The nonparametric method refers to a type of statistic that does not make any assumptions about the characteristics of the sample (its parameters) or whether the observed data is quantitative or qualitative.

Nonparametric statistics can include certain descriptive statistics, statistical models, inference, and statistical tests. The model structure of nonparametric methods is not specified a priori but is instead determined from data. The term nonparametric is not meant to imply that such models completely lack parameters, but rather that the number and nature of the parameters are flexible and not fixed in advance. A histogram is an example of a nonparametric estimate of a probability distribution.

In contrast, well-known statistical methods such as ANOVA, Pearson’s correlation, t-test, and others do make assumptions about the data being analyzed. One of the most common parametric assumptions is that population data have a “normal distribution.”

The nonparametric method is a branch of statistics in which the data are not assumed to come from prescribed models that are determined by a small number of parameters.
Nonparametric analysis is often best suited when considering the order of something, where even if the numerical data changes, the results will likely stay the same.
This is in contrast to parametric methods, which make assumptions about the shape or characteristics of the data. Examples of such methods include the normal distribution model and the linear regression model.

Parametric and nonparametric methods are often used on different types of data. Parametric statistics generally require interval or ratio data. An example of this type of data is age, income, height, and weight in which the values are continuous and the intervals between values have meaning.

In contrast, nonparametric statistics are typically used on data that nominal or ordinal. Nominal variables are variables for which the values have not quantitative value. Common nominal variables in social science research, for example, include sex, whose possible values are discrete categories, “male” and “female.”‘ Other common nominal variables in social science research are race, marital status, educational level, and employment status (employed versus unemployed).

Ordinal variables are those in which the value suggests some order. An example of an ordinal variable would be if a survey respondent asked, “On a scale of 1 to 5, with 1 being Extremely Dissatisfied and 5 being Extremely Satisfied, how would you rate your experience with the cable company?”

Parametric statistics may too be applied to populations with other known distribution types, however. Nonparametric statistics do not require that the population data meet the assumptions required for parametric statistics. Nonparametric statistics, therefore, fall into a category of statistics sometimes referred to as distribution-free. Often nonparametric methods will be used when the population data has an unknown distribution, or when the sample size is small.

Although nonparametric statistics have the advantage of having to meet few assumptions, they are less powerful than parametric statistics. This means that they may not show a relationship between two variables when in fact one exists.

Nonparametric statistics have gained appreciation due to their ease of use. As the need for parameters is relieved, the data becomes more applicable to a larger variety of tests. This type of statistics can be used without the mean, sample size, standard deviation, or the estimation of any other related parameters when none of that information is available.

Since nonparametric statistics makes fewer assumptions about the sample data, its application is wider in scope than parametric statistics. In cases where parametric testing is more appropriate, nonparametric methods will be less efficient. This is because nonparametric statistics discard some information that is available in the data, unlike parametric statistics.

Common nonparametric tests include Chi-Square, Wilcoxon rank-sum test, Kruskal-Wallis test, and Spearman’s rank-order correlation.

Consider a financial analyst who wishes to estimate the value-at-risk (VaR) of an investment. The analyst gathers earnings data from hundreds of similar investments over a similar time horizon. Rather than assume that the earnings follow a normal distribution, she uses the histogram to estimate the distribution nonparametrically. The 5th percentile of this histogram then provides the analyst with a nonparametric estimate of VaR.

For a second example, consider a different researcher who wants to know whether average hours of sleep is linked to how frequently one falls ill. Because many people get sick rarely, if at all, and occasional others get sick far more often than most others, the distribution of illness frequency is clearly non-normal, being right-skewed and outlier-prone. Thus, rather than use a method that assumes a normal distribution for illness frequency, as is done in classical regression analysis, for example, the researcher decides to use a nonparametric method such as quantile regression analysis.