(11-19-2014 09:50 AM)Tad Carlucci Wrote: 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.
Not sure you understood my assumptions. I never assumed the data set was random, or the dice were fair. If you assume the data is from a true unbiased random set, that no unequal weights have been applied to the probability of an event, then what you say would be true. But that is an extreme case of researcher bias. Also we are not talking about strings, but the total occurrences of each event, no matter what their order or position in the data set might be. If you were given a set of dice by a casino owner, and asked to determine if they were fair or biased, I do not think you would tell him they were fair and not loaded after testing them a statistically significant number of times, because all dice are fair - and that the dealer and his accomplice were just experiencing a string of really good luck that cleaned out the casinos's bank account.
Of course it might be easier to stick the dice under a scanning electron microprobe and observe the higher density weights inside the dice. ( Heavy metals will backscatter more electrons than the organic plastic of the dice, and show up as bright areas with the right preparation.)
In the case of gender, instead of assuming gender weights are equal, consider weighted random number generation for each cat when first born in the database, and those weighted numbers represented gender weight. The overall distribution of gender for all cats would still be 50% and appear random, while each cat could still have a gender weight, say between 0.10 and 0.90, with 0.50 being the dividing line between males and females. In other words think outside your random box, and find another way the gender bias for a particular breeding pair could happen, and continure to happen, for many generations. Two and 1/2 years for one Pure breeding pair and their pure offspring in my experiment.
