First, thank you for your prompt review.

1), 8), 12), 13) Some oversights indeed. This will be fixed.

2) I believe the comparison of means provides enough information. I of course performed regression models as a complementary analysis. I included only one parent variable (mother or father, coded 0 for majority and 1 for minority group). It is redundant to use a second parent variable since I have restricted the sample to intermarried couples (not doing this may eventually lead to the same problem as in Arcidiacono's analysis). Mother variable in this case is the mirror of the father variable. They both show the same beta regression values but of opposite signs. 

3) SEI is a composite variable in the CPP, including income, parent education etc. But for more clarity I can replace both SEI and SES words with "socio economic" so as to avoid confusion. Also I believe there are merits in controlling for SES. For example, in an analysis of Black and White infants, adding control may eventually show in a better way the superiority of Black scores as reflecting their precocious motor skills. But more generally, Willerman assumes that the effect of mother's race will remain significant after SES or, put it otherwise, mother's race has an effect beyond SES-related factors. I mentioned it briefly in the paper. Should I explain it more thoroughly? Finally, because Arcidiacono and Willerman always consider SES factors, I believe it's only fair to also include results with controls for SES variables if I want to replicate earlier findings. Obviously, controlling for environment also confounds genetic effects but this is why I display uncontrolled results.

4) I have read this article now, thanks. The cultural hypothesis revolves around the mother's socialization and that is why they expect a positive effect, and it seems most research found confirmation for such effect, although almost none had studied the long-term effect of these cognitive/achievement gains.

5) Do you suggest I upload output on OSF ?

6) This was an interesting finding. I did mention the possibility that if the mother's effect is positive at early age, it may eventually fade out as multiple research suggested prior, especially Beaver et al (2014).

7) There is no such parents' race variables in the NLSY unfortunately. But if that is required I can analyze the Add Health, although I cannot access the full dataset. 

9) Fine. I deleted the 2nd column of Tables 1 and 4 and modified the top cells from "Father's education" to "Husband's education". 

10) Good point, I will change these numbers accordingly in the next version.

11) Only the CPP data required merging to be working properly for testing at both ages 4 and 7.

14) Many studies actually found a positive effect of the mother's variable on the children cognitive or achievement test scores. This study is meant to address the question with respect to interracial children. Perhaps the sentence must be rewritten. My point was merely saying that, instead of having the children score closely resembles the mother, now in the HSLS it seems their score more closely resemble the father.

15) I have read many of those studies citing Willerman (1974). At least among those I can access, only one study replicated Willerman, and it was Arcidiacono (2015). Others weren't insightful.

Thank you for your patience.

I have updated the paper, and added the analysis on the Add Health data.

The updated PDF and related materials can be found here:

https://osf.io/jfuhv/

Author has updated the submission to version #2

 I think the topic of choice is interesting and I’m glad to see it being investigated. Here are my comments on your paper. Feel free to take them or leave them.

The tables are quite hard to follow because they look rather similar to how summary statistics might be presented. It might be easier if you present your results in regression tabes, with asterisks for p values and standard errors underneath coefficients. Then without using standardised betas, the coefficients will show the estimated IQ difference between children with and without white mothers.

But I’m not too fussed about presentation. 

I agree with reviewer 2 that the p values look too low and meta-analysis would be useful given some of the sample sizes are very low. Alternatively, it’s worth considering whether you can combine the samples to gain more power.

“A large body of evidence shows that educational induced gains often do not have a lasting effect on intelligence test scores (Brody, 1992, pp. 174-185; Besharov et al., 2011; te Nijenhuis et al., 2015; Protzko, 2015; Ritchie et al., 2015).”

Ritchie and Tucker-Drob (2018) find IQ gains find gains do not completely fade out in their meta-analysis. 

https://labs.la.utexas.edu/tucker-drob/files/2019/08/Ritchie-Tucker-Drob-2018-Psych-Science-How-Much-Does-Education-Improve-Intelligence.pdf

It might be worth mentioning that these improvements don’t appear to be on general intelligence.

https://psyarxiv.com/8s2vx

“Out of the 41,911 children who were followed and underwent neurological examination at age 7, those who had no or inadequate intelligence test results were excluded as well as children whose mothers did not report socioeconomic data.”

Do we know any details on which children had to be omitted from the sample? I’d guess selection bias would slightly reduce any true effect of the mother’s race. Might be worth commenting on this issue.

It might be worth considering whether pre-natal hypotheses for why the mother’s race could matter for the intelligence of mixed-race women. 

The race of the mother has some association with gestation time, even in mixed-race children. 

https://pubmed.ncbi.nlm.nih.gov/1754497/

And a  longer gestation period is associated with higher intelligence in the child.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5721566/

If these associations are causal ie. mother’s race -> gestational time - > IQ, then we should expect a small effect of the mother’s race on intelligence. 

You do state that an association between mother’s race and IQ could indicate differences in “postnatal environments”, but it could also indicate differences in prenatal environments. I don’t know how good the literature is, but there’ll be some effect of the pregnant mother’s behaviour on the child’s IQ. There might be some data on this already, but I imagine black pregnant women are more likely to make unhealthy decisions than white pregnant women eg. drug use. 

Maybe you’d like to comment on prenatal environmental differences in your paper?

It is also worth considering whether parental race associations with IQ could be caused by assortative mating? My hunch is that black women who are smarter are more likely to marry white men, whilst IQ probably doesn’t have so much of an effect on the likelihood to miscegenate in black men. If so, this genetic confound could hide any detrimental environmental effect of having a black mother. I imagine data on this issue has probably been touched on in some of the Admixture papers or maybe one of Dr Dutton’s papers.

Regardless, it is probably worth noting this problem with the methodology and asking whether or not it is a serious issue.

Thank you both for your time to review the paper.

Reviewer #1

1. Right now I don't know how to improve the tables. I mainly followed Willerman's presentation of the tables, except I added extra columns (since I looked at age 7 as well). I think they are easy to read but of course I'm open to suggestions. Remember these are all summary statistics (table means) and not regression tables. I have means, N, SD as my columns. 

2. See my reply to Reviewer #2.

3. Thanks, I will add it and adjust accordingly the write-up.

4. I just reread Niswander & Gorden (1972) and I believe the CPP was well conducted. They mentioned for example that women who dropped out of the study before completion of their pregnancy didn't not bias estimates of mortality rates etc., but of course it's difficult to know whether these cases were missing at random when not having either IQ or education variables. As I use listwise deletion for all of my analyses, the problem pertains to all datasets. I'll add a note about that. 

5. This review study is interesting. I'll add it in the update. The children were tested at a young age (1, 4 and 6-yrs old) so we don't really know how much of the gains would sustain, but it's worth mentioning due to its biological correlates.

6. Yes, I did mention it briefly in the paper. See section 3.2. The Add Health and HSLS black mothers who intermarried had more education levels (therefore, likely higher IQ) than white mothers who intermarried, and the only exception was the CPP. I reported results controlling for SES, therefore, some of the IQ effect has been partialled out. But I will add a note about it too.

Reviewer #2

"The p values appear to be incorrect. The sample sizes listed are quite tiny, so p < .001 seems impossible 6 times in a row. Is this because you are using sampling weights, which in some contexts messes up the p values?"

It is true that sampling weights artifiially reduce p-values, but reporting p-values on the unweighted result isn't wise either, especially on the Add Health for which, as explained in a footnote, the result is sensitive to the use/non-use of sampling weight. Generally, since p-values are a function of sample size and effect size (and probably data spread as well), I usually ignore p-values for inflated samples. I will adjust the write-up.

"You can test this by repeating the regressions using the full sample as they did."

I cannot access the full Add Health data, but on the public one at least I failed to replicate their findings. 

"There must be newer studies than these, since 2014-16."

I'll look for them.

"The samples are quite small. However, it is possible to integrate the findings with meta-analysis to obtain more precise results."

This is indeed a great idea. I think the inverse-variance method however isn't best used on this data. It requires standard errors and those are affected by sample size. The Add health and HSLS had inflated N compared to the CPP and it wouldn't be wise to use the SEs on the unweighted result. While Bootstrap fixes the issue of biased SEs owing to distribution, it doesn't seem to handle biased estimates owing to inflated Ns. Even if it does, the sampling weights on both the Add Health and HSLS have non-integer values, which means I probably have to round them if Bootstrap has to be used, but some research reported this method being flawed.

Andreis, F., & Mecatti, F. (2015). Rounding Non-integer Weights in Bootstrapping Non-iid Samples: actual problem or harmless practice?. In Advances in complex data modeling and computational methods in statistics (pp. 17-35). Springer, Cham.
https://air.unimi.it/retrieve/handle/2434/250358/341637/Andreis%20-%20Mecatti%20-%20Short%20paper.pdf

Andreis, F., Conti, P. L., & Mecatti, F. (2019). On the role of weights rounding in applications of resampling based on pseudopopulations. Statistica Neerlandica, 73(2), 160-175.
https://dspace.stir.ac.uk/bitstream/1893/27562/1/AndConMec_review_clean.pdf

Is there another method ? I just looked at alternatives and I believe it's best to weight by the inverse of the sample size instead of the standard errors. I might end up doing the analysis but remember the data use cognitive tests which aren't comparable. In the CPP, we have the Wechsler, in the Add Health, a vocabulary test, in the HSLS, an achievement test (math) rather than cognitive test.

Finally, with respect to averaging waves, I believe it's more accurate not to aggregate, especially in the CPP. Willerman's main point was that black mother is associated with a very large cognitive deficit for the children at age 4, but I showed this wasn't the case at age 7. And the hereditarian argument is that the mother's involvement effect decreases over time. 

On the other hand, the Add Health respondents' age at Wave I and Wave III range from 12-19 to 18-26, respectively, there might be some rationale as for aggregating, if one suspects sampling errors. Some of these respondents are quite young but likely this won't affect the result too much. I can aggregate these result for the meta analysis however. 

Author has updated the submission to version #3

I uploaded the new version of the article. In blue are the changes to this version. I added footnotes on p-value issues, intermarried black mothers being of higher education and its potential issue, the meta-analysis (section 3.4) and added finally the studies suggested. I also updated the supplemental material at OSF (specifically, the spreadsheet with meta-analysis full displays, and syntax for the combined Wave I-III PVT of the Add Health). Let me know if you have any suggestion or any disagreement.

Author has updated the submission to version #4

Author has updated the submission to version #5

I agree with Reviewer 2's comments and think his approach works perfectly well. But I'd like to suggest a simple alternative - don't use the sampling weights at all. Sampling weights are useful for dealing with endogeneity created by sampling bias. But the sampling bias of your data, as I understand it, is that it just oversamples ethnic minorities. It is not clear to me how having more ethnic minorities in the sample impacts your test of the effect of parental race on intelligence. As such, I think it is probably appropriate and simpler to not use the weights at all. 

That's my two cents.

Author has updated the submission to version #6

The submission was accepted for publication.

Author has updated the submission to version #8

Author has updated the submission to version #9