Non-parametric methods are widely used for studying populations that take on a ranked order (such as movie reviews receiving one to four stars). The use of non-parametric methods may be necessary when data have a ranking A ranking is a relationship between a set of items such that, for any two items, the first is either 'ranked higher than', 'ranked lower than' or 'ranked equal to' the second. In mathematics, this is known as a weak order or total preorder of objects. It is not necessarily a total order of objects because two different objects can have the same but no clear numerical A number is a mathematical object used in counting and measuring. A notational symbol which represents a number is called a numeral, but in common usage the word number is used for both the abstract object and the symbol, as well as for the word for the number. In addition to their use in counting and measuring, numerals are often used for labels , interpretation, such as when assessing preferences In economics and other social sciences, Preference refers to the set of assumptions relating to a real or imagined "choice" between alternatives and the possibility of rank ordering of these alternatives, based on the degree of happiness, satisfaction, gratification, enjoyment, or utility they provide; in terms of levels of measurement The "levels of measurement", or scales of measure are expressions that typically refer to the theory of scale types developed by the psychologist Stanley Smith Stevens. Stevens proposed his theory in a 1946 Science article titled "On the theory of scales of measurement". In this article Stevens claimed that all measurement in, for data on an ordinal scale.
As non-parametric methods make fewer assumptions, their applicability is much wider than the corresponding parametric methods. In particular, they may be applied in situations where less is known about the application in question. Also, due to the reliance on fewer assumptions, non-parametric methods are more robust Robust statistics seeks to provide methods that emulate classical methods[clarification needed], but which are not unduly affected by outliers or other small departures from model assumptions. In statistics, classical methods rely heavily on assumptions which are often not met in practice. In particular, it is often assumed that the data residuals.
Another justification for the use of non-parametric methods is simplicity. In certain cases, even when the use of parametric methods is justified, non-parametric methods may be easier to use. Due both to this simplicity and to their greater robustness, non-parametric methods are seen by some statisticians as leaving less room for improper use and misunderstanding.
The wider applicability and increased robustness Robustness is the quality of being able to withstand stresses, pressures, or changes in procedure or circumstance. A system, organism or design may be said to be "robust" if it is capable of coping well with variations in its operating environment with minimal damage, alteration or loss of functionality of non-parametric tests comes at a cost: in cases where a parametric test would be appropriate, non-parametric tests have less power The power of a statistical test is the probability that the test will reject the null hypothesis when the alternative hypothesis is true . As power increases, the chances of a Type II error decrease. The probability of a Type II error is referred to as the false negative rate (β). Therefore power is equal to 1 − β. In other words, a larger sample size can be required to draw conclusions with the same degree of confidence.
Non-parametric models
Non-parametric models differ from parametric Parametric statistics is a branch of statistics that assumes data come from a type of probability distribution and makes inferences about the parameters of the distribution. Most well-known elementary statistical methods are parametric models in that the model structure 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 that the number and nature of the parameters are flexible and not fixed in advance.
- A histogram In statistics, a histogram is a graphical display of tabulated frequencies, shown as bars. It shows what proportion of cases fall into each of several is a simple nonparametric estimate of a probability distribution
- Kernel density estimation In statistics, kernel density estimation is a non-parametric way of estimating the probability density function of a random variable. As an illustration, given some data about a sample of a population, kernel density estimation makes it possible to extrapolate the data to the entire population provides better estimates of the density than histograms.
- Nonparametric regression Nonparametric regression is a form of regression analysis in which the predictor does not take a predetermined form but is constructed according to information derived from the data. Nonparametric regression requires larger sample sizes than regression based on parametric models because the data must supply the model structure as well as the model and semiparametric regression Semiparametric regression refers to regression models which combine parametric and nonparametric models. They are often used in situations where the fully nonparametric model may not perform well or when the researcher wants to use a parametric model but the functional form with respect to a subset of the regressors or the density of the errors is methods have been developed based on kernels, splines In mathematics, a spline is a special function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees, and wavelets Loosely speaking, a wavelet is a wave-like oscillation with an amplitude that starts out at zero, increases, and then decreases back to zero. It can typically be visualized as a "brief oscillation" like one might see recorded by a seismograph or heart monitor. Generally, wavelets are purposefully crafted to have specific properties that.
- Data Envelopment Analysis provides efficiency coeficients similar to those obtained by Multivariate Analysis without any distributional assumption.
Methods
Non-parametric (or distribution-free) inferential statistical methods are mathematical procedures for statistical hypothesis testing which, unlike parametric statistics Parametric statistics is a branch of statistics that assumes data come from a type of probability distribution and makes inferences about the parameters of the distribution. Most well-known elementary statistical methods are parametric, make no assumptions about the probability distributions In probability theory and statistics, a probability distribution identifies either the probability of each value of an unidentified random variable , or the probability of the value falling within a particular interval (when the variable is continuous). The probability distribution describes the range of possible values that a random variable can of the variables being assessed. The most frequently used tests include
- Anderson–Darling test
- Cliff's delta
- Cochran's Q
- Cohen's kappa
- Efron–Petrosian test
- Friedman two-way analysis of variance The Friedman test is a non-parametric statistical test developed by the U.S. economist Milton Friedman. Similar to the parametric repeated measures ANOVA, it is used to detect differences in treatments across multiple test attempts. The procedure involves ranking each row together, then considering the values of ranks by columns. Applicable to by ranks
- Kendall's tau In statistics, the Kendall rank correlation coefficient, more commonly referred to as Kendall's tau coefficient or a tau test, is a non-parametric statistic used to measure the association or statistical dependence between two measured quantities. More specifically, it is a measure of rank correlation: that is, the similarity of the orderings of
- Kendall's W
- Kolmogorov–Smirnov test
- Kruskal-Wallis one-way analysis of variance by ranks
- Kuiper's test
- Mann–Whitney U or Wilcoxon rank sum test
- median test
- Pitman's permutation test
- Rank products
- Siegel–Tukey test
- Spearman's rank correlation coefficient In statistics, Spearman's rank correlation coefficient or Spearman's rho, named after Charles Spearman and often denoted by the Greek letter ρ or as rs, is a non-parametric measure of statistical dependence between two variables. It assesses how well the relationship between two variables can be described using a monotonic function. If there are
- Student–Newman–Keuls (SNK) test
- Van Elteren stratified Wilcoxon rank sum test
- Wald–Wolfowitz runs test
- Wilcoxon signed-rank test The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test for the case of two related samples or repeated measurements on a single sample. It can be used as an alternative to the paired Student's t-test when the population cannot be assumed to be normally distributed. The test is named for Frank Wilcoxon who, in a single paper,.
General references
- Corder, G.W. & Foreman, D.I, "Nonparametric Statistics for Non-Statisticians: A Step-by-Step Approach", Wiley (2009) (ISBN: 9780470454619)
- Wasserman, Larry, "All of Nonparametric Statistics", Springer (2007) (ISBN: 0387251456)
- Gibbons, Jean Dickinson and Chakraborti, Subhabrata, "Nonparametric Statistical Inference", 4th Ed. CRC (2003) (ISBN: 0824740521)
See also
- Parametric statistics Parametric statistics is a branch of statistics that assumes data come from a type of probability distribution and makes inferences about the parameters of the distribution. Most well-known elementary statistical methods are parametric
- Resampling (statistics) Bootstrapping is a statistical method for estimating the sampling distribution of an estimator by sampling with replacement from the original sample, most often with the purpose of deriving robust estimates of standard errors and confidence intervals of a population parameter like a mean, median, proportion, odds ratio, correlation coefficient or
- Robust statistics Robust statistics seeks to provide methods that emulate classical methods[clarification needed], but which are not unduly affected by outliers or other small departures from model assumptions. In statistics, classical methods rely heavily on assumptions which are often not met in practice. In particular, it is often assumed that the data residuals
- Particle filter Particle filters, also known as sequential Monte Carlo methods , are sophisticated model estimation techniques based on simulation for the general theory of sequential Monte Carlo methods
Categories: Non-parametric statistics | Statistical inference | Robust statistics
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They proposed a nonparametric smoothing based method to identify those outliers using robust variance estimation instead of variance-stabilizing ...
Q. Ok, i am doing a frequency distribution graph and it has a negative skew and is non parametric but i don't know what any of this means and what consequences this has on my data. Also, can i have some good pointers as to how to evaluate my graph. Thanks in advance people :)
Asked by Katy : ) - Mon Mar 30 15:55:14 2009 - - 1 Answers - 0 Comments
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