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Dataplot Vol 2 Vol 1

STATISTIC PPCC

Name:
    <dist> PPCC
Type:
    LET Subcommand
Purpose:
    Compute the probability plot correlation coefficient (also called the ppcc) value for a variable for a specified distribution.
Description:
    The ppcc value is the correlation coefficient of the straight line fitted to a probability plot (see the documentation for PPCC PLOT for details).

    Although this value is normally determined using either a probability plot or a ppcc plot, for a limited number of distributions you can also generate this as a statistic LET subcommand. The advantage in this case is that you can use it with any of the commands that support built-in statistics (e.g., the STATISTIC PLOT or the TABULATION command).

    This command was updated 2013/02 in the following ways.

    1. In addition to the PPCC value, you can now extract the estimates of the location and scale parameters based on the probability plot. See Syntax 2 and Syntax 3 below.

    2. For certain one and two shape parameter distritutions, you can extract the shape parameter based on the PPCC plot/probability plot method.

      In using these commands, the shape parameter can be be handled in one of two ways.

      • You can assume a fixed shape parameter. For example,

          LET GAMMA = 2.6
          WEIBULL PPCC STATISTIC PLOT Y X

        This command will plot the ppcc value for a Weibull distribution with a shape parameter of 2.6 for the groups defined by the X variable.

      • The shape parameter is not pre-defined.

        In the example above, if GAMMA is not pre-defined then the shape parameter will be estimated using the PPCC plot method (this is done in the background) for each distinct group.

      See the Note section below for a list of supported distributions.

Syntax 1:
    LET <par> = <dist> PPCC <y>             <SUBSET/EXCEPT/FOR qualification>
    where <y> is a response variable;
                <dist> is one of the distributions listed in the Note section below;
                <par> is the parameter where the ppcc value is saved;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Syntax 2:
    LET <par> = <dist> PPCC LOCATION <y>             <SUBSET/EXCEPT/FOR qualification>
    where <y> is a response variable;
                <dist> is one of the distributions described in the Note section below;
                <par> is the parameter where the location value is saved;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    This syntax returns the estimate of the location parameter rather than the PPCC value.

Syntax 3:
    LET <par> = <dist> PPCC SCALE <y>             <SUBSET/EXCEPT/FOR qualification>
    where <y> is a response variable;
                <dist> is one of the distributions described in the Note section below;
                <par> is the parameter where the scale value is saved;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    This syntax returns the estimate of the location parameter rather than the PPCC value.

Syntax 4:
    LET <par> = <dist> PPCC STATISTIC <y>             <SUBSET/EXCEPT/FOR qualification>
    where <y> is a response variable;
                <dist> is one of the distributions with shape parameters described in the Note section below;
                <par> is the parameter where the ppcc value is saved;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    When the distribution has a shape parameter, then the word STATISTIC is required to distinguish this command from the PPCC PLOT command. Specifically the following can conflict

    WEIBULL PPCC PLOT Y
    WEIBULL PPCC STATISTIC PLOT Y X

    The first command is the Weibull PPCC plot while the second command plots the PPCC value for Y for each group in X.

Syntax 5:
    LET <par> = <dist> PPCC SHAPE <y>             <SUBSET/EXCEPT/FOR qualification>
    where <y> is a response variable;
                <dist> is one of the distributions with a single shape parameter described in the Note section below;
                <par> is the parameter where the shape value is saved;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    This syntax returns the estimate of the shape parameter rather than the PPCC value.

Syntax 6:
    LET <par> = <dist> PPCC SHAPE ONE <y>             <SUBSET/EXCEPT/FOR qualification>
    where <y> is a response variable;
                <dist> is one of the distributions with two shape parameters described in the Note section below;
                <par> is the parameter where the shape value is saved;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    This syntax returns the estimate of the first shape parameter rather than the PPCC value.

Syntax 7:
    LET <par> = <dist> PPCC SHAPE TWO <y>             <SUBSET/EXCEPT/FOR qualification>
    where <y> is a response variable;
                <dist> is one of the distributions with two shape parameters described in the Note section below;
                <par> is the parameter where the shape value is saved;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    This syntax returns the estimate of the second shape parameter rather than the PPCC value.

Examples:
    LET A = LOGISTIC PPCC Y
    LET A = DOUBLE EXPONENTIAL PPCC Y SUBSET Y > -3
Note:
    The following location/scale distributions are supported.

      LET A = ANGLIT PPCC Y
      LET A = ARCSINE PPCC Y
      LET A = CAUCHY PPCC Y
      LET A = COSINE PPCC Y
      LET A = DOUBLE EXPONENTIAL PPCC Y
      LET A = EXPONENTIAL PPCC Y
      LET A = HALF CAUCHY PPCC Y
      LET A = HALF NORMAL PPCC Y
      LET A = HYPERBOLIC SECANT PPCC Y
      LET A = LOGISTIC PPCC Y
      LET A = MAXWELL PPCC Y
      LET A = MAXIMUM GUMBEL PPCC Y
      LET A = MINIMUM GUMBEL PPCC Y
      LET A = MAXWELL PPCC Y
      LET A = NORMAL PPCC Y
      LET A = RAYLEIGH PPCC Y
      LET A = SEMICIRCULAR PPCC Y
      LET A = SLASH PPCC Y
      LET A = UNIFORM PPCC Y

    In addition, the following distributions with a single shape parameter are supported. If you want a fixed value of the shape parameter, you can specify it as shown here.

      LET GAMMA = <value>
      LET A = WEIBULL PPCC STATISTIC Y
      LET A = 2PARAMETER WEIBULL PPCC STATISTIC Y

      LET GAMMA = <value>
      LET A = INVERTED WEIBULL PPCC STATISTIC Y

      LET GAMMA = <value>
      LET A = GAMMA PPCC STATISTIC Y

      LET GAMMA = <value>
      LET A = WALD PPCC STATISTIC Y

      LET GAMMA = <value>
      LET A = GENERALIZED PARETO PPCC STATISTIC Y

      LET GAMMA = <value>
      LET A = FATIGUE LIFE PPCC STATISTIC Y

      LET SIGMA = <value>
      LET A = LOGNORMAL PPCC STATISTIC Y

      LET LAMBDA = <value>
      LET A = TUKEY LAMBDA PPCC STATISTIC Y

      LET G = <value>
      LET A = G PPCC STATISTIC Y

    In addition, the following distribution with two shape parameters is supported. If you want a fixed value of the shape parameters, you can specify it as shown here.

      LET G = <value>
      LET H = <value>
      LET A = G AND H PPCC STATISTIC Y

Note:
    Dataplot statistics can be used in a number of commands. For details, enter

Default:
    None
Synonyms:
    None
Related Commands: Reference:
    James J. Filliben (1975), "The Probability Plot Correlation Coefficient Test for Normality," Technometrics, Vol. 17, No. 1.
Applications:
    Exploratory Data Analysis
Implementation Date:
    2011/06
    2013/02: Support for location, scale, and shape parameters
    2013/02: Additional distributions
    2015/02: g distribution
    2016/06: Support for 2-parameter Weibull
Program 1:
     
    SKIP 25
    READ GEAR.DAT  Y X
    .
    LABEL CASE ASIS
    Y1LABEL Correlation
    X1LABEL Batch
    Y1LABEL DISPLACEMENT 15
    X1LABEL DISPLACEMENT 12
    TITLE CASE ASIS
    TITLE OFFSET 2
    XLIMITS 1 10
    X1TIC MARK OFFSET 0.5 0.5
    YLIMITS 0.92 0.99
    TIC MARK OFFSET UNITS DATA
    LINE BLANK SOLID
    CHARACTER X BLANK
    .
    MULTIPLOT CORNER COORDIANTES 2 2 98 98
    MULTIPLOT SCALE FACTOR 2
    MULTIPLOT 2 2
    .
    TITLE Normal PPCC Values
    NORMAL PPCC PLOT Y X
    TITLE Logistic PPCC Values
    LOGISTIC PPCC PLOT Y X
    TITLE Double Exponential PPCC Values
    DOUBLE EXPONENTIAL PPCC PLOT Y X
    TITLE Uniform PPCC Values
    UNIFORM PPCC PLOT Y X
    .
    END OF MULTIPLOT
        
    plot generated by sample program
Program 2:
     
    skip 25
    read gear.dat y x
    .
    tic mark offset units screen
    tic mark offset 5 5
    char X
    line blank
    .
    multiplot scale factor 2
    multiplot corner coordinates 5 5 95 95
    .
    y1label displacement 16
    x1label displacement 12
    title offset 2
    label case asis
    title automatic
    x1label Batch
    .
    multiplot 2 2
    y1label Correlation
    normal ppcc statistic plot y x
    y1label Location
    normal ppcc location plot y x
    y1label Scale
    normal ppcc scale plot y x
    char X all
    line blank all
    y1label Raw Data
    plot y x x
    end of multiplot
        
    plot generated by sample program

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Date created: 06/23/2011
Last updated: 02/19/2015

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