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.

Wilcoxon Signed Rank Test

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.

Non-parametric 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 Non-Parametric 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 Non-Parametric 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.

Parametric and Non-Parametric Tests

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

Test your knowledge about Non-Parametric: Non-Parametric Quiz

Online Quiz Hypothesis Testing

Multiple Choice Questions (Online Quiz Hypothesis Testing and Estimation) from Statistical Inference for the preparation of exams and different statistical job tests in Government/ Semi-Government or Private Organization sectors. These tests are also helpful in getting admission to different colleges and Universities. The Estimation and Hypothesis Testing Quiz will help the learner to understand the related concepts and enhance the knowledge too.

MCQs Hypothesis Testing 06MCQs Hypothesis Testing 05MCQs Hypothesis Testing 04
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Online Quiz Hypothesis Testing

Most of the MCQs on this Post cover Estimate and Estimation, Testing of Hypothesis, Parametric and Non-Parametric tests, etc.

Hypothesis testing

Online Quiz Estimation

MCQs from Statistical Inference covering the topics of Estimation and Hypothesis Testing for the preparation of exams and different statistical job tests in Government/ Semi-Government or Private Organization sectors. These tests are also helpful in getting admission to different colleges and Universities. The Online Quiz Estimation and Hypothesis Testing Quiz will help the learner to understand the related concepts and enhance the knowledge too.

MCQs EStimation 08MCQs EStimation 07
MCQs EStimation 06MCQs EStimation 05MCQs EStimation 04
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Online Quiz Estimation

Most of the Online MCQs on this Post cover Estimate and Estimation, Testing of Hypothesis, Parametric and Non-Parametric tests, etc.

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.

Online Estimation
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