Uncomfortable science

Uncomfortable science is the term coined by statistician John Tukey for cases in which there is a need to draw an inference from a limited sample of data, where further samples influenced by the same cause system will not be available. More specifically, it involves the analysis of a finite natural phenomenon for which it is difficult to overcome the problem of using a common sample of data for both exploratory data analysis and confirmatory data analysis. This leads to the danger of statistical bias through testing hypotheses suggested by the data.

A typical example is Bode's law, which provides a simple numerical rule for the distances of the planets in the solar system from the Sun. Once the rule has been derived, through the trial and error matching of various rules with the observed data (exploratory data analysis), there areren't enough planets remaining for a rigorous and independent test of the hypothesis (confirmatory data analysis). We have exhausted the natural phenomena. The agreement between data and the numerical rule should be no suprise, as we have deliberately chosen the rule to match the data. If we are concerned about what Bode's law tells us about the cause system of planetary distribution then we demand confirmation which is not available.