weldone
Hall of Fame Member
...having sqrt(n-1) as the deominator in the formula for sample standard deviation solves this problem to an extent...Yeah. Smaller the sample, smaller the absolute standardized z-score for same amount of deviation from the mean is what you are saying.
But what he was saying was different if I understand it correctly. He was saying that even considering the same distribution, the 99% positive tail (or so) will have more number of observations as we increase the sample size. The answer to that would be it doesn't matter, as z-score for the 99% point remains almost the same.
In simple words, if we measure how much the batsman was better than the second-best of his era that would be a wrong measure. But if we are comparing him with the 'average' batsman of his era, that should be fine to an extent. [Because as number of good cricketers increase with increasing number of cricketers, number of bad cricketers should increase as well.]
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