Get Help to Conduct a Wilcoxon Test Statistic

When comparing two groups in a study, one may require experts' help to conduct a Wilcoxon test statistic on the data set provided for analysis. The nonparametric test compares two groups that are paired; calculating the differences between the sets of pairs and analyzing them to determine their statistical significance. The Wilcoxon test statistics occur in two versions; the Wilcoxon signed-rank test and the rank-sum test. Both the Wilcoxon sign rank and the rank-sum test versions operate under the assumption that matched pairs are drawn from dependent populations.

Originally, the Wilcoxon test statistics were used in hypothesis testing of nonparametric statistics for population data that is rankable but does not have quantifiable numerical values such as the degree of customer satisfaction for a particular service. The models of the test statistic assume that the data were drawn from two matched or dependent populations. The data are also assumed to be continuous with no requirement for the probability distribution of the dependent variable. This article contains information about the factors considered in the Wilcoxon test statistic calculation done by experts from our company.

Factors We Consider When Conducting a Wilcoxon Test

The Wilcoxon test statistic is the nonparametric alternative for the t-test that is used when the data are not normally distributed. It occurs in two forms; one sample and two samples. Whereas the t-test statistic is used for comparing means, the Wilcoxon tests compare two paired groups to determine whether a statistically significant difference exists between two or more sets of pairs. The factors we consider in our help to conduct a Wilcoxon test statistic include:

1. Types of Wilcoxon test to be conducted

The Wilcoxon test occurs in different versions which are useful in various conditions and circumstances. The versions include:

a). The Wilcoxon signed-rank test

Wilcoxon sign rank test is the nonparametric version of the dependent samples t-test statistic that uses ordinal or ranked data. It requires repeated measurements to compare the observations. The signed-rank test assumes that there is information in the sizes and difference scores between paired observations. There are two variants of the Wilcoxon signed-rank test which include a one-sample test and the paired samples test.

• One sample Wilcoxon signed-rank test

One sample Wilcoxon sign rank test is applicable when assessing whether the population median is equal to a known constant or theoretical value. It is the nonparametric alternative for the one-sample t-test. When computing the one-sample Wilcoxon signed-rank test, we consider the sum of the ranks corresponding to either the positive or negative differences. The calculations are based on a prior understanding that the critical value of the test statistic depends on the smaller of the positive and negative ranks. When using the normal approximation to find the probability distribution (p-value), using the right and left-sided alternative hypotheses makes the process straightforward.

• Paired samples Wilcoxon signed-rank test

The two/paired-samples Wilcoxon rank test is the alternative for the paired t-test test. It is used when comparing paired samples when the data do not follow a normal distribution.

When calculating the Wilcoxon signed ranks test statistics in a sample of items, we obtain the difference scores between two measurements by subtracting one from the other. We ignore the negative or positive signs to obtain absolute differences and omit the difference scores of zero to obtain the actual sample size. Negative and positive signs are assigned to the ranks. The sum of the positive ranks provides the Wilcoxon test statistic.

b). Wilcoxon rank-sum test

The rank-sum test is used to test the null hypothesis that two populations possess similar continuous distribution. The rank tests assume that the data are drawn from the same population, are paired, were randomly and independently selected, and can be measured on an interval scale. The Wilcoxon rank-sum test is the nonparametric alternative for the independent samples t-test. The statistic can be further divided into one-sided and two-sided tests. The two-sided test scrutinizes the alternative hypothesis without showing the directionality. A one-sided test is used when the interest is in detecting negative or positive differences between one population against another. When the distribution of observed differences for one group shifts to the right or left of the other, we reject the null hypothesis that the populations or groups have the same distribution and median.

With our help to conduct the Wilcoxon test statistic, one can assign ranks to each value in the two groups being compared. The rank sums are then obtained for each column(group) for comparison. We compare the sum of the ranks to table values to determine the availability and the magnitude of a significant difference between the two groups. The test can be calculated using statistical software packages such as the R and the SPSS.

2. Assumptions of the Wilcoxon test statistic

The assumptions and requirements that a data set should be compliant with are dependent on the type of Wilcoxon test that is to be conducted. We, therefore, classify the assumptions based on the test statistic type required as demonstrated below.

a). Assumptions for Wilcoxon signed-rank test

The signed-rank test requires that the data complies with the following requirements to produce valid results in analysis. The assumptions are related to the study design, type of variables, and the nature of the data being analyzed. They include:

• The dependent variable must be measured on a continuous or an ordinal scale.
• The independent variable should comprise two categorical matched pairs or related groups.
• The symmetrical shape should exist in the distribution of differences between the two related groups.
• The data set is a simple random sample drawn from the population.

These requirements must be complied with if the data should produce valid results that are statistically significant after conducting the Wilcoxon signed-rank test statistic.

b). Assumptions for Wilcoxon rank-sum test

The basic assumptions for the Wilcoxon rank-sum test are that:

• The observations from the two groups being compared are independent of each other.
• The responses are at least ordinal.
• The distributions for both populations are the same under the null hypothesis.
• The distributions are not equal under the alternative hypothesis.
• The sample comprises paired data.

The requirements and assumptions must be complied with for the test to produce valid results. Clients who purchase the services of a statistician for a Wilcoxon test statistic from us are assured that their data will be evaluated for compliance with the requirements before conducting the test. We assess the alignment of the data type, variables, and research design with the Wilcoxon test statistics and act accordingly.

3. Effect size

The Wilcoxon effect size can be calculated for the one-sample test, two samples/paired samples test, and the independent-samples tests. The value for the effect size can be obtained by dividing the standardized distribution test statistic by the square root of the sample size. The effect size ranges from zero to close to one. Effect sizes between 0.10 and 0.30 are said to be small, 0.30 to 0.50 moderate, and these above 0.50 large.

4. Statistical significance of Wilcoxon test statistic results

There are different ways to find out whether the test statistics results are statistically significant or not. How to determine the statistical significance of the results is influenced by the sample size and the type of test conducted as explained below. The standard normal probabilities table can be used for large sample sizes.

a). For two-sided test

In two-sided tests, we determine whether the standardized test statistic observed in a sample is as extreme as the critical value or find the two-sided p-value that corresponds to the observed value and confirm if it is smaller than or equal to the alpha significance value.

b). Right-sided test

The statistical significance of a right-sided test statistic can be determined by checking if the standardized test statistic observed in the sample is larger than the critical value or by finding the right-sided p-value that corresponds to the observed standardized test statistic and confirming whether it is equal to or smaller than the alpha significance value.

c). Left-sided test

We determine whether the standardized test statistic observed in a sample is smaller than or equal to the critical value or the left-sided p-value corresponding to the observed standardized test statistic and check if it is smaller than or equal to the alpha significance value. The null hypothesis in the one-sample Wilcoxon signed-rank test is that the population median is equal to the hypothesized median.

Carefully considering these factors enables us to effectively help to conduct a Wilcoxon test statistic on a specific data set under the requirements and assumptions of each type of test. The nature of the data, type of variables, and the study designs affect the choice of Wilcoxon test statistic for the particular data. We assist researchers and students pursuing studies with repeated measures or matched pairs designs where the data collected can be measured on an ordinal scale. Our services are affordable and readily available on a 24/7 basis. Those wishing to hire a statistician for a Wilcoxon test statistic can place their orders with us for the best and most systematic process that assures them of valid results. The Wilcoxon test statistic calculated by experts in our company is credible and professionally proven across fields globally.