g08acf

Purpose

Synopsis

[i1,i2,p,ifail] = g08acf(x,n1<,ifail>)

Description

 
 The Median test investigates the difference between the medians 
 of two independent samples of sizes n  and n , denoted by:
                                      1      2          
 
            x ,x ,...,x 
             1  2      n 
                        1
 
 and
 
            x    ,x    ,...,x  , n=n +n .
             n +1  n +2      n      1  2
              1     1                   
 
 The hypothesis under test, H , often called the null hypothesis, 
                             0                                   
 is that the medians are the same, and this is to be tested 
 against the alternative hypothesis H  that they are different.
                                     1               
 
 The test proceeds by forming a 2*2 frequency table, giving the 
 number of scores in each sample above and below the median of the
 pooled sample:
 
                       Sample 1  Sample 2  Total
 
     Scores <= pooled  i         i         i +i 
     median             1         2         1  2
 
     Scores >= pooled  n -i      n -i      n-(i +i )
     median             1  1      2  2         1  2
 
     Total             n         n         n
                        1         2        
 
 Under the null hypothesis, H , we would expect about half of each
                             0                                
 group's scores to be above the pooled median and about half 
 below, that is we would expect i, to be about n /2 and i  to be 
                                                1        2      
 about n /2.
        2  
 
 G08ACF returns:
 
 (a)   The frequencies i  and i ;
                        1      2
 
 (b)   The probability, p, of observing a table at least as
       'extreme' as that actually observed, given that H  is true. 
                                                       0         
       If n<40, p is computed directly ('Fisher's exact test'); 
                        2                                   
       otherwise a (chi)  approximation is used (see G01AFF).
                        1                                   
 
 H  is rejected by a test of chosen size (alpha) if p<(alpha).
  0                                                          
 

Parameters

g08acf

Required Input Arguments:

x (:)                                 real
n1                                    integer

Optional Input Arguments:                       <Default>

ifail                                 integer  -1

Output Arguments:

i1                                    integer
i2                                    integer
p                                     real
ifail                                 integer