Discuss the assumptions that must be made about the data in order to use the Wilcoxon.

- What is the rationale for the test statistics used in the Wilcoxon Signed-Rank test?

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1)**Discuss the assumptions that must be made about the data in order to use the Wilcoxon.**

The Wilcoxon Sign Test requires two repeated measurements on a commensurate scale, that is, that the values of both observations can be compared. If the variable is interval or ratio scale, the differences between both samples need to be ordered and ranked before conducting the Wilcoxon sign test (Park, 2015).

The Wilcoxon Sign test makes four important assumptions:

1. Dependent samples – the two samples need to be dependent observations of the cases. The Wilcoxon sign test assess for differences between a before and after measurement, while accounting for individual differences in the baseline.

2. Independence – The Wilcoxon sign test assumes independence, meaning that the paired observations are randomly and independently drawn.

3. Continuous dependent variable – Although the Wilcoxon signed rank test ranks the differences according to their size and is therefore a non-parametric test, it assumes that the measurements are continuous in theoretical nature. To account for the fact that in most cases the dependent variable is binominal distributed, a continuity correction is applied.

4. Ordinal level of measurement – The Wilcoxon sign test needs both dependent measurements to be at least of ordinal scale. This is necessary to ensure that the two values can be compared, and for each pair, it can be said if one value is greater, equal, or less than the other.

**What is the rationale for the test statistics used in the Wilcoxon Signed-Rank test?**

The Wilcoxon test is a nonparametric statistical test that compares two paired groups, and comes in two versions the Rank Sum test or the Signed Rank test. The goal of the test is to determine if two or more sets of pairs are different from one another in a statistically significant manner (Park, 2015).

Reference:

Park, H. I. (2015). A generalization of Wilcoxon rank sum test. Applied Mathematical Sciences, 9, 3155–3164. https://doi.org/10.12988/ams.2015.52129

2) Four important assumptions must be made about data to use the Wilcoxon Sign test; ordinal level of measurement, continuous dependent variable, independence, and dependent samples (Abid et al., 2018). In the dependent samples assumption, the Wilcoxon Sign test requires that the two samples are dependent on each other to evaluate variances amid before and after measurement while considering for particular variances in the reference line. The Wilcoxon Sign test presumes individuality in the independence assumption, denoting that the two observations are independently and randomly attained.

In the continuous dependent variable assumption, the Wilcoxon sign test assumes that the measurements are continually theoretical to rank the variances concerning their size (Hayes, 2020). A continuity correlation is used to justify the detail that the dependent variable is distributed binomially in most scenarios. In the ordinal level of measurement assumption, the Wilcoxon Sign test presumes that the two dependent measures are at the slightest ordinal scale. The assumption is essential to certify that both values can be likened and that each pair can be said to be less or greater than the other.

The Wilcoxon Signed-Rank test is a nonparametric statistical test, and it is used to test the null hypothesis that the continuous distribution of two populations is alike. The test fundamentally calculates the variance between pair sets and evaluates the variances to determine if they are statistically significantly diverse from each other. According to King & Eckersley (2019), the straightforward idea supporting the Wilcoxon signed-rank test is to create a null and alternate hypothesis, decide a confidence degree, compute the statistic test, and equate a critical value to the test statistic. If the determined test statistic is barely as much as the critical value, then the null hypothesis gets rejected.

**References**

Abid, M., Nazir, H. Z., Tahir, M., & Riaz, M. (2018). On designing a new cumulative sum, Wilcoxon signed-rank chart for monitoring process location. PLOS ONE, 13(4), e0195762. https://doi.org/10.1371/JOURNAL.PONE.0195762

Hayes, A. (2020, April 13). Wilcoxon Test Definition. https://www.investopedia.com/terms/w/wilcoxon-test…

King, A., & Eckersley, R. (2019). Statistics for Biomedical Engineers and Scientists. In Statistics for Biomedical Engineers and Scientists. Elsevier. https://doi.org/10.1016/C2018-0-02241-0

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