"The late astronomer [[Carl Sagan]], a devoted promoter of scientific thinking and an obsessive enemy of nonscience, examined the cures from cancer that resulted from a visit to [[Lourdes]] in [[France]], where people were healed by simple contact with the holy waters, and **found out the interesting fact that, of the total cancer patients who visited the place, the cure rate was, if anything, lower than the statistical one for spontaneous remission**s. It was lower than the average for those who did not go to Lourdes! "**Should a statistician infer here that cancer patients’ odds of surviving deteriorates after a visit to [[Lourdes]]** would further illustrate the point with the study of a phenomenon well-known as cancer clusters. "**Consider a square with 16 random darts** hitting it with equal probability of being at any place in the square. If we divide the square into 16 smaller squares, **it is expected that each smaller square will contain one dart on average—but only on average. There is a very small probability of having exactly 16 darts in 16 different squares. The average grid will have more than one dart in a few squares, and no dart at all in many squares**. It will be an exceptionally rare incident that no (cancer) cluster would show on the grid. Now, transpose our grid with the darts in it to overlay a map of any region. **Some newspaper will declare that one of the areas (the one with more than the average of darts) harbors radiation that causes cancer, prompting lawyers to start soliciting the patients**." --- **Tags** -- [[quotes]], [[clustering-illusion]], [[fooled-by-randomness]], [[data-analytics]], [[statistics]], [[regression-to-the-mean]] **Source** -- [[202410121132 - B - Fooled by Randomness]]