Testing a Radon–Earthquake Claim
A citizen group claims that radon in well water predicts earthquakes. They present three years of weekly radon measurements from one well and a regional earthquake catalog. During the period, one magnitude 5.2 earthquake occurred six days after a radon spike to four times baseline. The group also recorded 14 other spikes of at least three times baseline with no earthquake within 30 days, and two earthquakes of magnitude 4.5 or larger that occurred without any preceding spike. The group asks the school board to fund a public warning system based on a radon threshold. The board asks a science class to review the claim. The well is 12 km from the nearest mapped fault; the catalog is complete for magnitude 4.5 and above in the region.
1. Evaluate the evidence using the concepts of false positives and false negatives. Does it support the proposed warning system?
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The record has one true positive, 14 false positives, and two false negatives. If the threshold were used for warnings, 15 alarms would produce one earthquake within the stated window-a positive predictive value of about 1/15, or 7%. That is too low for a public warning system, especially because false alarms have costs and the two missed events show the method is not reliable.
The single successful prediction is not strong evidence by itself: with many spikes and a 30-day window, some spike will sometimes precede an earthquake by chance. The claim needs a comparison of earthquake rates after spikes versus baseline, not just a count of hits.
2. Design a testable study that could fairly evaluate the claim. Include at least three features that control for chance and bias.
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The study should pre-register the radon threshold and the time window before looking at the earthquake catalog. It should use multiple wells, including wells far from faults as controls, and sample on a fixed schedule. Analysts should be blind to earthquake times while processing radon data. The key test is whether the earthquake rate in the 30 days after a spike is significantly higher than the rate in randomly chosen 30-day periods; a randomization or time-shift test can estimate chance. The study should also report false positives and false negatives and correct for multiple thresholds. Independent replication in a second region would be needed before any warning system.
3. The group says the one successful prediction proves the method works. How should the class respond, and what result would count as meaningful support?
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One success does not prove the method; it is exactly the kind of event that can occur by chance when many spikes are counted. The class should ask for a prospective test with a pre-specified rule. Meaningful support would be a statistically significant increase in earthquake rate after spikes, a low false-positive rate, successful prediction in an independent region, and a plausible physical mechanism. A single hit after the fact is anecdotal. Even a plausible mechanism would not substitute for prospective predictive skill.