# Nonparametric Statistics Explained: Types, Uses, and Examples

![Nonparametric Statistics](https://www.investopedia.com/thmb/PFvnIccPfnaBw5Mo26u28jQqYik=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/nonparametric-statistics-resized-b0ca820274924f5788dbf2e314f58867.jpg)

*— Zoe Hansen / Investopedia*

> **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 use methods where data doesn't need to fit a specific model, like the normal distribution. Nonparametric statistics often use ordinal data, which is based on rank or order instead of numbers. For example, a survey conveying consumer preferences ranging from like to dislike would be considered ordinal data.

Nonparametric statistics can also include [descriptive statistics](https://www.investopedia.com/terms/d/descriptive_statistics.asp), statistical models, inference, and statistical tests. "Nonparametric" doesn't mean the models lack parameters; instead, the parameters are flexible and not predetermined. A histogram is an example of a nonparametric estimate of a probability distribution.

### Key Takeaways

*   Nonparametric statistics do not require data to fit a normal distribution, making them versatile.
*   This method is useful when analyzing ordinal data or rankings, rather than numerical values.  
    
*   Nonparametric models derive their structure from data, offering flexibility in parameters.  
    
*   While easy to use, nonparametric statistics may be less precise than parametric methods.  
    
*   These statistics are widely applicable but may be less efficient than parametric techniques when parametric testing is suitable.

## Nonparametric Statistics Explained

In statistics, parametric statistics include 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.

Parametric statistics assume data comes from a normal distribution with unknown parameters like mean and variance, estimated from samples.

> **Important**
>
> Nonparametric statistics make no assumption about the sample size or whether the observed data is quantitative.

Nonparametric statistics don’t assume data comes from a normal distribution. Instead, the shape of the distribution is estimated under this 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.

## Illustrative Examples of Nonparametric Statistics

For example, a financial analyst wants to estimate an investment's value at risk (VaR). 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 then provides the analyst with a nonparametric estimate of VaR.

For a second example, consider a researcher who wants to know whether average hours of sleep are linked to how frequently one falls ill. Many people rarely get sick, while some fall ill more often, creating a non-normal, right-skewed distribution. 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.

## Important Considerations for Using Nonparametric Statistics

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 make fewer assumptions 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 whether the 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 where the data are not assumed to come from a prescribed model, such as the normal distribution or the linear regression model. This is particularly useful for ordinal data, where items are ranked in relation to each other rather than assigned an absolute value. Although they are less precise than parametric models, nonparametric methods are more flexible for data sets that do not meet parametric assumptions.