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Non Parametric Statistics

The statistics can be divided into two main branches - parametric and non parametric. The parametric statistics has a certain number of parameters. On the contrary, the non-parametric statistics does not have a family of parameterized probability distributions. The mean and variance are the main parameters. The typical parameters are the mean, variance, etc. The non-parametric statistics develops no assumptions about the variables being assessed. Rather it develops different parameters with training data. It is to be noted that non-parametric model does not mean that it is none parametric; in fact the parameters are evaluated by the training data, not by model.

Non-parametric statistics is a kind of statistics in which the interpretations are not based upon the population that fits some parameterized distribution. The statistics depending upon the ranks of observations may be referred as an example of non-parametric statistics. We may also understand a non-parametric statistic as a method in which the given data generally does not observe the normal distribution. It rather makes use of the ordinal data. We can say that the non-parametric statistics depend upon the order or ranking of observations.

Non-parametric statistics is being appreciated because it is very easy to use. Since the parameters are not required, the data can be applied to a variety of tests. Hence, this statistics can be used even if we do not have information of sample size, mean, standard deviation, or some other type of parameter as these are not required in non-parametric model.

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Methods of Non Parametric Statistics

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For each general parametric test, there exists at least one one non-parametric equivalent. The non-parametric methods can be classified as below.

(1)
Methods for differences between independent samples

(2)
Methods for differences between dependent samples

(3)
Methods for relationships between variables

Let us understand them in brief.
Methods for differences between independent samples

In case of having two samples which are being compared on the basis of their means, generally t-test is used for independent samples. The non-parametric alternatives for t-test could be Mann-Whitney U testKolmogorov-Smirnov two-sample test and Wald-Wolfowitz runs test.
Where there are multiple independent samples are given, we would use ANOVA or MANOVA parametric test. While, nonparametric equivalent methods to this test are median test and Kruskal-Wallis analysis of ranks method.
Methods for differences between dependent samples

The non-parametric methods for the comparison of two variables measured in the same sample are Wilcoxon's matched pairs test and Sign test. In the cases where we have dichotomous variables of interest, the McNemar's Chi-square non-parametric method is appropriate.
When we have more than two variables measured in one sample, we would use analysis of variance whose non-parametric alternative methods may be Friedman's two-way ANOVA and Cochran Q test (when variable of interest determined in terms of two categories, such as pass vs fail).
Methods for relationships between variables

In order to determine the relationship between two variables, generally the correlation coefficient is calculated. The non-parametric equivalents to the correlation coefficient are Kendall Tau, Spearman and coefficient Gamma. In case when these two variables are categorical in nature, such as male or female, pass or fail, the most appropriate non-parametric methods would be Phi coefficient, Chi-square test and Fisher exact test. For expressing relationships among multiple variables, Kendall coefficient of concordance method is used.

The choice of use of these non-parametric methods is not so simple, since each non-parametric method has its own blind spots and sensitivities. For instance - the Kolmogorov-Smirnov two-sample test is sensitive to differences of distributions location and also it is greatly sensitive to the differences in shapes of distributions.

But the non-parametric methods are less statistically sensitive than their parametric counterparts.

Non Parametric Statistics Examples

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Below are given the examples of uses of non-parametric statistics.
(1) The uses of non-parametric statistics can be widely seen for the study of populations taking ranked order. For example - reviewing a movie giving stars from one to five.

(2) The non-parametric methods should be necessarily used when given data has an order, but no numerical interpretation. These methods would result in the form of ordinal data, in the sense of levels of measurement.

(3) The applicability of a non-parametric method is much more than its corresponding parametric methods since non-parametric statistics make less assumptions. So, they can be easily applied when very few facts are given. Therefore, these methods are said to be more robust.

(4) The non-parametric methods are more used due to their simplicity. Sometimes, when even parametric methods can be used, the non-parametric methods may be more justified and simpler to use.

(5) The examples of non-parametric tests can be widely seen as they are less costly as compared to their parametric equivalents.
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