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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 are not 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 surprise, 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.
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