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We previously analyzed data from the U.S. National Health Interview Survey (NHIS, 1998 to 2002) on families with two biological children (10 years of age and younger) and found that the distribution of families with two boys, two girls, and one boy + one girl did not statistically conform to a binomial distribution regardless of the boy/girl sex ratio used. Using the best estimate of the sex ratio from the data, we found that there were significantly more families with opposite-sex siblings than families with same-sex siblings. No biological mechanism could explain these results at the time. In the present study we conducted an analysis of the first two children in sibships of size 3 from the same data source and found that there are significantly more same-sex sibships than unlike-sex sibships. Combining the two sets of data for the first two children produced observed numbers in close agreement with the expected numbers. A hypothesis of parental choice (family planning) appears to be strongly supported as an explanation for the discrepancies in the two sets of data individually. For example, parents who have a boy and a girl (either order) as their first two children are more likely to stop having children (“stopping rule”) than are parents whose first two children are of the same sex.