Non-Parametric Tests

MCQs Non-Parametric Methods

Most of the MCQs on this page covered Estimate and Estimation, Testing of Hypothesis when the assumption of population parameters are unknown, that is Non-Parametric Methods, etc.

MCQs Non-Parametric Methods List

MCQS Non-Parametric Methods- 6MCQS Non-Parametric Tests- 5MCQS Non-Parametric Tests- 4
MCQS Non-Parametric Tests- 3MCQS Non-Parametric Tests – 2MCQS Non-Parametric Tests – 1

The relationship/ Dependency between the attributes is called association and the measure of degrees of relationship between the attributes is called the coefficient of association. The Chi-Square Statistic is used to test the association between the attributes. The Chi-Square Association is defined as

$$\chi^2 = \sum \frac{(of_i – ef_i)^2}{ef_i}\sim \chi^2_{v},$$

where $v$ denotes the degrees of freedom.

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Wilcoxon Signed Rank Test

The Wilcoxon Signed Rank test assumes that the population of interest is both continuous and symmetric (not necessarily normal). Since the mean and median are the same (for symmetrical distribution), the hypothesis tests on the median are the same as the hypothesis test on the mean.

The Wilcoxon test is performed by ranking the non-zero deviations in order of increasing magnitude (that is, the smallest non-zero deviation has a rank of 1 and the largest deviation has a rank of $n$). The ranks of the deviations with positive and negative values are summed.

These sums are used to determine whether or not the deviations are significantly different from zero. Wilcoxon Signed Rank Test is an alternative to the Paired Sample t-test.

One-Tailed Test

$H_0: \mu = \mu_0\quad $ vs $\quad H_1: \mu < \mu_0$

Test Statistics: $T^-$: an absolute value of the sum of the negative ranks

Two-tailed Test

$H_0: \mu = \mu_0 \quad$ vs $\quad H_1:\mu \ne \mu_0$

Test Statistics: $min(T^+, T^-)$

Because the underlying population is assumed to be continuous, ties are theoretically impossible, however, in practice ties can exist, especially if the data has only a couple of significant digits.

Two or more deviations having the same magnitude are all given the same average rank. The deviations of zero are theoretically impossible but practically possible. Any deviations of exactly zero are simply thrown out and the value of $n$ is reduced accordingly.

Single Sample Wilcoxon Signed Rank Test

Wilcoxon Signed Rank Test

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NonParametric Tests: Introduction

Nonparametric 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. Nonparametric methods are also called distribution-free tests since they do not have any underlying population.

Nonparametric Tests/ Statistics are Helpful when

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

Advantages of NonParametric Methods

  • 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

Disadvantages of NonParametric Methods

  • 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.

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

nonparametric-tests

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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