Editing 2400: Statistics
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For a simplified example, imagine there are 10 000 people in the vaccinated group, and each has a 5% chance of catching COVID under the null hypothesis; we expect 500 people to catch COVID. If only 490 catch COVID, the null hypothesis remains plausible, but if just 10 do, the odds are (in Python; see {{w|binomial distribution}}) <code>sum([math.comb(10000, i) * 0.05**i * 0.95**(10000-i) for i in range(0,10)])</code> = 1.5 Γ 10<sup>-204</sup>. In other words, it is wildly improbably that an ineffective vaccine would have produced such excellent results. We therefore conclude that the vaccine is not ineffective, and have rejected the null hypothesis. | For a simplified example, imagine there are 10 000 people in the vaccinated group, and each has a 5% chance of catching COVID under the null hypothesis; we expect 500 people to catch COVID. If only 490 catch COVID, the null hypothesis remains plausible, but if just 10 do, the odds are (in Python; see {{w|binomial distribution}}) <code>sum([math.comb(10000, i) * 0.05**i * 0.95**(10000-i) for i in range(0,10)])</code> = 1.5 Γ 10<sup>-204</sup>. In other words, it is wildly improbably that an ineffective vaccine would have produced such excellent results. We therefore conclude that the vaccine is not ineffective, and have rejected the null hypothesis. | ||
β | Most people however, on seeing the raw results, would have concluded that the vaccine worked and statistics were just a formality. As the title | + | Most people however, on seeing the raw results, would have concluded that the vaccine worked and statistics were just a formality. As the title test says, they would have "reject[ed] the null hypothesis based on the 'hot damn, check out this chart' test." |
==Transcript== | ==Transcript== |