Wilcoxon Signed-Rank Test for One Sample

This method is an alternative to a one-sample t-test when the data cannot be assumed to be normally distributed. This method is based on the ranks of observations rather than on their actual values

1. Functionalities

  • To determine if the median/location of the population from which your data is drawn statistically significantly different from the specified median
  • To know the basic descriptive statistics about your data
  • To know the descriptive statistics plot such as box-plot, distribution histogram, and density distribution plot about your data

2. About your data

  • Your data contain only 1 group of values (or 1 numeric vector)
  • Your data are meaningful to measure the distance from the specified median
  • The values are independent observations
  • No assumption on the distributional shape of your data, which means your data may be not normally distributed

Case Example

Suppose we collected the Depression Rating Scale (DRS) measurements of 9 patients from a particular group of patients. DRS Scale > 1 indicated Depression. We wanted to know if the DRS of patients was significantly greater than 1.

Please follow the Steps, and Outputs will give real-time analytical results.

Output 1. Descriptive Results




Explanations
  • The band inside the box is the median
  • The box measures the difference between 75th and 25th percentiles
  • Outliers will be in red, if existing


Explanations
  • Histogram: to roughly assess the probability distribution of a given variable by depicting the frequencies of observations occurring in certain ranges of values
  • Density Plot: to estimate the probability density function of the data

Histogram

When the number of bins is 0, plot will use the default number of bins

Density plot

Output 2. Test Results

Results of the Wilcoxon Signed-Rank Test


Explanations
  • P Value < 0.05, then the population median is significantly different from the specified median. (Accept the alternative hypothesis)
  • P Value >= 0.05, then the population median is NOT significantly different from the specified median. (Accept the null hypothesis)

From the default settings, we concluded that the scales were significantly greater than 1 (P = 0.006), which indicated the patients were suffering from Depression.

Wilcoxon Rank-Sum Test (Mann–Whitney U test) for Two Independent Samples

This method is an alternative to two-sample t-test when the data cannot be assumed to be normally distributed

1. Functionalities

  • To determine if the medians of two population from which your 2 groups data drawn are statistically significantly different from each other
  • To determine if the distributions of 2 groups of data differ in locations
  • To know the basic descriptive statistics about your data
  • To know the descriptive statistics plot such as box-plot, distribution histogram, and density distribution plot about your data

2. About your data

  • Your data contain only 2 groups of values (or 2 numeric vectors)
  • Your data are meaningful to measure the distance between 2 groups values
  • The values are independent observations
  • No assumption on the distributional shape of your data
  • Your data may be not normally distributed

Case Example

Suppose we collected the Depression Rating Scale (DRS) measurements of 19 patients from a particular group of patients. Among 19 people, 9 were women, and 10 were men. We wanted to know if the DRS of patients was significantly different among different genders; or, whether age was related to DRS scores.

Please follow the Steps, and Outputs will give real-time analytical results.

Output 1. Descriptive Results




Notes:
  • The band inside the box is the median
  • The box measures the difference between 75th and 25th percentiles
  • Outliers will be in red, if existing


Notes:
  • Histogram: to roughly assess the probability distribution of a given variable by depicting the frequencies of observations occurring in certain ranges of values
  • Density Plot: to estimate the probability density function of the data

Histogram

When the number of bins is 0, plot will use the default number of bins

Density plot

Output 2. Test Results

Results of Wilcoxon Rank-Sum Test



Explanations
  • P Value < 0.05, then the population medians of 2 groups are significantly different. (Accept alternative hypothesis)
  • P Value >= 0.05, no significant differences between the medians of 2 groups. (Accept null hypothesis)

From the default settings, we concluded that there was no significant differences in 2 groups Rating scale (P=0.44).

Wilcoxon Signed-Rank Test for Two Paired Samples

In the paired case, we compare the differences between 2 groups to zero. Thus, it becomes a one-sample test problem.

This method is an alternative to paired-sample t-test when the data cannot be assumed to be normally distributed.

1. Functionalities

  • To determine if the difference of paired data is statistically significantly different from 0
  • To know the basic descriptive statistics about your data
  • To know the descriptive statistics plot such as box-plot, distribution histogram, and density distribution plot about your data

2. About your data

  • Your data contain 2 groups of values (or 2 numeric vectors)
  • Your data are meaningful to measure the distance from the specified median
  • The values are paired or matched observations
  • No assumption on the distributional shape of your data
  • Your data may be not normally distributed

3. Examples for Matched or Paired Data

  • One person's pre-test and post-test scores
  • When two samples have been matched or paired

Case Example

We wanted to know if the DRS of patients before and after were significant; or, whether the differences were significantly different from 0, which could indicate if the treatment was effective.

Please follow the Steps, and Outputs will give real-time analytical results.

Output 1. Descriptive Results 





                    

                    Notes:
          
    
            
  •  The band inside the box is the median
    • 
            
  •  The box measures the difference between 75th and 25th percentiles
    • 
            
  •  Outliers will be in red, if existing
    • 
          

                  

                  

                    

                      

                    

                    Notes:
          
    
            
  •  Histogram: to roughly assess the probability distribution of a given variable by depicting the frequencies of observations occurring in certain ranges of values
    • 
            
  •  Density Plot: to estimate the probability density function of the data
    • 
          

                    

                      Histogram
                    

                    

                    

                      
                      
                    

                    
When the number of bins is 0, plot will use the default number of bins

                    

                      Density plot
                    

                    

                  

                

              

              

              

                Output 2. Test Results
              

              

                

              

              Results of Wilcoxon Signed-Rank Test
              

               Explanations 
    
    
    
  •  P Value < 0.05, then the Before and After are significantly different. (Accept the alternative hypothesis)
    • 
    
  •  P Value >= 0.05, then the Before and After are NOT significantly different. (Accept the null hypothesis)
    • 
    

              

                

                  From the default settings, we concluded that there was no significant difference after the treatment. (P=0.46)