## Non-Parametric Tests: Introduction

Non-parametric tests are experiments that do not require the underlying population for assumptions. It does not rely on data referring to any particular parametric group of probability distributions. Non-parametric methods are also called distribution-free tests since they do not have any underlying population.

• Inferences must be made on categorical or ordinal data
• The assumption of normality is not appropriate
• The sample size is small

• Easy application (does not even need a calculator in many cases)
• It can serve as a quick check to determine whether or not further analysis is required
• Many assumptions concerning the population of the data source can be relaxed
• Can be used to test categorical (yes/no) data
• Can be used to test ordinal (1, 2, 3) data

• Nonparametric procedures are less efficient than parametric procedures. It means that nonparametric tests require a larger sample size to have the same probability of a type-I error as the equivalent parametric procedure.
• Nonparametric procedures often discard helpful information. That is, the magnitudes of the actual data values are lost. As a result, nonparametric procedures are typically less powerful.

That is they produce conclusions that have a higher probability of being incorrect. Examples of widely used Parametric Tests: include the paired and unpaired t-test, Pearson’s product-moment correlation, Analysis of Variance (ANOVA), and multiple regression.

Do not use nonparametric procedures if parametric procedures can be used.

Some widely used Non-Parametric Tests are:

• Sign Test
• Runs Test
• Wilcoxon Signed Rank Test
• Wilcoxon Rank Sum Test
• Spearman’s Rank Correlation
• Kruskal Wallis Test
• Chi-Square Goodness of Fit Test

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Statistical inference is a branch of statistics in which we draw conclusions (make wise decisions) about the population parameter by making use of sample information. To draw wise decisions, one can use estimation and hypothesis testing techniques on the basis of extracted information from descriptive statistics. Statistical inference can be further divided into the Estimation of parameters and testing of the hypothesis.

Estimation is a way of finding the unknown value of the population parameter from the sample information by using an estimator (a statistical formula) to estimate the parameter. One can estimate the population parameter by using two approaches (I) Point Estimation and (ii) Interval Estimation.
In point Estimation, a single numerical value is computed for each parameter, while in interval estimation a set of values (interval) for the parameter is constructed. The width of the confidence interval depends on the sample size and confidence coefficient. However, it can be decreased by increasing the sample size. The estimator is a formula used to estimate the population parameter by making use of sample information.

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