Short answers, pulled from the story.
Nonparametric statistics refers to techniques that do not rely on data belonging to any particular parametric family of probability distributions. These distribution-free methods make no assumptions about whether data comes from a given parametric family and allow model structures to grow in size to accommodate the complexity of the data.
Stuart A. Ord and J.K. Arnold published the sixth edition of Kendall's Advanced Theory of Statistics in 1999. This publication clarified how statisticians label their work by describing two distinct meanings for the term nonparametric statistics.
Researchers use nonparametric methods when studying populations with a ranked order like movie reviews receiving one to five stars because such data often have ranking but lack clear numerical interpretation. These methods become necessary situations where less is known about the application in question before analysis begins and result in ordinal data that apply much more generally than corresponding parametric methods.
Early nonparametric statistics include the median which dates back to the 13th century or earlier as an estimation tool. Edward Wright used this method in 1599 to analyze navigational data during his maritime explorations while John Arbuthnot published findings on human sex ratios at birth in 1710 using the sign test.
Specific nonparametric procedures include the Anderson Darling test, Cochran's Q test, Cohen's kappa measure, Friedman two-way analysis of variance by ranks, Kaplan Meier estimates, Kendall tau correlation, Kolmogorov Smirnov tests, and Kruskal Wallis one-way analysis of variance by ranks. Kernel density estimation and support vector machines with Gaussian kernels also serve as nonparametric methods for estimating distributions or classifying datasets.