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Dataplot Vol 2 Vol 1

SPEARMAN DISSIMILARITY

Name:
    SPEARMAN DISSIMILARITY (LET)
Type:
    Let Subcommand
Purpose: Description:
    If the measurements in the two samples are replaced with their ranks (and average ranks in the case of ties) and the Pearson correlation coefficient is computed, the result is the Spearman rho correlation coefficient.

    The rank correlation is recommended 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.

    A perfect linear relationship yields a correlation coefficient of +1 (or -1 for a negative relationship) and no linear relationship yields a correlation coefficient of 0.

    In some applications, such as clustering, it can be useful to transform the correlation coefficient to a dissimilarity measure. The transformation used here is

      \( d = \frac{1 - r}{2} \)

    This converts the correlation coefficient with values between -1 and 1 to a score between 0 and 1. High positive correlation (i.e., very similar) results in a dissimilarity near 0 and high negative correlation (i.e., very dissimilar) results in a dissimilarity near 1.

    If a similarity score is preferred, you can use

      \( s = 1 - d \)

    where d is defined as above.

Syntax:
    LET <par> = SPEARMAN DISSIMILARITY <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 Spearman dissimilarity is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = SPEARMAN DISSIMILARITY Y1 Y2
    LET A = SPEARMAN DISSIMILARITY Y1 Y2 SUBSET TAG > 2
Note:
    The two variables must have the same number of elements.
Default:
    None
Synonyms:
    None
Related Commands: Reference:
    Kaufman and Rousseeuw (1990), "Finding Groups in Data: An Introduction To Cluster Analysis", Wiley.
Applications:
    Clustering
Implementation Date:
    2017/08:
Program 1:
     
    SKIP 25
    READ BERGER1.DAT Y X
    LET CORR = RANK CORRELATION Y X
    LET D    = SPEARMAN DISSIMILARITY Y X
    SET WRITE DECIMALS 4
    PRINT CORR D
        
    The following output is generated
     PARAMETERS AND CONSTANTS--
    
        CORR    --         0.9486
        D       --         0.0257
        
Program 2:
     
    SKIP 25
    READ IRIS.DAT Y1 Y2 Y3 Y4
    SET WRITE DECIMALS 3
    .
    LET M = GENERATE MATRIX SPEARMAN DISSIMILARITY Y1 Y2 Y3 Y4
    PRINT M
        
    The following output is generated
            MATRIX M       --            4 ROWS
                           --            4 COLUMNS
    
     VARIABLES--M1             M2             M3             M4      
    
              0.000          0.583          0.059          0.131
              0.583          0.000          0.655          0.506
              0.059          0.655         -0.000          0.084
              0.131          0.506          0.084         -0.000
        
Program 3:
     
    SKIP 25
    READ IRIS.DAT Y1 Y2 Y3 Y4 TAG
    .
    TITLE CASE ASIS
    TITLE OFFSET 2
    CASE ASIS
    TIC MARK OFFSET UNITS DATA
    YLIMITS 0 1
    MAJOR YTIC MARK NUMBER 6
    MINOR YTIC MARK NUMBER 1
    Y1TIC MARK LABEL DECIMAL 1
    XLIMITS 1 3
    MAJOR XTIC MARK NUMBER 3
    MINOR XTIC MARK NUMBER 0
    XTIC MARK OFFSET 0.3 0.3
    CHARACTER X BLANK
    LINES BLANK SOLID
    .
    MULTIPLOT CORNER COORDINATES 5 5 95 95
    MULTIPLOT SCALE FACTOR 2
    MULTIPLOT 2 3
    .
    TITLE Sepal Length vs Sepal Width
    SPEARMAN DISSIMILARITY PLOT Y1 Y2 TAG
    .
    TITLE Sepal Length vs Petal Length
    SPEARMAN DISSIMILARITY PLOT Y1 Y3 TAG
    .
    TITLE Sepal Length vs Petal Width
    SPEARMAN DISSIMILARITY PLOT Y1 Y4 TAG
    .
    TITLE Sepal Width vs Petal Length
    SPEARMAN DISSIMILARITY PLOT Y2 Y3 TAG
    .
    TITLE Sepal Width vs Petal Width
    SPEARMAN DISSIMILARITY PLOT Y2 Y4 TAG
    .
    TITLE Petal Length vs Petal Width
    SPEARMAN DISSIMILARITY PLOT Y3 Y4 TAG
    .
    END OF MULTIPLOT
    .
    JUSTIFICATION CENTER
    MOVE 50 5
    TEXT Species
    DIRECTION VERTICAL
    MOVE 5 50
    TEXT Spearman Rank Dissimilarity Coefficient
    DIRECTION HORIZONTAL
        
    plot generated by sample program

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Date created: 09/20/2017
Last updated: 09/20/2017

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