in the study - as hard as that may be?

I appreciate the addition of the exploratory analysis on the number of synaesthesia types that was also recommended by other reviewers. In the added section, it is now not made explicit how the number of synaesthesia types may affect the results. Perhaps one sentence can be added to clarify this for the reader?  

Thank you for inviting me to review the preregistration of this interesting study. The methods are clearly described and sound in my view, and the conclusions that the authors will be able to draw from their findings will likely be very informative and of interest for a wide research field. I have only a few minor comments suggesting additional clarifications.

1A) The research questions seem valid to me. One aspect could be made a bit clearer in the introduction, namely to what extent whether the link between perception and memory has been explored in other populations previously.

1B) The hypotheses are plausible. I have one comment regarding hypothesis 2A): Correlations between the precision of perception and the precision in memory.

If a person cannot differentiate between, for instance, 2 colours, it should be impossible to for them to remember which of those 2 colours was presented. A high accuracy in perception should therefore be a pre-requisite for high accuracy in memory, but someone being highly accurate in perception does not necessarily need to have a highly accurate memory. Can the data somehow be used to differentiate whether a relationship between accuracy and memory could de due to high accuracy being a pre-requisite for high memory precision? 

1C) The methods and analysis plan seem to be sound and well thought through. I have a few questions regarding methodological details, listed below the next point.

1D) The clarity and degree of methodological detail is sufficient overall, but I have a few minor questions:

-       Are only grapheme colour synesthetes recruited who score below the cut-off for all graphemes or also those only scoring below the cut-off for either letters or digits but not both? If a person only reports, for instance, colours for digits, will that person only be tested for 10 digits? The validated consistency test used all graphemes, I believe, so many more items. Of course there are known cases of digit-colour synesthetes without letter-colour synaesthesia, but it might be relatively easy to memorize colours for only 10 items. So perhaps, there should be a minimum of items in the consistency test, even if only as “distractors”?

-       What types of sequence-space synaesthesia will be tested for? Month, weekdays, alphabet, numbers, any reported?

-       The power calculation seems to have been based on power for comparison of 2 independent means. Relatives of synesthetes are not really an independent group. It would be of interest to discuss expected effect sizes for comparisons between synaesthetes and their relatives, especially since you do not expect to be able to recruit more than the minimum of 61. I understand that it is difficult since the study is the first on memory in relatives of synaesthetes, but maybe one can get an idea based on a different measure or a condition other than synaesthesia…

-       As I understand your methods plan, you will only ask relatives once whether they have synaesthesia ones, if if they claim not to have it it is assumed that is true. How high is the chance that some of them are actually synaesthetes and what consequences does that have for your results?

-       What do you mean by corrected to normal colour vision? Do you mean corrected to normal vision?

-       Could you please comment why the feedback given during the learning phase of the long term memory task will be based on a non-linear scale?

-       I am assuming that there will be some overlap between grapheme-colour synaesthesia and sequence-space so that some individuals contribute to both groups. How much overlap are you expecting?

-       Are you planning to also analyse the influence of having several synaesthesia types?

-       One thing that was a bit difficult to follow was how exactly the guess rate is estimated. I understand that the guessing likelihood should be higher if answer error degree differences are distributed randomly. Does this mean that the similarity between perfect randomness and the error distribution will be somehow expressed as a model fit score or alike?

-       Why did you choose Bayes factor of at least 6 as a threshold? Is this based on previous articles or recommendations you could cite here?

1E. The possibility of floor or ceiling effects is very low, given the pilot data and a previous study using the same task. 

The authors provide a well-written registered report detailing the plan for a set of novel and elegantly crafted experiments examining color memory and spatial memory abilities in synesthetes, non-synesthetic relatives, and unrelated controls. The use of visual perception and memory tasks, alongside assessments of mental imagery, cognitive style, and motivation, underscores this study's holistic and innovative approach. The methodological rigor is high in comparing synaesthetes, non-synaesthetic relatives, and unrelated controls, ensuring a comprehensive understanding of the perceptual/cognitive profiles across these groups. The results are expected to strongly inform our understanding about the broader phenotype of synesthesia. Minor comments and requests for clarification are detailed below:

The study provides a strong framing and testable hypotheses. Though it should also be noted that the absence of an effect within family members is not evidence for the alternative view. E.g., if synesthetes but not family members demonstrate a benefit this could be due to either the dual coding account or the enhanced processing account, if the phenotypical differences in synesthetes are weaker in their relatives and thus creating non-detectable effects on memory and perception. Some of this is of course the common difficulty of arguing for the null hypothesis and will depend on the strength of the observed data in each group (and potentially explainable using proposed baysean statistics). Though, given the results of Ward & Filiz, 2020, the absence of an effect for family members is perhaps the less likely outcome.

It is reported that controls will be recruited through internet-based participants databases, such as Prolific. Are the researchers concerned about confounding group differences separate from synesthesia? It is a strength to the design that the authors are using a motivational scale questionnaire to try and quantify some of the differences that may exist between the groups but a more closely yoked control group may prevent ambiguous results if large motivational differences are observed. Additionally, is there any dimension of the data that can be used to show the selectivity of the results (e.g., a measure that synesthetes and non-synesthetes would not be expected to differ on)? This level of control condition/analyses would help rule out effects purely due to how subjects were selected. Another option would be a synesthetic control group (e.g., Mirror Touch Synesthetes) who would not be expected to show enhancements but would be motivated nonetheless.

Please confirm that for the Visual Perception task, the dependent measure is the recalled location/color as opposed to the left/right color/position matching accuracy. 

Additional information is additionally needed for the Visual Perception task. How many blocks are presented and what is the total number of trials (it is noted 15 objects per block).  Do subjects recall location and color for each object sequentially or only one feature for each trial? If both features for each trial is the order of recalled feature randomized to prevent order effects?

For the Short-term Memory Task the text description states "Following a delay of one second, participants will be cued to recall the colour and location of each object from the array in turn" whereas the figure states "Following a delay of one second, participants are asked to report the colour and location of one of the previously presented items." Are subjects presented which each item or only one single item after each trial? Similar to the Visual Perception task, do subjects report both the spatial position and color or only one (and if both, please confirm the order of feature recalled is randomized).

--David Brang

1A. The scientific validity of the research question(s)

The research question is scientifically justifiable and the different aspects of the study are explained and introduced well. 

In the first two paragraphs of the introduction, however, I miss a rigorous motivation for studying the link between perception and memory specifically. It is mentioned that this link is important, and the authors refer to it later in the introduction as well, but I feel the importance of the set-up study can be emphasized more at this point.  

1B. The logic, rationale, and plausibility of the proposed hypotheses (where a submission proposes hypotheses)

The hypotheses are plausible and the theory subserving them is discussed prior to the proposal of the hypotheses. 

1C. The soundness and feasibility of the methodology and analysis pipeline (including statistical power analysis or alternative sampling plans where applicable)

The tasks are well-designed and clearly described. All DVs are tested within a similar task, justifying cross-comparison of scores across perception and memory tasks.

Randomizations are solid; description of how the stimuli will be created are clear.

The power analysis is well motivated and the sampling plan is realistic. I would, however, like the authors to comment on the feasibility of recruiting 61 first-degree non-synaesthetic relatives from 100 synaesthete participants. Perhaps the authors can refer to other papers that have successfully done this, or comment on their own experience with this? Also, I was wondering whether there would be any preference to recruit siblings of synaesthetes (rather than parents or children), to avoid large age differences between the groups. 

2.2.1 Consistency tests: With regard to synaesthetes already in the Sussex database, it is mentioned that recruitment ID will be retrieved to verify which types of synaesthesia the participants have. This is a rather crucial aspect as the number of synaesthesia types matters for the cognitive profile to be expected, e.g., the strength of attention to detail-like profiles (including perhaps, colour sensitivity, as it belongs to the parvocellular visual system), for instance. In this respect, it has been shown that the more types of synaesthesia someone has, the more autism-like the profile is and the more deviant the Glasgow Sensory Questionnaire scores are (Ward et al., Cortex, 2017). I therefore feel the number of synaesthesia types is a confound to control for when assessing especially perceptual performance across the groups of synaesthetes, as synaesthetes with a stronger ‘synaesthetic profile’ might score very different from synaesthetes with only 1 type (Hypothesis 3). Additionally, synaesthetes with a stronger profile might differ more clearly from control participants in their accuracy (Hypothesis 1). 

2.2.1. Consistency test for SSS: perhaps the authors can, in the paper itself, briefly comment on the ability of their questionnaire (in combination with the consistency test) to discriminate between synaesthetes and non-synaesthetes. It is our experience that with the consistency test only, this can be hard to do because non-synaesthetes can easily adopt a structured order for e.g., the days of the week, artificially lowering their consistency score (Van Petersen et al., Cortex, 2020). So it would be relevant to stress the additional qualities of the questionnaire in the paper itself As an alternative verification task, I can suggest a drawing tasks that previously worked well to discriminate between synaesthetes and non-synaesthetes (Van Petersen et al., Cortex, 2020), although I acknowledge this would be impractical to implement online, perhaps. 

1D. Whether the clarity and degree of methodological detail is sufficient to closely replicate the proposed study procedures and analysis pipeline and to prevent undisclosed flexibility in the procedures and analyses.

There is a clear referral to the hypotheses for the different proposed analyses and it is explained how the different analyses are dependent upon each other, and in which order these will be performed. Enough care is taken to investigate the role of possible confounds. The summary table of the analysis plan is clear and explains the relations between the different hypotheses well.

1E. Whether the authors have considered sufficient outcome-neutral conditions (e.g. absence of floor or ceiling effects; positive controls; other quality checks) for ensuring that the obtained results are able to test the stated hypotheses or answer the stated research question(s).

The research is based on a previous paper that has used a very similar experimental paradigm, and which gives the authors a good estimate of expected performance and effect sizes. The authors include Bayesian statistics and follow-up analyses to confirm their initial findings and present clear plans for regression analyses that would allow for fine discrimination between relevant variables. 

Pilot data indicate floor and ceiling effects are not to be expected, and the task manipulations work (e.g., load manipulations, etc). 

The inclusion of a questionnaire on motivation is important to ensure synaesthetes do not outperform controls simply for motivational reasons.

Signed: Tessa M. van Leeuwen