
PARTIAL KENDALLS TAU CORRELATIONName:
\( \frac{Y_j  Y_i}{X_j  X_i} \) < 0  pair is discordant \( \frac{Y_j  Y_i}{X_j  X_i} \) = 0  pair is considered a tie X_{i} = X_{j}  pair is not compared Kendall's tau is computed as
with N_{c} and N_{d} denoting the number of concordant pairs and the number of discordant pairs, respectively, in the sample. Ties add 0.5 to both the concordant and discordant counts. There are \( \left( \begin{array}{c} n \\ 2 \end{array} \right) \) possible pairs in the bivariate sample. A perfect linear relationship between the ranks yields a Kendall's tau 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 Kendall's tau correlation is the Kendall's tau 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 Kendall's tau correlation can be computed based on standard Kendall's tau correlations between the three variables as follows:
with \( \tau_{xy} \) denoting the Kendall's tau correlation between x and y. As with the standard Kendall's tau 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 Kendall's tau 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 Kendall's tau correlation absolute value is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax computes the absolute value of the partial Kendall's tau 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 KENDALLS TAU CORRELATION Y1 Y2 Z SUBSET TAG > 2 LET A = PARTIAL KENDALLS TAU 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 kendall tau correlation m1 m2 m3 let c2 = partial kendall tau correlation absolute value m1 m2 m3 print c1 c2The following output is generated. PARAMETERS AND CONSTANTS C1  0.4610 C2  0.4610  
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Date created: 12/19/2012 