Parametric versus non-parametric statistics

There is no such thing as parametric or non-parametric data. There are parametric and non-parametric statistical models.

“The term nonparametric may have some historical significance and meaning for theoretical statisticians, but it only serves to confuse applied statisticians.”

– Noether, G. E. (1984, p. 177)

“. . . the distribution functions of the various stochastic variables which enter into their problems are assumed to be of known functional form, and the theories of estimation and of testing hypotheses are theories of estimation of and of testing hypotheses about, one or more parameters, finite in number, the knowledge of which would completely determine the various distribution functions involved. We shall refer to this situation for brevity as the parametric case, and denote the opposite situation, where the functional forms of the distributions are unknown, as the non-parametric case.”

– Wolfowitz, J. (1942, p. 264)


Noether, G. E. (1984). Nonparametrics: The early years—impressions and recollections. American Statistician, 38(3), 173–178.

Wolfowitz, J. (1942). Additive Partition Functions and a Class of Statistical Hypotheses. The Annals of Mathematical Statistics, 13(3), 247–279.