# 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.