# Nonparametric statistics

**non-parametricnon-parametric statisticsnonparametricnonparametric testnonparametric methodsnon-parametric modelnon-parametric testdistribution-freenonparametric inferencenon-parametric methods**

Nonparametric statistics is the branch of statistics that is not based solely on parametrized families of probability distributions (common examples of parameters are the mean and variance).wikipedia

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### Ranking

**rankrankedrankings**

The use of non-parametric methods may be necessary when data have a ranking but no clear numerical interpretation, such as when assessing preferences.

Analysis of data obtained by ranking commonly requires non-parametric statistics.

### Descriptive statistics

**descriptivedescriptive statisticstatistics**

Nonparametric statistics includes both descriptive statistics and statistical inference.

This generally means that descriptive statistics, unlike inferential statistics, is not developed on the basis of probability theory, and are frequently nonparametric statistics.

### Statistical inference

**inferential statisticsinferenceinferences**

Nonparametric statistics includes both descriptive statistics and statistical inference.

### Ordinal data

**ordinalordinal variableordered categorical data**

In terms of levels of measurement, non-parametric methods result in ordinal data.

Nonparametric methods have been proposed as the most appropriate procedures for inferential statistics involving ordinal data, especially those developed for the analysis of ranked measurements.

### Kernel density estimation

**Parzen windowkernel densitykernel**

In statistics, kernel density estimation (KDE) is a non-parametric way to estimate the probability density function of a random variable.

### Power (statistics)

**statistical powerpowerpowerful**

The wider applicability and increased robustness of non-parametric tests comes at a cost: in cases where a parametric test would be appropriate, non-parametric tests have less power.

In addition, the concept of power is used to make comparisons between different statistical testing procedures: for example, between a parametric test and a nonparametric test of the same hypothesis.

### Data envelopment analysis

Data envelopment analysis (DEA) is a nonparametric method in operations research and economics for the estimation of production frontiers.

### K-nearest neighbors algorithm

**k-nearest neighbor algorithmk-nearest neighbork-nearest neighbors**

In pattern recognition, the k-nearest neighbors algorithm (k-NN) is a non-parametric method used for classification and regression.

### Parametric statistics

**parametricparametric testparametric inference**

Non-parametric (or distribution-free) inferential statistical methods are mathematical procedures for statistical hypothesis testing which, unlike parametric statistics, make no assumptions about the probability distributions of the variables being assessed.

A non-parametric estimate of the same thing is the maximum of the first 99 scores.

### Kernel (statistics)

**kernelkernelskernel function**

In nonparametric statistics, a kernel is a weighting function used in non-parametric estimation techniques.

### Nonparametric regression

**non-parametric regressionnonparametricnon-parametric**

### Sign test

**sign statistic**

Early nonparametric statistics include the median (13th century or earlier, use in estimation by Edward Wright, 1599; see ) and the sign test by John Arbuthnot (1710) in analyzing the human sex ratio at birth (see ).

The sign test is a non-parametric test which makes very few assumptions about the nature of the distributions under test – this means that it has very general applicability but may lack the statistical power of the alternative tests.

### Jean D. Gibbons

**Gibbons, J.D.Gibbons, Jean DickinsonJean Dickinson Gibbons**

Jean Dickinson Gibbons (née Dickinson, born 1938) is an American statistician, an expert in nonparametric statistics and an author of books on statistics.

### Semiparametric model

**semiparametricsemi-parametricsemi-parametric model**

In statistics, a semiparametric model is a statistical model that has parametric and nonparametric components.

### John Arbuthnot

**ArbuthnotDr John ArbuthnotDr. Arbuthnot**

Early nonparametric statistics include the median (13th century or earlier, use in estimation by Edward Wright, 1599; see ) and the sign test by John Arbuthnot (1710) in analyzing the human sex ratio at birth (see ).

This is credited as "… the first use of significance tests …", the first example of reasoning about statistical significance and moral certainty, and "… perhaps the first published report of a nonparametric test …".

### Resampling (statistics)

**resamplingstatistical supportpermutation test**

Permutation tests are a subset of non-parametric statistics.

### Human sex ratio

**Sex ratioGender ratiogender imbalance**

Early nonparametric statistics include the median (13th century or earlier, use in estimation by Edward Wright, 1599; see ) and the sign test by John Arbuthnot (1710) in analyzing the human sex ratio at birth (see ).

This is credited as "… the first use of significance tests …" the first example of reasoning about statistical significance and moral certainty, and "… perhaps the first published report of a nonparametric test …"; see details at.

### CDF-based nonparametric confidence interval

**Cumulative distribution function-based nonparametric confidence interval**

### Statistics

**statisticalstatistical analysisstatistician**

Nonparametric statistics is the branch of statistics that is not based solely on parametrized families of probability distributions (common examples of parameters are the mean and variance).

### Statistical parameter

**parametersparameterparametrization**

Nonparametric statistics is the branch of statistics that is not based solely on parametrized families of probability distributions (common examples of parameters are the mean and variance).

### Probability distribution

**distributioncontinuous probability distributiondiscrete probability distribution**

Non-parametric (or distribution-free) inferential statistical methods are mathematical procedures for statistical hypothesis testing which, unlike parametric statistics, make no assumptions about the probability distributions of the variables being assessed. Nonparametric statistics is the branch of statistics that is not based solely on parametrized families of probability distributions (common examples of parameters are the mean and variance).

### Number

**number systemnumericalnumbers**

The use of non-parametric methods may be necessary when data have a ranking but no clear numerical interpretation, such as when assessing preferences.

### Preference

**preferencespenchantpreferential**

The use of non-parametric methods may be necessary when data have a ranking but no clear numerical interpretation, such as when assessing preferences.

### Level of measurement

**quantitativelevels of measurementscale**

In terms of levels of measurement, non-parametric methods result in ordinal data.

### Robust statistics

**robustbreakdown pointrobustness**

The wider applicability and increased robustness of non-parametric tests comes at a cost: in cases where a parametric test would be appropriate, non-parametric tests have less power. Also, due to the reliance on fewer assumptions, non-parametric methods are more robust.