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RE: Will I only get males?
So, take that random sample of 800 out of 1000 throws of a pair of fair dice. As a researcher, you claim that would cause you to examine the fairness of the dice, rather than your pre-conditions. It seems to me that the problem was the researcher asking for the wrong dataset. You say you wanted 'random' but, when presented with 'random' discarded the data because what you really wanted was 'normal distribution'
What most claims of bias in gender boil down to is the simple statement, "Having looked at the offspring of pairs which did not fit my expectation I find that most do not fit fit expectations. Therefore the expectations were incorrect."
Or, in terms of your dice, "Having thrown millions of pairs, I was able to locate a series of 1000 throws which produced 800 snake-eyes. Therefore the entire series of millions of throws was not random." When, in fact, the converse would be true .. had the series not appeared, we might suspect the entire dataset was not random.
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