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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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

(1)

(2)

(3)

Let us understand them in brief.

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

Where there are multiple independent samples are given, we would use ANOVA or MANOVA parametric test. While, nonparametric equivalent methods to this test are

The non-parametric methods for the comparison of two variables measured in the same sample are

When we have more than two variables measured in one sample, we would use analysis of variance whose non-parametric alternative methods may be

In order to determine the relationship between two variables, generally the correlation coefficient is calculated. The non-parametric equivalents to the correlation coefficient are

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.

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

Below are given the examples of uses of non-parametric statistics.

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