Originally Posted by
Endus
Scale the sample up, say it lands on heads 600,000,000 times out of 1,000,000,000. What this suggests is that the coin's unbalanced, because with a high enough sample, we can determine that its performance is exceedingly unlikely if it were truly a 50/50 chance either side would turn up.
You're doing this entirely backwards. You look at the evidence first, and you see what the reality actually is. If your assumptions do not describe that reality, then it is most likely that your assumptions are wrong. And you should adjust those assumptions to account for the evidence. In your coin flip case, you should be considering that your coin is not a fair coin, for some reason; it's turning up heads 60% of the time, and tails only 40%, rather than the 50/50 you had assumed. Your assumption as to how it performs is factually incorrect.
Again, this is completely backwards, and completely irrational. You are literally arguing that if data contradicts your fantasies about how you think things "should be", then the data must be flawed and you should ignore it.
That's not how anything works.