Signed-Rank Test

The signed-rank test is also known as the Wilcoxon signed-rank test which is a nonparametric test, equivalent to the student’s paired t-test, analyzing whether there is a difference between pairs which are not normally distributed. There are many similarities between this test and the Mann-Whitney U test. The way ranking is computed in the Mann-Whitney U test is identical to how it is done in the Wilcoxon singed-rank test. However, in a Wilcoxon signed-rank test, absolute values are ranked because sign does not have an influence on the ranking procedure.

A Wilcoxon signed-rank test requires there to be two nominal data sets which correspond to one categorical variable. In this type of statistical test, the scores come from the same participants. In the Wilcoxon signed-rank test, it is the difference between the pairs which is being tested. So for instance the subjects analyzed may be exposed to a before and after treatment.

For example, a researcher may have wanted to record the weights of 12 individuals before they started a diet and then again, after being on the same diet for 2 months. In this case the sample size is 12.

1. The first step involves writing the null and alternative hypotheses.

Ho = There is no difference in the participant's weight before and after the diet.

Ha = The mean weight before the diet is greater than the mean weight after the diet.

2. Next it is necessary to determine the critical value (Tcritical) using a Critical Value Table. So in this case:

n (sample size) = 12
chosen significance level of 0.05

After looking at a Critical Value Table¹ the Tcritical value = 13

3. Now it is necessary to draw a table which allows for the calculation of Rank D and Sign Rank D. The ranking system is the same as that used for the Mann-Whitney U test. As well, the paired difference and absolute difference between the before and after treatments need to be calculated first so that the ranking can be completed.

Table 1. This table provided illustrates the necessary calculations for the Wilcoxon signed-rank test. The "Absolute Difference" column requires the computation of the absolute difference, meaning that the value cannot be negative. However, if a paired difference is negative, the negative sign reappears in the "Sign Rank D" column.

4. The calculation of W (which is the sum of all sign rank D values) is the next step. This value gets compared to the Tcritical value.

W = 73

The test statistic (W) is greater than the critical value of 10 and so we reject the null hypothesis.

References:

1. Zaiontz, C. (2013). Wilcoxon Signed-Ranks Table. Retrieved from: http://www.real-statistics.com/statistics-tables/wilcoxon-signed-ranks-table/

BrainMass Solutions Available for Instant Download

Signed-Rank Test

A company is evaluating the impact of a wellness program offered on-site as a means of reducing employee sick days. A total of 8 employees agree to participate in the evaluation which lasts 12 weeks. Their sick days in the 12 months prior to the start of the wellness program and again over the 12 months after the completion of

Wilcoxon Rank Test: Occupation and Wage

I need to Perform the five-step hypothesis test on the data. Explain which nonparametric test you used to analyze your data and why you chose that test. I came up with this Use a Wilcoxon signed-rank test H0: M1= M2 (No difference in the mean salaries in manager and clerical positions) H1: M1 not equal to M2 (Salaries di

Wilcoxon Signed Rank Test: Job Satisfaction Survey

See attached data set. Using AIU's survey responses from the AIU data set, complete the following requirements in the form of a report: Perform a two-tailed hypothesis test on both the intrinsic and the extrinsic variable's data, using a .05 significance level. Begin by creating a null and an alternate statement. Use Microsof

Wilcoxon Signed-Rank Test and Kruskal-Wallis Test

a) What is the purpose of a Wilcoxon signed-rank test? Explain. b) The Wilcoxon signed-rank test resembles which parametric test(s)? Explain. c) What is the purpose of a Kruskal-Wallis test? Explain. d) The Kruskal-Wallis test is analogous to which parametric test? Explain.

Wilcoxon: Hypothesis Testing and Finding P-Values

Use the Wilcoxon signed-rank test to perform the required hypothesis test. 1) In 1995, the median age of the residents of one city was 36 years. A random sample taken this year of 10 residents of the town yielded the following ages in years. 5 28 37 49 30 68 11 58 40 34 At the 0.05 significance level, do the data provi

Using: The Wilcoxon Signed Rank Test

Use the following data set for parts A& B (units unimportant). Treatment Group 1 Treatment Group 2 92 102 90 89 92 96 85 80 89 92 97 77 88 101 86 87 85 102 78 76 A. Perform the sign test to analyze the difference in the matched pairs. It is not important what the numbers mean. B. Perform the Wilcoxon signed-r

Nonparametric methods: analysis of ranked data

Problem 16- 3 3. Determine the absolute differences for the values computed in column 4. Recall that in an absolute difference we ignore the sign of the difference. The absolute differences are shown in column 5. TABLE 16-3 Flavor Rating for Current and Spicy Flavors (1) (2) (3) (4) (5) (6)

Non-parametric Methods

--- 1. Complete the following exercises using Non-parametric Methods: a. Exercise 1-Sign Test Are stock splits beneficial to stockholders? SNL Securities studied stock splits in the banking industry over an 18-month period and found that stock splits tended to increase the value of an individual's stock holding. Assume that o

Wilcoxon-Signed rank test

The 1997 price/earnings ratios for a sample of 12 stocks are shown in the following list ( Barron's, December 8, 1997). Assume that a financial analyst has provided the estimated price/earnings ratio for 1998. Using a .05 level of significance, what is your conclusion about the differences between the price/earnings ratios for

The Wilcoxon Signed Rank Test

Explain Wilcoxon signed rank test, its application and how you would set up equations in this test?

Statistic sign test & Wilcoxon signed-rank test

Use the following data set for parts A& B Treatment Group 1 Treatment Group 2 97 96 88 86 75 79 90 89 85 91 94 89 77

Wilcoxon

Wilcoxon-Signed Rank Test The 1997 price/earnings ratios for a sample of 12 stocks are shown in the following list ( Barron's, December 8, 1997). Assume that a financial analyst has provided the estimated price/earnings ratio for 1998. Using a .05 level of significance, what is your conclusion about the differences between the

Hypothesis Testing: Considering the Wilcoxon Test

It has been suggested that daily production of a subassembly would be increased if better portable lighting were installed and background music and free coffee and doughnuts were provided during the day. Management agreed to try the scheme for a limited time. The number of subassemblies produced per week by a sample of employee