Table of Contents

Nonparametric Statistics: Overview, Types, and Examples

By

澳洲幸运5开奖号码历史查询:Mitchell Grant

Updated October 22, 2021

Reviewed by Margaret James

Fact checked by

Timothy Li

Definition

Nonparametric statistics are statistical methods that do not assume data follows a specific distribution model defined by a limited number of parameters, allowing for greater flexibility in analysis.

What Are Nonparametric Statistics?

Nonparametric statistics refer to a statistical method in ⛦which the data are not assumed to come from prescribed models that are determined by a small number of parameters. Examples of such models include the normal distribution model and the linear regression model.

Nonparametric statistics sometimes use data that is ordinal, meaning it relies not on numbers but on a ranking or order of sorts. For example, a survey 🐭conveying consumer preferences ranging from like to dislike would be con🐈sidered ordinal data.

Nonparametric statistics include nonparametric descriptive statistics, statistical models, inference, and statistical tests. The modeꦯl structure of nonparametric models 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.

Key Takeaways

Nonparametric statistics are easy to use but do not offer the pinpoint accuracy of other statistical models.
This type of 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.

Understanding Nonparametric Statistics

In statistics, parametric statistics includ🔜e parameters such as the mean, standard deviation, Pearson correlation, variance, etc. This form of statistics uses the observed data to estimate the parameters of the distribution.

Under parametric statistics, data are often assumed to come from a normal distribution with unknown parameters μ (population mean) and σ2 (population varianc𒈔e), which are then estimated using the sample mean and sample variance.

Important

Nonparametric statistics make no assumption about the sample siz𓃲e or whether the observed data is quantitative.

Nonparametric statistics do not assume that data is drawn from a normal distribution. Instead, the shape of the distribution is estimated under thisꦫ form of statistical measurement. While there are many situations in which a normal distribution can be assumed, there are also some scenarios in which the true data-generating process is far from normally distributed.

Examples of Nonparametric Statistics

In the first example, consider a financial analyst who wishes to estim💟ate 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, they use the histogram to estimate the distribution nonparametrically. The 5th percentile of this histogram t⛎hen provides the analyst with a nonparametric estimate of VaR.

For a second ex🔯ample, consider a researcher who wants to know whether average hours of sleep are 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.

Special Considerations

Nonparametric statistics have gained appreciation due to their ease of use. As th๊e 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 make fewer assum🌟ptions about the sample data, their 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.

What Do Nonparametric Statistics Include?

Nonparametric statistics include nonparametric descriptive statistics, statistical🐭 models, inference, and statistical tests. The model structure of nonparametric models is determined from data.

How Do Nonparametric Statistics Work?

Nonparametric statistics do not assume the sample size, whether the observed data is quantitative, or w🌱hether th🐭e data is drawn from a normal distribution. Instead, the shape of the distribution is estimated under this form of statistical measurement.

How Are Nonparametric Statistics Applied?

Because nonparametric statistics make fewer assumptions about sample data, they are more widely applied and easily used than parametric statistics. However, nonparametric testing is less efficient in cases where parametric testing is more appropriate. The reason is that nonparametric statistics discard some information that is available in the data, unlike parametric statistics.

The Bottom Line

Nonparametric statistics are a statistical method in which the data are not assumed to come from prescribed models that are determined by a small number of parameters, such as the normal distribution model and the linear regression model. Nonparametric statistics sometimes use ordinal data, meaning it relies not on numbers but on a ranking or order.

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