Thank you for these good suggestions. Changes:

1. All the language suggestions were implemented.
2. Correlation about time use and score added to abstract (r = -0.02, given in the table on page 3).
3. "What is the metric for the item-level bias reported at the bottom of the page?". It is Cohen's d. This metric is from https://rdrr.io/cran/mirt/man/empirical_ES.html "ESSD: Expected Score Standardized Difference. Cohen's D for difference in expected scores." I have added a note to the table caption.
4. "Page 12: Don't include an author's given name(s) in a citation." It's a bug from the citation manager (Zotero) that I can't fix. The typesetter should before it before publication.
5. "Please state whether your data analysis was pre-registered or not." Nothing was pre-registered for this archival data study.
6. I compiled results for vocabulary differences for adults from large samples. Added a new table with these results. As R1 says, it is unusual, usually the gap is about 0 in European-ancestry samples. I think the difference here has to do with differential self-selection by male and females. I expanded a paragraph in the discussion to include these data.
7. The discussion, paragraph 3 already discusses the IRT and simple sum scores. However, I added a bit more to this.

There appears to be a bug on the site, I will upload the new PDF whenever possible.

New version uploaded (after bugfix).

Implemented suggestions 1-3 and 6. I prefer the plain language simple comparative duller over formal 2-word less intelligent.

Richard Lynn has coincidentally published a relevant meta-analysis on sex differences in verbal ability. He finds the same results as me, but used a lot more datasets. https://mankindquarterly.org/archive/issue/61-3/16

I will update to add a reference to this work once Reviewer 2 has given their comments.

Thanks for the review.

Add page numbers.
Add table and figure numbering.
r should be in italics.

These will be done at the typesetting step.

Scale scoring, four different methods: Which method is theoretically the best? Describe the advantages and disadvantages of each method. Give a recommendation only based on theoretical considerations before analyzing empirical relationships.

We added some discussion of these:

The simple sum is the most commonly used method, and can be interpreted as a latent variable model with equal loadings (McNeish & Wolf, 2020). The advantage here is the simplicity of use, especially for manual scoring by hand, and the fact that one does not need to estimate factor loadings. Estimation of factor loadings in small samples produces unreliable results, and it may be better to simply assume equal loadings (Gorsuch, 2015; Ree et al., 1998). The simple sum with subtraction for incorrect responses attempts to deal with differences in guessing rates, by subtracting the expected score gains from this. This method should produce better estimates if all guessing is done completely at random and individuals simply vary in how much they guess. This assumption is not likely to be accurate, so it is unclear how this correction will affect estimates. The binary 2-parameter logistic model (2PL) allows for items to vary in difficulty and factor loading. Thus, items that are more informative for a subject are given more weight in the scoring, and there is no bias from the binary nature of the data. This model should produce more accurate estimates than the simple sum when items actually vary in factor loadings, which almost any collection of items will do to a large degree. The nominal nominal model further extends this by allowing that different incorrect responses may be differentially informative. In the binary models, each response is assumed to be informative only in two degrees, whether it is correct or incorrect. In the nominal, some incorrect responses are deemed more incorrect than others, and thus used to estimate the ability. This approach should be slightly more effective if a large sample is available for the model training (Storme et al., 2019).

“Table X. Correlations between test scores and criterion variables” -> “Table X. Correlations between four different variants of test scores and criterion variables”

Updated.

What is “mirt”? Explain.

Added:

(MIRT = Multidimensional Item Response Theory)

We only used unidimensional IRT here, that is just the software package's name. https://cran.r-project.org/web/packages/mirt/index.html

“Of the 45 items, not all are good items, as scored using the site’s key.” What are the criteria? Explain.

I don't understand the comment. The next sentence already explains this. The factor loadings are very low.

 “Of the 45 items, 13 showed evidence of sex-bias” – what is the criterion, describe/explain.

I don't understand the comment. This was explained in the previous section in the study which showed the item response functions. Male bias is seen in the table as well, the effect size is given in Cohen's d, so it is easy to understand. E.g., item 8 favors women by 0.23 d, and item 9 men by 0.12 d.

“may be smarter or duller” -> “may be smarter or less smart”

I prefer the simpler language.

How such a result can emerge? “ On this test, males obtained somewhat higher scores, d = 0.28 (4.2 IQ points). We found evidence of sex bias in 13 of the 45 items. However, the directions of bias were roughly balanced (6 and 7 items) such that the test level bias was near zero.” – Explain.

I don't know what needs to be explained. Some items favor one sex, others favor the other. Their opposite effects cancel out, so the test score does not have any notable sex bias.

Table X: “studies of sex difference” -> “studies of sex differences”

Fixed.

For your empirical analysis which scoring method is better you have used only two criteria. This should be critically mentioned.

Added some dicussion of this limitation. Unfortunatel, there are no more criterion variables to use here:

The main limitation of this criterion analysis is that we only have 2 variables to investigate. It would be preferable to repeat this method comparison using a wider range of criterion variables, and preferably in a larger dataset, so that precision would be sufficiently high to detect even small differences between correlations (e.g., r = .20 vs. .22).

R2,

The requests for the forum software are not best handled here.

Content:

Quote from the abstract: ”With Jensen’s method, we see ... association ... with sex (r = .32). ... However, the item pool contains roughly even numbers of male-favored and female-favored items, so the test level bias is negligible (|d| < 0.05).”

Here are two messages: 1. Males have better results. 2. If there are sex differences in items, about 50% favor males and 50% favor females. This is (at least at first glance) contradictory. This I noticed also in my first review and you wrote

”I don't know what needs to be explained. Some items favor one sex, others favor the other. Their opposite effects cancel out, so the test score does not have any notable sex bias.”

That is no answer. I think the answer is: Items, in which males have an advantage, also show higher g-loadings compared to items in which females show better results. This leads at the end to a higher male mean. Correct? Clarify this. Give numbers. Explain, why it is. [See also your Table with regressions.]

You are missing the part where the part talks about item bias. The latter part you quote is about items with a sex bias in favor of a sex, not a sex difference in favor of that sex (these may be highly correlated (here r = .71) but conceptually distinct). The first part is talking about differences, not biases. There is no conflict here.

The better items (higher g-loadings) show larger male advantages, even adjusting for item difficulty (males do better on the harder items as well, a greater male variance effect?), and item directional bias. That is model what 3 in the regression table shows.

What is ”model training”?

Fitting a model (finding the best parameters for that model on a given dataset). In machine learning, the more common term is training the algorithm or the model. Discplinary semantic differences.

Write one to three sentences about ”LOESS”, explain it and its advantages.

Included a footnote: " LOESS = locally estimated scatterplot smoothing, a method for deriving a moving average that will include nonlinear effects. This is the most common algorithm for handling the simple case of two continuous variables." I don't know if it has any particular advantages over any other set of alternatives, but it is widely used and the default algorithm in the ggplot2 plotting package. https://ggplot2.tidyverse.org/reference/geom_smooth.html defaults to LOESS for n < 1000 (because it is slow, not because it is inaccurate for larger n), it is done with the base R function https://rdrr.io/r/stats/loess.html.

”(when the lines are not overlapping, e.g., item 37 has male-bias).” -> ”(when the lines are not overlapping, e.g., item 37 has male-bias and item 21 female-bias).”

Added.