Non-parametric test for trend across ordered groups               (STB-9: snp4)
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   ^nptrend^ varlist [^if^ exp] [^in^ range]^, by(^groupvar) [^tr^end^(^scorevar^)^]


Description
-----------
   
^nptrend^ performs a non-parametric test for trend across ordered groups.  This
test, developed by Cuzick (1985), is an extension of the Wilcoxon rank-sum test
and is a useful adjunct to the Kruskal-Wallis test (see ^help kwallis^).  Formula
for the test statistic is given by Cuzick(1985) and Altman(1991).  Correction
for ties is incorporated into the formula. 

^groupvar^ is a grouping variable, and ^scorevar^ defines scores for groups. When
^trend(scorevar)^ is not specified, the values of the variable ^groupvar^ are
used as the scores.  




Example
-------

Consider the following data (Altman 1991):


Group    Transmission of     Ocular exposure to ultraviolet radiation
         visible light       
-----------------------------------------------------------------------
  1       < 25%              1.4 1.4 1.4 1.6 2.3 2.3
  2       25 to 35%          0.9 1.0 1.1 1.1 1.2 1.2 1.5 1.9 2.2 2.6 2.6 
                             2.6 2.8 2.8 3.2 3.5 4.3 5.1
  3       > 35%              0.8 1.7 1.7 1.7 3.4 7.1 8.9 13.5
-------------------------------------------------------------------------


We can use ^nptrend^ to test for a trend of increasing exposure across the three
groups. When we do not specify scores for groups, they are defined by the
grouping variable ^group^:





Example, continued
------------------

	. ^nptrend exp, by(group)^

	Test: Trend across groups

	       gr     _Score        _Obs   _RankSum  
	        1          1           6      76.00  
	        2          2          18     290.00  
	        3          3           8     162.00  

	          z =     1.519
	probability =     0.1288


When the groups are given any equally spaced scores, such as -1 0 1, we obtain
the same answer as above. To illustrate the effect of changing scores, an
analysis of these data with scores 1, 2, 5 (admittedly not very sensible in
this case) gives:




Example, concluded
------------------


	. ^nptrend exp, by(group) tr(score)^

	Test: Trend across groups

	    group     _Score        _Obs   _RankSum  
	        1          1           6      76.00  
	        2          2          18     290.00  
	        3          5           8     162.00  

	          z =     1.464
	probability =     0.1432


This example suggests that the analysis is not all that sensitive to the 
scores chosen.





References
----------

Altman, D. G. 1991.  ^Practical Statistics for Medical Research^.  
      London: Chapman and Hall, 215-217.

Cuzick, J. 1985.  A Wilcoxon-type test for trend.  ^Statistics in^
   ^Medicine^ 4: 87-90.


Authors
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K. A. Stepniewska and D. G. Altman, Imperial Cancer Research Fund, London. 
     EMAIL k_stpniewska@@icrf.ac.uk