g08aaf

Purpose

Synopsis

[is,n1,p,ifail] = g08aaf(x,y<,ifail>)

Description

 
 The Sign test investigates the median difference between pairs of
 scores from two matched samples of size n, denoted by {x ,y }, 
                                                         i  i  
 for i=1,2,...,n. The hypothesis under test, H , often called the 
                                              0                  
 null hypothesis, is that the medians are the same, and this is to
 be tested against a one- or two-sided alternative H  (see below).
                                                    1            
 
 G08AAF computes:
 
 (a)   The test statistic S, which is the number of pairs for 
       which x <y ;
              i  i
 
 (b)   The number n  of non-tied pairs (x /=y );
                   1                     i   i 
 
 (c)   The lower tail probability p corresponding to S (adjusted 
       to allow the complement (1-p) to be used in an upper 1-
       tailed or a 2-tailed test). p is the probability of 
                                    1                            
       observing a value <= S if S< -n ; or of observing a value <
                                    2 1                          
               1                                 1               
       S if S> -n , given that H  is true. If S= -n , p is set to 
               2 1              0                2 1             
       0.5.
 
 Suppose that a significance test of a chosen size (alpha) is to 
 be performed (i.e., (alpha) is the probability of rejecting H  
                                                              0
 when H  is true; typically (alpha) is a small quantity such as 0.
       0                                                        
 05 or 0.01). The returned value of p can be used to perform a 
 significance test on the median difference, against various 
 alternative hypotheses H , as follows:
                         1     
 
 (i)   H : median of x /= median of y. H  is rejected if 
        1                               0               
       2*min(p,1-p)<(alpha).
 
 (ii)  H : median of x> median of y. H  is rejected if p<(alpha).
        1                             0                         
 
 (iii) H : median of x< median of y. H  is rejected if 1-p<(alpha)
        1                             0                
 

Parameters

g08aaf

Required Input Arguments:

x (:)                                 real
y (:)                                 real

Optional Input Arguments:                       <Default>

ifail                                 integer  -1

Output Arguments:

is                                    integer
n1                                    integer
p                                     real
ifail                                 integer