Manuals/calci/WILCOXONSIGNEDRANKTEST

WILCOXONSIGNEDRANKTEST(xRange,yRange,Confidencelevel,Logicalvalue)


  • is the array of x values.
  • is the array of y values.
  • is the value between 0 and 1.
  • is either TRUE or FALSE.

Description

  • This function gives the summary values of Wilcoxon signed rank test.
  • This test is the one of the Non Parametric test.
  • Nonparametric test is also called Distribution Free Test.
  • So Wilcoxon Rank test is not depending on the parameters.
  • This test is designed to test a hypothesis about the median of a population distribution.
  • It often involves the use of matched pairs, for example, before and after data, in which case it tests for a median difference of zero.
  • Also this test does not require the assumption that the population is normally distributed.
  • This test is the alternative of the Student's T-test.
  • Normally this test is the version of the dependent samples t-test that can be performed on the ranked data.
  • i.e., When the requirements for the t-test for two paired samples are not satisfied, the Wilcoxon Signed-Rank Test for Paired Samples non-parametric test can often be used.
  • It is a more powerful alternative to the sign test, but does assume that the population probability distribution is symmetric.
  • For this test let us consider the n subjects from the population with two observations   and  .
  • The requirements for the Wilcoxon Signed-Rank Tests for Paired Samples where Failed to parse (syntax error): {\displaystyle z_i = y_i–x_i} for all i = 1, … ,n, are as follows:
     1.the   are independent. 
     2.  and   are interval data. 
  • This test containing the following steps:
  • 1.Define Null and Alternative hypothesis:
    • Null hypothesis   = There is no difference between the two observations.
    • Alternative hypothesis   = There is a difference between the two observations.
  • 2.State alpha(Confidence level): alpha value is from 0 to 1.
  • 3.State Decision Rule: Fix the hypothesis value according to the z table.
  • 4.Calculate Test Statistic: 

where T is the smallest rank value and n is the number of observations.

  • 5.State Result: In this step we have to take a decision of null hypothesis either accept or reject depending on the z value.
  • 6.State Conclusion: How far the value of the test before and after the grouping.
  • The Wilcoxon signed Rank test result is contains the following values in the table:Difference of the ach observation, Absolute value of the difference,Rank value,Signed Rank and the test value.

Examples

Spreadsheet
A B
1 15 18
2 20 26
3 29 32
4 30 28
5 19 16

=WILCOXONSIGNEDRANKTEST(A1:A5,B1:B5,0.05,TRUE)