The Seven Pillars of Statistical Wisdom

Clearly the calculation of a single probability is not the answer to all questions. A probability itself is a measure and needs a basis for comparison. And clearly some restriction on allowable hypotheses is needed, or else a self-fulfilling hypothesis such as “the data are preordained” would give probability one to any data set.

A Preliminary Discourse on the Study of Natural Philosophy. Herschel gave particular emphasis to what he called residual phenomena.

Granted that more evidence is better than less, but how much better? For a very long time, there was no clear answer.

with exactness, and subducted, the residual facts are constantly appearing in the form of phenomena altogether new, and leading to the most important conclusions.

In order to make the case for evolution by natural selection, it was essential to establish that there was sufficient within-species heritable variability:

Galton was, in essence, able to establish some of the practical consequences of Mendelian genetics without the benefit of knowing any genetics, nearly two decades before Mendel’s work was rediscovered.

In even approximate equilibrium, the variability Darwin both required and demonstrated existed was in conflict with the observed short-term stability in populations.

it being taken for granted that at least one other hypothesis (Divine Providence or Newtonian dynamics) would yield a much higher probability for the observed data than the probability found under a hypothesis of “chance.”

statistical comparisons may be made strictly in terms of the interior variation in the data,