For n=.
Like the
ttest for correlated samples, the Wilcoxon signedranks test applies to twosample designs involving repeated measures, matched pairs, or "before" and "after" measures. Beginning with a set of paired values of X
_{a} and X
_{b}, this page will
 take the absolute difference X_{a}−X_{b} for each pair;
 omit from consideration those cases where X_{a}−X_{b}=0;
 rank the remaining absolute differences, from smallest to largest, employing tied ranks where appropriate;
 assign to each such rank a "+" sign when X_{a}−X_{b}>0 and a "−" sign when X_{a}−X_{b}<0;
 and then calculate the value of W for the Wilcoxon test, which in the present version of the procedure is equal to the sum of the signed ranks. The number of signed ranks, here designated as n_{s/r}, is equal to the number of X_{a}X_{b} pairs with which you begin minus the number of pairs for which X_{a}−X_{b}=0.
When
n_{s/r} is equal to or greater than 10, the sampling distribution of
W is a reasonably close approximation of the normal distribution. In this case, the present page calculates the appropriate
zratio along with the associated onetail and twotail probabilities. For smaller sample sizes (
n_{s/r} = 5 through 9), the obtained value of
W can be referred to the separate table of critical values of ±
W.
Procedure:
 Direct Entry into Data Cells:_{T}
Enter the values of X_{a} and X_{b} into the cells of the designated columns, beginning in the topmost cell of each column. After each entry, depressing the «tab» key will take you down to the next cell in the column. After all values of X_{a} and X_{b} have been entered in this fashion, scroll down to the button labeled «Calculate» and click it.
_{T}
 Importing Data via Copy & Paste:_{T}
When importing data from a spreadsheet, the paired values of X_{a} and X_{b} must be in the form of two adjacent columns. Within the spreadsheet application, select and copy the two columns of data for X_{a} and X_{b}. Then return to your web browser, click the cursor into the text area of the Import/Export Box and perform the 'Paste' operation from the 'Edit' menu. After pasting the data, make sure that the final entry is not followed by an extra blank line. To do this, click the cursor immediately to the right of the final entry in the list, then press the downarrow key. If an extra line is present, the cursor will move downward. Extra lines can be removed by pressing the downarrow key until the cursor no longer moves, and then pressing the 'Backspace' key (on a Mac platform, 'delete') until the cursor stands immediately to the right of the final entry. After this datacheck procedure has been performed, click the line labeled 'Import data to data cells', then click the «Calculate» button._{T}
 If you wish to perform another analysis with a different set of data: click the «Reload» button and enter the new value of n at the prompt.
Data Entry_{Q}
Critical Values of ±W for Small Samples_{Q}

Level of Significance for a 
Directional Test 
.05 
.025 
.01 
.005 
NonDirectional Test 
n_{s/r} 
 
.05 
.02 
.01 
5 
15 
 
 
 
6 
17 
21 
 
 
7 
22 
24 
28 
 
8 
26 
30 
34 
36

9 
29 
35 
39 
43 
Please note that these smallsample critical values pertain to the version of the Wilcoxon test in which the test statistic, W, is calculated as the sum of
all the signed ranks, positive and negative combined. Descriptions of this version of the Wilcoxon test can be found in Subchapter 12a of
Concepts and Applications of Inferential Statistics and in
Frederick Mosteller & Robert E. K. Rourke, Sturdy Statistics: Nonparametrics and Order Statistics, AddisonWesley, 1973, 89ff.
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