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Originally Posted by willravel
What are the odds of getting a 1/6 poll from a statistic like 6,000/every recruit in the past year? Not good, which leads us to...
What is more reasonable, we got a lotto winner or it's more common? The most likely answer is that it's more common, thus Occam's Razor is applicable.
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If you spoke with six people and one of them had won the lottery, would it be logical to conclude that one in six people will win the lottery? This is precisely how and why probability doesn't work on a small scale. The larger the sample size, the more accurate the result. It gets misapplied in such situations, because fractions are often reduced in such situations. This is not the purpose of reducing the fractions. Rather, it's because 1/6 is much easier to work with then, say, 874/5244.
Occam's razor isn't applicable because neither scenario ('our sample is representative' vs. 'our sample is not representative') is inherently more complex. One may be more probable, but that speaks nothing to the relative complexity.