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TagSimpson's Paradox

Vaccine or flu shot in injection needle. Doctor working with patient's arm. Physician or nurse giving vaccination and immunity to virus, influenza or HPV with syringe. Appointment with medical expert.

COVID-19, Bayes’ Rule, and Simpson’s paradox

Israeli data, when studied carefully, confirm the effectiveness of COVID-19 vaccines

Israel has a very high COVID-19 vaccination rate and yet, on August 15, 2021, 58% of those Israelis hospitalized for COVID-19 were fully vaccinated — suggesting that vaccinations are ineffective or even harmful. This is a great example of two common statistical traps. The first is confusion about inverse probabilities. One hundred doctors were once asked this hypothetical question: In a routine examination, you find a lump in a female patient’s breast. In your experience, only 1 out of 100 such lumps turn out to be malignant, but, to be safe, you order a mammogram X-ray. If the lump is malignant, there is a 0.80 probability that the mammogram will identify it as malignant; if the lump is benign, there is a 0.90 probability that…