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Dataplot Vol 1 Auxiliary Chapter

KENDELLS TAU

Name:
    KENDELLS TAU (LET)
Type:
    Let Subcommand
Purpose:
    Compute Kendell's tau coefficient between two paired variables.
Description:
    Kendell's tau coefficient is a measure of concordance between two paired variables. Given the pairs (Xi,Yi) and (Xj,Yj), then

      (Y(j) - Y(i))/(X(j) - X(i)) > 0 - pair is concordant

      (Y(j) - Y(i))/(X(j) - X(i)) < 0 - pair is discordant

      (Y(j) - Y(i))/(X(j) - X(i)) = 0 - pair is considered a tie

      Xi = Xj - pair is not compared

    Kendell's tau is computed as

      tau = (Nc - Nd)/(Nc + Nd)

    with Nc and Nd 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 (n 2) possible pairs in the bivariate sample.

    Kendell's tau is an alternative to the Spearman's rho rank correlation.

    Kendell's tau or the rank correlation may be preferred to the standard correlation coefficient in the following cases:

    1. When the underlying data does not have a meaningful numerical measure, but it can be ranked;

    2. When the relationship between the two variables is not linear;

    3. When the normality assumption for two variables is not valid.
Syntax:
    LET <par> = KENDELLS TAU <y1> <y2>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y1> is the first response variable;
                <y2> is the second response variable;
                <par> is a parameter where the computed Kendell's tau is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = KENDELLS TAU Y1 Y2
    LET A = KENDELLS TAU Y1 Y2 SUBSET TAG > 2
Note:
    The two variables must have the same number of elements.
Note:
    Support for the Kendell's tau statistic has been added to the following plots and commands:

      KENDELLS TAU PLOT Y1 Y2 X
      CROSS TABULATE KENDELLS TAU PLOT Y1 Y2 X
      BOOTSTRAP KENDELLS TAU PLOT Y1 Y2
      JACKNIFE KENDELLS TAU PLOT Y1 Y2
      KENDELLS TAU INTERACTION PLOT Y1 Y2 X1 ... XK
      DEX ... KENDELLS TAU PLOT Y1 Y2 X1 ... XK

      TABULATE KENDELLS TAU Y1 Y2 X
      CROSS TABULATE KENDELLS TAU Y1 Y2 X1 X2

Default:
    None
Synonyms:
    None
Related Commands:
    CORRELATION (LET) = Compute the Pearson correlation coefficient between two variables.
    RANK CORRELATION (LET) = Compute the Spearman's rho correlation coefficient between two variables.
    STATISTIC PLOT = Generate a statistic versus index plot.
    BOOTSTRAP PLOT = Generate a bootstrap plot for a statistic.
    TABULATE = Compute a statistic for one group variable.
    CROSS TABULATE = Compute a statistic for two group variables.
Applications:
    Exploratory Data Analysis
Implementation Date:
    10/2004
Program: 
     
    . Following data from page 320 of Conover, "Practical
    . Nonparametric Statistics", Third Edition, 1999, Wiley.
    LET Y1 = DATA 7 8 4 5.5 4.5 4 5 3 2 0.5 1
    LET Y2 = DATA 4 2 5 0.5 1.5 2 0 1 0 1.5 0
    LET A1 = KENDELLS TAU Y1 Y2

    The computed value of Kendell's tau is 0.4355.

    Date created: 12/22/2004
    Last updated: 12/22/2004
    Please email comments on this WWW page to alan.heckert@nist.gov.