This paper makes the proposition that the only statistical analyses to achieve widespread popular use in statistical practice are those whose formulations are based on very smooth mathematical functions. The argument is made on an empirical basis, through examples. Given the truth of the proposition, the question ‘why should it be so?’ is intriguing, and any discussion has to be speculative. To aid that discussion, the paper starts with a list of statistical desiderata, with the view of seeing what properties are provided by underlying smoothness. This provides some rationale for the proposition. After that, the examples are considered. Methods that are widely used are listed, along with other methods which, despite impressive properties and possible early promise, have languished in the arena of practical application. Whatever the underlying causes may be, the proposition carries a worthwhile message for the formulation of new statistical methods, and for the adaptation of some of the old ones.
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