
PARTIAL RANK CORRELATIONName:
where D_{i} is the difference between the ranks assigned to the corresponding pairs and N is the sample size. Ties are assigned average ranks. A perfect linear relationship between the ranks yields a rank correlation coefficient of +1 (or 1 for a negative relationship) and no linear relationship between the ranks yields a rank correlation coefficient of 0. Partial rank correlation is the correlation between two variables after removing the effect of one or more additional variables. This command is specifcally for the the case of one additional variable. In this case, the partial rank correlation can be computed based on standard rank correlations between the three variables as follows:
with r_{xy} denoting the correlation between x and y. As with the standard rank correlation coefficient, a value of +1 indicates a perfect positive linear relationship, a value of 1 indicates a perfect negative linear relationship, and a value of 0 indicates no linear relationship.
<SUBSET/EXCEPT/FOR qualification> where <y1> is the first response variable; <y2> is the second response variable; <y3> is the third response variable; <par> is a parameter where the computed partial rank correlation is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
<SUBSET/EXCEPT/FOR qualification> where <y1> is the first response variable; <y2> is the second response variable; <y3> is the third response variable; <par> is a parameter where the computed partial rank correlation absolute value is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax computes the absolute value of the partial rank correlation coefficient. This is typically used in screening applications where there is an interest in identifying high magnitude correlations regardless of the direction of the correlation.
LET A = PARTIAL RANK CORRELATION Y1 Y2 Z SUBSET TAG > 2 LET A = PARTIAL RANK CORRELATION ABSOLUTE VALUE Y1 Y2 Z
Peavy, Bremer, Varner, Hogben (1986), "OMNITAB 80: An Interpretive System for Statistical and Numerical Data Analysis," NBS Special Publication 701.
. This data is from page 202 of . . Peavy, Bremer, Varner, Hogben (1986), "OMNITAB 80: . An Interpretive System for Statistical and Numerical . Data Analysis," NBS Special Publication 701. . . Original source of the data is from . Draper and Smith (1981), "Applied Regression Analysis", . Wiley, p. 373. . dimension 40 columns . read matrix m 42.2 11.2 31.9 167.1 48.6 10.6 13.2 174.4 42.6 10.6 28.7 160.8 39.0 10.4 26.1 162.0 34.7 9.3 30.1 140.8 44.5 10.8 8.5 174.6 39.1 10.7 24.3 163.7 40.1 10.0 18.6 174.5 45.9 12.0 20.4 185.7 end of data . set write decimals 4 let c1 = partial rank correlation m1 m2 m3 let c2 = partial rank correlation absolute value m1 m2 m3 print c1 c2The following output is generated: PARAMETERS AND CONSTANTS C1  0.6603 C2  0.6603  
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Date created: 12/19/2012 