Editing 2400: Statistics
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==Explanation== | ==Explanation== | ||
− | This comic is another in a [[:Category:COVID-19|series of comics]] related to the {{w| | + | |
+ | This comic is another comic in a [[:Category:COVID-19|series of comics]] related to the {{w|2019–20 coronavirus outbreak|2020 pandemic}} of the {{w|coronavirus}} {{w|SARS-CoV-2}}, which causes {{w|COVID-19}}. | ||
===Graph=== | ===Graph=== | ||
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− | + | The main focus of the comic is a graph showing cases of COVID-19 versus time for two groups: one group was vaccinated and the other group was not. Graphs are ways to visualize data, and for real data indicate specific values. This graph seems to be based on [https://www.zq1.de/~bernhard/images/share/mRNA-1273-trial.png the Moderna vaccine's results] but is somewhat fictionalised. The higher line ("placebo group") rises in a steep curve. The lower line ("vaccine group") follows the first for a bit but then levels out to a much slower rate of climb. The caption eschews statistical analysis in favor of a holistic assessment: the vaccine is clearly working; just look how much those lines diverge. | |
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+ | This comic was released one day after the [https://www.fda.gov/media/144434/download FDA's Dec 17th briefing document] for the {{w|mRNA-1273|Moderna COVID-19 vaccine}} was released. The document includes the following [https://www.zq1.de/~bernhard/images/share/mRNA-1273-trial.png chart]. The charts draw the integral of the incidence data rather than the data itself ("cumulative" rather than "rate"): this results in changes in disease rate towards the left side of the chart, being added into the data on the right side, amplifying their difference. This technique for emphasizing the data is valid: the spread between the lines only continues to increase if the effect continues happening, such that the total spread at the right is proportional to the total effect the vaccine had. The charts do not show any information on other possible variables. Randall has described previously in his webcomics how very clear charts can be made to hide misleading data. The linked graph does not leave the numbers out, and the numbers indicate the vaccine is 91% effective at preventing the disease (and a 95% chance of being between 85 and 95% efficient). | ||
The advice here could be seen as the inverse of the "science tip" in [[2311: Confidence Interval]], in which the data was so ''bad'' that its error bars fell outside of the graph and were not shown. Also there's some association with [[1725: Linear Regression]] where the data is not so good that you don't need to perform linear analysis. | The advice here could be seen as the inverse of the "science tip" in [[2311: Confidence Interval]], in which the data was so ''bad'' that its error bars fell outside of the graph and were not shown. Also there's some association with [[1725: Linear Regression]] where the data is not so good that you don't need to perform linear analysis. | ||
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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 × 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 × 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. | ||
− | 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== | ||
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[[Category:COVID-19]] | [[Category:COVID-19]] | ||
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[[Category:Comics with color]] | [[Category:Comics with color]] | ||
[[Category:Statistics]] | [[Category:Statistics]] | ||
[[Category:Tips]] | [[Category:Tips]] | ||
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