g08akf

Purpose

Synopsis

[p,ifail] = g08akf(n1,n2,ranks,u<,tail,ifail>)

Description

 
 G08AKF computes the exact tail probability for the Mann-Whitney U
 test statistic (calculated by G08AHF and returned through the 
 parameter U), for the case where there are ties in the pooled 
 sample.
 
 The Mann-Whitney U test investigates the difference between two 
 populations defined by the distribution functions F(x) and G(y) 
 respectively. The data consist of two independent samples of size
 n  and n , denoted by x ,x ,...,x   and y ,y ,...,y  , taken from
  1      2              1  2      n       1  2      n          
                                   1                 2        
 the two populations.
 
 The hypothesis under test, H , often called the null hypothesis, 
                             0                                   
 is that the two distributions are the same, that is F(x)=G(x), 
 and this is to be tested against an alternative hypothesis H  
                                                             1
 which is
 
      H  : F(x)/=G(y); or
       1               
 
      H  : F(x)>G(y); or
       1              
 
      H  : F(x)<G(y),
       1            
 
 using a two-tailed, upper-tailed or lower-tailed probability 
 respectively. The user selects the alternative hypothesis by 
 choosing the appropriate tail probability to be computed.
 
 Note that when using this test to test for differences in the 
 distributions one is primarily detecting differences in the 
 location of the two distributions. That is to say, if we reject 
 the null hypothesis H in favour of the alternative hypothesis H :
                      0                                         1
 F(x)<G(y) we have evidence to suggest that the location, of the
 distribution defined by F(x), is less than the location, of the 
 distribution defined by G(y).
 
 G08AKF returns the exact tail probability, p, corresponding to U,
 depending on the choice of alternative hypothesis, H .
                                                     1
 
 The value of p can be used to perform a significance test on the 
 null hypothesis H  against the alternative hypothesis H . Let 
                  0                                     1     
 (alpha) be the size of the significance test (that is (alpha) is 
 the probability of rejecting H  when H  is true). If p<(alpha) 
                               0       0                       
 then the null hypothesis is rejected. Typically (alpha) might be 
 0.05 or 0.01.
 

Parameters

g08akf

Required Input Arguments:

n1                                    integer
n2                                    integer
ranks (n1+n2)                         real
u                                     real

Optional Input Arguments:                       <Default>

tail (1)                              string   't'
ifail                                 integer  -1

Output Arguments:

p                                     real
ifail                                 integer