The manuscript, entitled "Putting things into perspective: Which visual cues facilitate automatic extraretinal symmetry representation?", by Elena Karakashevska, Marco Bertamini, and Alexis D.J. Makin, the authors addressed issues raised by the reviewers. I do not have any further concerns. 

I recommend its acceptance.

Thank you for the detailed reply and engaging with all the queries and comments. The changes are appropriate and have addressed all my points. Congratulations on completing your ambitious project. 

The new figures are great and will help set higher standards in the field. This is a very useful contribution that should help widen the impact of your work.

Also great job with the equivalence testing -- that's really the way to do it given how you carefully thought about a minimum effect size of interest for your design. That will be another reason for me to cite your work as an example of good practice.

About the normality assumptions: In practice, nothing we measure in psychology and neuroscience is normally distributed, but the extend to which this is a problem when applying parametric tests is an empirical issue. There are plenty of relatively simple alternatives to t-test on means:
https://currentprotocols.onlinelibrary.wiley.com/doi/full/10.1002/cpz1.719
For instance, by default for ERP data I would recommend to make inferences about 20% trimmed means, to decrease the impact of the tails, which could be contaminated by outliers. But ultimately mixed-effect models will become the norm. 

I have no further suggestions.  The manuscript does an excellent job motivating the experiment, the methods and results are described very clearly and comprehensively, and the conclusions are appropriate.

The manuscript, entitled "Putting things into perspective: Which visual cues facilitate automatic extraretinal symmetry representation?", by Elena Karakashevska, Marco Bertamini, and Alexis D.J. Makin, the authors addressed issues raised by the reviewers.
This manuscript is a Stage-2 registered report. The authors collected data, analyzed the data, and reported the results with following the registered procedure. The authors conducted some additional exploratory analyses. The additional analyses are rational and they are clearly separated from the planned analyses in the manuscript.

I also found that the reported results and the authors’ discussion on the results are interesting. I only have a few very-minor issues.

P. 20. > In each block, we obtained obtain …

I think "obtained obtain" is a typo.

P. 22. Figure 8.

The description of the left two columns of the figure is missing.

P. 25. > … differences significantly less that our …

Less than?

P. 27. > Given the current results, we considered whether the brain …

This paragraph is not very clear. It will be great if the authors can revise the paragraph to fill the leaps of logic in the paragraph. From which part of the reported results, the authors considered the existence/absence of “extraretinal representations” in the visual system? The relationship between the ecological approach and the invariants is missing. The sentence about the “perceptual experiences check” is important for the conclusion of this paragraph but the sentence is not very clear.

Past work suggests that frontoparallel symmetry is detected automatically (an ERP difference [the 'Sustained Posterior Negativity', or SPN] between symmetric and asymmetric displays is observed both when symmetry is task-relevant, and when symmetry is task-irrelevant).  On the other hand, when the same planar displays are rotated so that they are seen from an oblique perspective angle, this 'extraretinal symmetry' is not detected automatically (an SPN ERP difference is observed only when symmetry is task-relevant).  However, given the importance and apparent effortlessness of detecting extraretinal symmetry, the authors ran a high-powered study to test how adding different depth cues might aid the recovery of task-irrelevant extraretinal symmetry, as indexed by the SPN.

Specifically, the authors predicted that the perspective cost (difference in SPN for frontoparallel and extraretinal displays) would be greatest when displays were viewed binocularly,  and lower in blocks of trials in which the displays were viewed (1) monocularly (which reduces conflicting disparity cues), (2) in a surrounding frame (which provides additional perspective cues), and (3) in a moving frame (providing motion parallax depth cues prior to the onset of the pattern).  Given that the moving frame block had the most depth information, they also predicted that in this block the perspective cost will be lower than in the static frame block, and possibly not different from 0 (as determined by one-sided equivalence testing).

Contrary to predictions, the authors observed a statistically equivalent perspective cost in all blocks of trials.  Directly viewed displays produced a larger SPN than obliquely viewed displays in all four blocks (and this difference was of about the same magnitude across all four blocks).

Overall, I was impressed by this proposed work.  The experiment was well motivated by the past literature.  The study design was clear and efficient for answering these research questions.  The  statistical tests were appropriate, and the sample size was well justified.  And the authors carried out the work as promised.  It is surprising that the perspective cost was not reduced by removing conflicting depth cues or by adding depth cues which should have been helpful for detecting extraretinal symmetry.  The authors discuss possible reinterpretations of past work based on their results, and possible manipulations which could be tried in the future (e.g. really rotating the computer monitor).

To answer the specific questions posed by the review request:

2A. Yes, the data are able to test the authors' proposed hypotheses by passing the approved outcome-neutral criteria.
 
2B. Yes, the introduction, rationale and stated hypotheses are the same as the approved Stage 1 submission. 
 
2C. Yes, the authors adhered precisely to the registered study procedures.  (In one minor case they departed from registered study procedures, but they mentioned this in a footnote.)

2D. The additional exploratory analyses and visualizations (which start on p. 25) are generally informative. I certainly think it was helpful to confirm the unpredicted null effects with equivalence testing. For each of the correlation matrices, the authors might write a little more about their reason for making it. E.g. or each matrix, was there a different way that it could have looked, which would have suggested a different reason for the hypothesized effects' not occurring?

2E. Yes, the authors' conclusions are justified by the evidence.

Minor comments:

P. 7: Change "within subject’s" to "within subjects"

P. 12, second to last line: Replace "SD = 0.561 t (123)" with "SD = 0.561, t (123)"

P. 13: Change "Similar stimuli have previously been found generate" to "Similar stimuli have previously been found to generate"

P. 17: Change "The participants were first presented with the instructions for the experiment and were informed that task was to classify dot element luminance." to "The participants were first presented with the instructions for the experiment and were informed that the task was to classify dot element luminance."

P. 27: Change "This indicates that they constructed internal visual representation, rather than solely picking up optic invariants." to "This indicates that they constructed internal visual representations, rather than solely picking up optic invariants."

P. 33, last line: Replace "We will referrer" with "We will refer"