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The most widely publicized gender problem in human genetics.
William D Stansfield1, Matthew A Carlton
1Biological Sciences Department, California Polytechnic State University, San Luis Obispo, CA 93407, USA.
Human Biology
|July 11, 2009
Summary
In two-child families with at least one boy, the probability of having two boys is higher than the commonly assumed 1/3 when the male birth ratio exceeds 1.0. Our data show observed proportions ranging from 0.3335 to 0.3941.
Area of Science:
- Demography
- Human Genetics
- Biostatistics
Background:
- The probability of two boys in two-child families with one boy is often cited as 1/3, assuming a 1.0 sex ratio at birth and binomial distribution.
- Human populations typically exhibit a sex ratio at birth greater than 1.0, a factor often overlooked in simplified models.
- Deviations from simple binomial distributions, including within- and between-sibship variations in male birth probability, complicate statistical inferences.
Purpose of the Study:
- To investigate the actual probability of two boys in two-child families with at least one boy, considering sex ratios greater than 1.0.
- To highlight the discrepancy between theoretical probabilities and observed data in human populations with skewed sex ratios.
- To discuss the implications of non-random factors, such as family planning, on gender distribution models.
Main Methods:
- Analysis of data from two federal surveys with observed sex ratios greater than 1.0.
- Calculation of the proportion of two-boy families among families of size 2 with at least one boy.
- Examination of potential variations (Poisson, Lexis) in male birth probability.
Main Results:
- Observed proportions of two boys in families of size 2 with at least one boy ranged from 0.3335 to 0.3941 in the studied populations.
- These observed proportions are higher than the theoretical 1/3 probability derived from a 1.0 sex ratio and simple binomial assumptions.
- Data suggest the presence of within-sibship variation in male birth probability.
Conclusions:
- The probability of two boys in two-child families with at least one boy is demonstrably higher than 1/3 in populations with a sex ratio at birth greater than 1.0.
- Standard binomial models with a 1.0 sex ratio are insufficient for accurate demographic and genetic inferences in many human populations.
- Factors like non-random mating, family planning, and variations in birth probability necessitate more complex models for reliable statistical analysis.
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