Type I error in statistical analysis is incorrectly rejecting the null hypothesis – being fooled by random chance into thinking something interesting is happening. The arcane machinery of statistical inference – significance testing and confidence intervals – was erected to avoid Type I error. Type II error is incorrectly accepting the null hypothesis: concluding there is nothing interesting going on when, in fact, there is. Type II error is the result of an under-powered study: a sample too small to detect the effect.
Type III error has various definitions that all, in some way, relate to asking the wrong question. 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.
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. The American mathematician Richard Hamming perceptively recognized that formulating a problem incorrectly sets you off on the wrong path earlier in the analytical journey:
It is better to solve the right problem the wrong way than to solve the wrong problem the right way.
Type III error typically extends beyond the realm of the technical aspects of statistical analysis. In years to come, the Boeing 737 Max fiasco will come to be seen as focusing on the wrong problem. 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. Boeing considered the problem to be “we need to debug the software, get re-certified by the FAA, and get the plane back in the air quickly.” In reality, the problem was “how can we restore public and regulator faith in Boeing’s management and quality control.”
Good data scientists will tell you that properly formulating the problem is 80% of the battle (to use the Pareto rule). Jeff Deal, the COO of Elder Research, Inc. (our parent company) describes in a white paper how consultants took a client’s expansive, poorly-focused agenda and narrowed it down to a specific task:
When the United States Postal Service Office of the Inspector General (USPS OIG) approached our firm a few years ago, they explained that their vision was to build an organization-wide analytics service to identify fraud, improve operations, and save taxpayer dollars. The need was great, because this unit is responsible for the oversight of approximately 500,000 employees, 200,000 vehicles, and an annual operating budget of $75 billion. But rather than trying to tackle the entire vision immediately, we jointly decided to focus initially on one relatively modest challenge that promised to generate a large return on investment.
Focusing on a specific, achievable task built confidence, interest and enthusiasm.
In subsequent years, as new areas of focus have been incrementally added, the USPS OIG has become a high-profile success story within the federal government, and they are steadily building toward a complete analytics service in line with their original vision.