Fisher 's Exact test

Arguably, Fisher’s towering contribution to statistics was his initiating a recasting of statistical induction from ‘induction by enumeration’ (see Pearson, 1920) to ‘model-based induction’. The key to his recasting was the notion of a statistical model providing an idealized description of the data generating process and specified in terms of probabilistic assumptions concerning ‘a hypothetical infinite population’.

..This included a formalization of a ‘random sample’ in the form of the Independence and Identically Distributed (IID) assumptions, to replace the ‘uniformity’ and ‘representativeness’ stipulations, and the explicitly introduction of a distributional assumption, such as Normality. The latter assumption was crucial for Fisher’s frequentist error probabilities, which are deductively derived from the statistical model for any sample size n, and provide a measure of the ‘trustworthiness’ of the inference procedure: how often a certain method will give rise to reliable inferences concerning the underlying actual data generating process. The form of induction envisaged by Fisher is one where the reliability of the inference is emanating from the ‘trustworthiness’ of the procedure used to arrive at the inference. In summary, an inference is reached by an inductive procedure which, with high probability, will reach true conclusions (estimation, testing, prediction) from true (or approximately true) premises (statistical model); see Mayo (1996). Fisher’s crucial contributions to the built-in deductive component, known as ‘sampling theory’, in the form of deriving the finite sampling distributions of several estimators and test statistics, pioneered the recasting of statistical induction in terms of ‘reliable procedures’ based on ‘ascertainable error probabilities’. Fisher envisaged the modeling process as revolving around a prespecified parametric statistical model Mθ(y), chosen so as to ensure that the observed data y0 can be realistically viewed as a truly typical realization of the stochastic mechanism (process) described by Mθ(y) :

“The postulate of randomness thus resolves itself into the question, "Of what population is this a random sample?" which must frequently be asked by every practical statistician.” (Fisher, 1922, p. 313)

Aris Spanos,Testing the Validity of a Statistical Model, 2007
http://www.economics.ox.ac.uk/hendryconference/Papers/Spanos_DFHVol.pdf