Nonparametric Method

What Is the Nonparametric Method?

The nonparametric method alludes to a type of statistic that makes no assumptions about the characteristics of the sample (its parameters) or whether the noticed data is quantitative or qualitative.

Nonparametric statistics can incorporate certain descriptive statistics, statistical models, induction, and statistical tests. The model structure of nonparametric methods isn't indicated a priori but is instead determined from data.

The term "nonparametric" isn't meant to suggest 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 illustration of a nonparametric estimate of a probability distribution.

In contrast, notable statistical methods like ANOVA, Pearson's correlation, t-test, and others really do make assumptions about the data being dissected. One of the most common parametric assumptions is that population data have a "normal distribution."

How the Nonparametric Method Works

Parametric and nonparametric methods are often utilized on different types of data. Parametric statistics generally require interval or ratio data. An illustration 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 utilized 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 instance, incorporate sex, whose potential 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 wherein the value suggests some order. An illustration of an ordinal variable could be if a survey respondent inquired, "On a scale of 1 to 5, with 1 being Extremely Dissatisfied and 5 being Extremely Satisfied, how might you rate your experience with the cable company?"

Parametric statistics may too be applied to populations with other realized distribution types, be that as it may. Nonparametric statistics don't need that the population data meet the assumptions required for parametric statistics. Nonparametric statistics, therefore, fall into a category of statistics sometimes alluded to as sans distribution. Often nonparametric methods will be utilized when the population data has an obscure distribution, or when the sample size is small.

Special Considerations

Although nonparametric statistics enjoy the benefit of meeting not many assumptions, they are less strong than parametric statistics. This means that they may not show a relationship between two variables when in fact one exists.

Nonparametric statistics have acquired appreciation due to their convenience. As the requirement for parameters is feeling better, the data turns out to be more applicable to a bigger variety of tests. This type of statistics can be utilized without the mean, sample size, standard deviation, or the estimation of whatever other related parameters when absolutely no part of that information is accessible.

Since nonparametric statistics makes less assumptions about the sample data, its application is more extensive in scope than parametric statistics. In situations where parametric testing is more appropriate, nonparametric methods will be less efficient. This is on the grounds that nonparametric statistics dispose of some information that is accessible in the data, in contrast to parametric statistics.

Common nonparametric tests incorporate Chi-Square, Wilcoxon rank-aggregate test, Kruskal-Wallis test, and Spearman's position order correlation.

Instances of the Nonparametric Method

Consider a financial analyst who wishes to estimate the value-at-risk (VaR) of an investment. The analyst gathers earnings data from many comparable investments throughout a comparable time horizon. Rather than expect that the earnings follow a normal distribution, she utilizes the histogram to estimate the distribution nonparametrically. The 5th percentile of this histogram then gives the analyst a nonparametric estimate of VaR.

Briefly model, consider a different researcher who wants to realize whether average hours of rest are linked to how frequently one falls ill. Since many individuals get sick rarely, if at all, and periodic others get sick undeniably more often than most others, the distribution of illness frequency is plainly non-normal, being right-slanted and outlier-inclined.

Thus, rather than utilize a method that expects a normal distribution for illness frequency, which would be considered normal in classical regression analysis, for instance, the researcher chooses to utilize a nonparametric method, for example, quantile regression analysis.

Highlights

• This is in contrast to parametric methods, which make assumptions about the shape or characteristics of the data. Instances of such methods incorporate the normal distribution model and the linear regression model.
• The nonparametric method is a branch of statistics wherein the data are not assumed to come from endorsed models that are determined by a small number of parameters.
• The nonparametric analysis is often best suited while thinking about the order of something, where even assuming the mathematical data changes, the results will probably stay something very similar.