Help to Conduct a Rank-Sum Test

To test the null hypothesis that two population distributions are equal when the data set comprises independent samples from such populations, one may require professional help to conduct a rank-sum test statistic. We reject the null hypothesis if the value of the test statistic is significantly greater or less than the alpha statistical significance value. If the null hypothesis is true, the test statistic will have an approximately normal distribution with the mean and variance. In the normal approximation to the rank-sum test, the null hypothesis can be rejected if the critical values obtained from the tables of probability distributions are less than the standardized test statistic(z).

The Mann Whitney test/Mann Whitney Wilcoxon test/Wilcoxon rank-sum test/Mann Whitney U test are some of the other names for the rank-sum test and can be used when determining whether two samples have the probability of being derived from the same population. In this article, we have outlined the various factors considered in the rank-sum test statistic calculation done by experts from our company.

Factors We Consider When Conducting a Rank Sum Test

The rank-sum test is used when evaluating the ranks of the combined scores from two independent groups. The rank-sum test statistic is based on the sum of the ranks for the observations drawn from one of the groups. The computational result of the rank-sum test statistic for large samples is mostly similar to that of the parametric t-test for two independent groups under comparison. After offering our clients help to conduct the rank-sum test statistic, we also assist them in evaluating the outcome against a critical value from the probability distribution table of standard values or computing a z-score to compare the ranks.

Anyone wishing to hire a statistician for a rank-sum test statistic can trust us with their orders. We deliver timely and high-quality data analysis services, not only by conducting the rank-sum test statistic but also by other statistical methods and procedures depending on the type of data presented by the clients. All the terms and instructions provided by the client or their receiving audiences and respective institutions are strictly complied with by our service delivery team. Discussed below are some of the factors we consider when conducting a rank-sum test statistic.

1. Assumptions of the rank-sum test

We conduct the rank-sum test statistic based on fundamental assumptions that the samples being compared are independent of each other and the two populations from which the samples were drawn have equal variance or spread. Being a nonparametric test, the rank-sum test does not assume a normal distribution of data, and thus, does not deal with parameters. The null hypothesis in the Wilcoxon Mann-Whitney test is that the populations have similar distributions with the same median. During hypothesis testing, we reject the null hypothesis if one of the distributions shifts to the left or right of the other; implying a significant difference between the medians of the two populations. The alternative hypothesis is that the distributions and, hence, the medians are not the same for the two populations.

2. Data types

The rank-sum test statistic, being the nonparametric alternative for the two samples t-test does not require normally distributed data to produce valid results. The Wilcoxon rank-sum test is the sum of the ranks for the observations of one of the two independent samples. The test statistic is used when the data types are ordinal rather than numerical such that, if we are given two data points, we can determine whether one of the data points is equal to, larger, or smaller than the other. Although there are no natural ways to assign numbers to the ordinal categories, those who purchase the services of a statistician for a rank-sum test statistic from us do not have to worry because our experts have all it takes to assign numbers to the data points and perform the test using the best of the statistical methods for valid results.

3. Research design

The research design corresponding to the rank-sum test is known as the parallel-groups design that is used in comparison situations such as the effectiveness of treatments in a clinical trial. The assumptions when conducting the test are a random sampling from each of the two populations being compared and that the measurements can be aligned on an ordinal scale.

4. Consistency of the hypothesis test

A hypothesis test is considered to be consistent if the probability of rejecting the null hypothesis (given that the null hypothesis is false) converges to one (1) as the sample size increases to infinity. Therefore, the probability of rejecting the null hypothesis gets larger with the increase in the sample size. We evaluate the consistency of the test by determining the relationship between sample sizes and the probability of rejecting the null hypothesis for the study.

5. Suitability of the Wilcoxon rank-sum test on the given data set

Every time a client presents data to be analyzed using statistical methods, it is our responsibility to evaluate the data for alignment with the test statistic that needs to be conducted. There are different situations and contexts when we can conduct the rank-sum test. These include:

• When comparing two groups of nonparametric interval and nonnormally distributed data measured within certain limits of a continuum.
• When there is no known variability in one of the groups under comparison.
• When there are outliers.
• When the sample sizes involved are so small that the central limit theorem may not be applicable.

The provided data set should meet the basic requirements to be feasible using the rank-sum test statistic. Before conducting the test, it is imperative to ascertain that it is the best option that can be used on the specific data type to generate valid results for the study.

6. The sample size

In research, especially in a clinical trial, the sample size is fundamental in determining the success and validity of an intervention/treatment. With our help to conduct a rank-sum test statistic, it is imperative to ascertain whether the sample sizes provided can achieve the desired power at given significance levels. If a study treatment for instance is actually different from the control group, the statistical difference can be detected at any significance level provided the sample size is sufficiently large. It is, therefore, imperative to justify the sample sizes for the groups being compared to be sure that they will truly reflect significant differences at given significance levels.

7. Different significance levels

The values are first arranged in ascending order with each number in the two groups being assigned a rank value. The ranks begin at the smallest value in either group. After ranking all the numbers, the rank-sum for each column/group is obtained. We must take into account all the ranks for each of the two independent groups being compared. The sum of the ranks is compared to the critical values read from tables of probability distributions to determine whether there is a significant difference between the groups. The upper and lower limits of the table depend on the probability level. Comparing the lowest rank sums to the table limit determines the degree of significant difference between the two groups under comparison. The p-value from the probability distribution table determines whether we accept or reject the null hypothesis.

8. The p-values from the tables

P-values are obtained from tables when the rank-sum test is conducted manually using a formula. The tables for Wilcoxon rank-sum test are provided for small samples. If the study involves large sample sizes, the tables are supplemented by using the normal approximation. If the two independent samples differ in size, the tables are set up for use with the rank sum of the smaller sample of the two. The Wilcoxon rank-sum produces a test statistic/Mann Whitney statistic which is converted into a p-value; the probability that the null hypothesis for both populations is similar is true. If the sample populations have significant differences, the p-value is equal to or less than 0.05.

9. Tied ranks

Sometimes ties occur between values in the data sets being analyzed. The data are organized in ascending order and an average rank is assigned to each observation in the tied ranks. We must, therefore, be keen when exploring the ranks to identify any ties and adjust accordingly for valid results.

The rank-sum test statistic calculation done by experts in our company is customized according to the needs of the client and the type of data/variables being analyzed. All the calculations can be conducted manually or using the relevant statistical software package. We are available at all times of the day and night, thus, one can contact us at any time of their convenience. We are readily available and accessible to respond to clients' queries, offer free consultations and unlimited revisions, and help the customer track work progress. Those who purchase the services of a statistician for a rank-sum test statistic from our company are always assured of excellent results, seamless work progress, timely service delivery, and high-quality care from our customer support team. All the data analysis needs using statistical methods and software can be sufficiently handled in our company.