
COX STUART TESTName:
Given a set of ordered observations X_{1}, X_{2}, ..., X_{n}, let
c = n/2 if n even = (n+1)/2 if n odd Then pair the data as X_{1},X_{1+c}, X_{2},X_{2+c}, ..., X_{nc},X_{n}. The CoxStuart test is then simply a sign test applied to these paired data. Syntax 1:
<SUBSET/EXCEPT/FOR qualification> where <LOWER TAILED/UPPER TAILED> is an optional keyword that specifies either a lower tailed or an upper tailed test; <y> is a response variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional. If neither LOWER TAILED or UPPER TAILED is specified, the Cox and Stuart test will return the results for the twotailed case, the lower tailed case, and the upper tailed case. If LOWER TAILED is specified, then only the results for the lower tailed case will be printed. If UPPER TAILED is specified, then only the results for the upper tailed case will be printed.
<SUBSET/EXCEPT/FOR qualification> where <LOWER TAILED/UPPER TAILED> is an optional keyword that specifies either a lower tailed or an upper tailed test; <y1> ... <yk> is a list of 1 to 30 response variables; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax will perform a CoxStuart test for each of the response variables. For example,
is equivalent to
COX STUART TEST Y2 COX STUART TEST Y3 COX STUART TEST Y4
COX STUART TEST Y1 Y2 Y3 COX STUART TEST Y1 TO Y5 LOWER TAILED COX STUART TEST Y UPPER TAILED COX STUART TEST Y
The paired data can also be analyzed using other techniques for comparing two response variables (e.g., ttest, bihistogram, quantilequantile plot).
. Purpose: Test the Cox Stuart Trend Test . Sample data from example 2 on page 171 of Conover. . let y = data 45.25 45.83 41.77 36.26 45.37 52.25 35.37 57.16 35.37 ... 58.32 41.05 33.72 45.73 37.90 41.72 36.07 49.83 36.24 ... 39.90 . set write decimals 4 cox stuart test yThe following output is generated. Cox Stuart Test for Trend (Compare Observations < Midpoint to Those > Midpoint) Response Variable: Y H0: There is No Trend Ha: There is a Trend Summary Statistics: Number of Observations 19 Number of Observations After Matching: 9 Summary Statistics for Points Below Midpoint: Sample Mean: 43.8477 Sample Median: 45.2500 Sample Standard Deviation: 7.5965 Sample Median Absolute Deviation 7.0000 Summary Statistics for Points Above Midpoint: Sample Mean: 40.2399 Sample Median: 39.8999 Sample Standard Deviation: 5.0799 Sample Median Absolute Deviation 3.6599 Test: Number of Positive Differences: 5 Number of Negative Differences: 4 Number of Ties: 0 CDF Value for Positive Values: 0.7460 CDF Value for Negative Values: 0.5000 PValue (2tailed test): 1.0000 PValue (lowertailed test): 0.7460 PValue (uppertailed test): 0.5000 TwoTailed Test H0: P(+) = P(); Ha: P(+) <> P()  Lower Upper Null Significance Test Critical Critical Hypothesis Level Statistic Value (<) Value (>) Conclusion  50.0% 5 3 6 ACCEPT 80.0% 5 3 6 ACCEPT 90.0% 5 2 7 ACCEPT 95.0% 5 2 7 ACCEPT 99.0% 5 1 8 ACCEPT 99.9% 5 0 9 ACCEPT  
Date created: 09/22/2011 Last updated: 12/11/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 