Statistics are infernal for a few basic reasons.
- Misuse of words. Using different meanings at different times. (Like ‘infer’);
- Assume a clever tool will give you a clever answer (like regression);
- The fallacy that inferential statistics works without random sampling;
- The worst fallacy that regression is always based on an inferential sampling process.
Let’s look at each of these briefly.
First, “inference.” The general meaning of inference is: “if A, then probably B.” In statistics, the meaning is much narrower and specific. Inferential statistics measures how well a random sample represents a population. The problem to be solved is to study or characterize (mean, median, standard deviation, etc.) a population in which you are interested.
Statistics also has two meanings, often in a confusing and confounding manner.
- Is the study of data;
- And, are measures of how well random samples represent a population.
Second, “regression.” A simple math formula to minimize a bunch of squared numbers. Impressive. If you assume the data was [here we go again] randomly selected, you can use even more clever statistics … of the second kind. And you can claim that you are clever at using statistics … of the first kind.
Third, “the inferential fallacy.” This claims that random selection or random assignment is not necessary to use the clever inferential statistics. But it is. It is a mathematical formula, not a modeling judgment. Appraisers do exactly the opposite of random selection. They carefully select a sample which is non-random, and is [carefully] similar to the subject property.
“Appraisers don’t do no random samples.”
And finally, infernality carries the above insensibilities to a deeper mystic and mystifying demonstration of overwhelming cleverness. This is the assumption that any regression is built on an inferential model, randomly sampled from an exactly defined population, AND that the purpose of the analysis is to characterize the population from which the regressed data came….
Yet we base much of our “advanced” quantitative analysis curricula on unsupported assumptions, as described above. We forgot the “beginning” and “intermediate” stuff.
Whew! Again: the appraiser “must be careful not to develop a result that is mathematically precise yet logically meaningless or inappropriate,” and “should be able to distinguish between descriptive and inferential statistics.” The Appraisal of Real Estate, 14th ed. p.400.
It’s not that hard!