![]() ![]() In quick succession, Boeing had two major fatal (and terrifying) crashes caused by autopilot software run amuck: the system was not robust to failure of a relatively simple probe. In years to come, the Boeing 737 Max fiasco will come to be seen as focusing on the wrong problem. Type III error typically extends beyond the realm of the technical aspects of statistical analysis. It is better to solve the right problem the wrong way than to solve the wrong problem the right way. The American mathematician Richard Hamming perceptively recognized that formulating a problem incorrectly sets you off on the wrong path earlier in the analytical journey: More commonly, and more meaningfully, Type III error is described as “getting the right answer to the wrong question,” or, even more generally, simply asking the wrong question in the first place. Some writers consider Type III error as “correctly concluding a result is statistically significant, but in the wrong direction.” This could happen when, due to a random sampling fluke, the treatment sample yields an extreme result in the opposite direction of the real difference. Type III error has various definitions that all, in some way, relate to asking the wrong question. ![]() ![]() Type II error is the result of an under-powered study: a sample too small to detect the effect. Type II error is incorrectly accepting the null hypothesis: concluding there is nothing interesting going on when, in fact, there is. The arcane machinery of statistical inference – significance testing and confidence intervals – was erected to avoid Type I error. Type I error in statistical analysis is incorrectly rejecting the null hypothesis – being fooled by random chance into thinking something interesting is happening. ![]()
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