This Case Caused Many People To See

In this article, we look at three consequential mistakes in the field of statistics. Two of them are famous, the third required a deep dive into the corporate annual reports of False positives generated by detection systems are a huge problem. In the U. They put personnel at risk, cost millions of dollars, and may hinder a response to a real fire. False alarms from smoke detectors cause many people to simply disable them. The key decision factor is the estimated probability that the alarm is real. Rather, the false positive rate is the proportion of true negatives that are misclassified as positives.

The idea is the same whether the detection system is a diagnostic medical test, a fire alarm, or a statistical or machine learning model. The idea is the same: a device to distinguish between classes.

The denominator False positive rate confusion is all about the denominator. Intrinsically, though, it is not a natural or useful metric. It comes closer to the practical importance of the idea, and has less presence in the formal definitions of statistics that might cause confusion.

The term false discovery came into common use with the advent of large-scale hypothesis testing, especially in genetic analysis. Analysts investigate the action of thousands of genes at once, to explore whether a specific gene or set of genes might be responsible for a disease. In such a case, it is easy to be fooled by chance associations.

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The standard statistical toolbox has devices such as the Bonferroni correction to adjust the p-value in the various tests so that the probability of being fooled in this way is controlled. Carlo Emilio BonferroniItalian probabilist — The classic adjustments like Bonferronithough, were meant for relatively small numbers of hypothesis tests, not thousands of simultaneous ones.

Generic researchers were frustrated at the classic criteria since it set such a high bar for statistical significance. Controlling The False Discovery Rate FDR In genetic testing, the classical procedures have been largely replaced by rules to control the false discovery rate — the rate at which null hypothesis rejections turn out to be false rejections. So we shift from the highly conservative approach of controlling the probability of even one false discovery to the more relaxed approach of This Case Caused Many People To See the rate of false discoveries — FDR. More useful is a decision rule that can control the expected but unknown FDR at a specified level, commonly called q.

The rank of the p-values is shown on the x-axis, the p-value corresponding to a given rank is visit web page on the y-axis. The FDR control line is a line sloping up from the origin. As you move from left to right, considering the hypothesis tests in declining significance, hypotheses are accepted as significant, provided they fall below the FDR control line. It is easy to see how this approach became popular among researchers: it allows far more results to meet the threshold for publication.

The latter is the probability of falsely rejecting a hypothesis under the null model, or, when divided up in a multiple testing setting, the probability of falsely rejecting one of the hypotheses. The former, q, is the rate at which rejected hypotheses are permitted to be This Case Caused Many People To See rejected. You can see that, under the FDR criterion, 28 hypotheses have been rejected, i.

Conclusion The FDR approach to hypothesis testing, while popular among genetic researchers, has drawn criticism from statisticians. They wonder how q is selected, and worry that the selection might be arbitrary, and helps to lower the bar to publishing results.

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Bobalink Reportedly, over , people from China flew to the U. But it appears more and more to me, that the root cause of why we were hit so badly is, China lied, WHO complied, and Americans died. I agree that Chinese travel to the US was the root cause of why we have so many cases. But let's not leave out Americans traveling to China, which is probably equal in numbers to Chinese that traveled to the US. I do blame the Chinese government for not locking down their country and containing the virus instead of spreading it worldwide. That was very selfish of them. No doubt due to economic concerns, lives are not valued as highly by the Chinese government, nor the US. After China failed to shut their own borders, the rest of the world should have shut them for them, refusing Chinese travelers and refusing entry into China. This Case Caused Many People To See