DIFFERENCE OF KURTOSIS

DIFFERENCE OF KURTOSIS (LET)

Let Subcommand

Compute the difference between the kurtosiss for two response variables.

The kurtosis is the standardized fourth central moment. The formula is:
\( \mbox{kurtosis} = \frac{\sum_{i=1}^{n}{(x - \bar{x})^4}/ (n-1)}{s^4} \)

with \( \bar{x} \), s, and n denoting the mean, standard deviation, and the number of observations, respectively.

For the differeence of kurtosiss, the kurtosis is computed for each of two samples then their difference is taken.

LET <par> = DIFFERENCE OF KURTOSIS <y1> <y2>             <SUBSET/EXCEPT/FOR qualification>
where <y1> is the first response variable;
            <y2> is the first response variable;
            <par> is a parameter where the computed difference of the kurtosiss is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET A = DIFFERENCE OF KURTOSIS Y1 Y2
LET A = DIFFERENCE OF KURTOSIS Y1 Y2 SUBSET X > 1

Dataplot statistics can be used in a number of commands. For details, enter
HELP STATISTICS

None

None

KURTOSIS	= Compute the kurtosis.
MEAN	= Compute the mean.
STANDARD DEVIATION	= Compute the standard deviation.
SKEWNESS	= Compute the skewness.
DIFFERENCE OF MEAN	= Compute the difference of the means.
DIFFERENCE OF SD	= Compute the difference of standard deviations.
DIFFERENCE OF SKEWNESS	= Compute the difference of the skewness.
DIFFERENCE OF QUANTILE	= Compute the difference of a quantile.
STATISTICS PLOT	= Generate a statistic versus subset plot.
BOOTSTRAP PLOT	= Generate a bootstrap plot.
TABULATE	= Perform a tabulation for a specified statistic.

Data Analysis

2003/03

SKIP 25 
READ IRIS.DAT Y1 TO Y4 X 
. 
LET A = DIFFERENCE OF KURTOSIS Y1 Y2 
TABULATE DIFFERENCE OF KURTOSIS Y1 Y2 X 
. 
XTIC OFFSET 0.2 0.2 
X1LABEL GROUP ID 
Y1LABEL DIFFERENCE OF KURTOSIS 
CHAR X 
LINE BLANK 
DIFFERENCE OF KURTOSIS PLOT Y1 Y2 X 
CHAR X ALL 
LINE BLANK ALL 
BOOTSTRAP DIFFERENCE OF KURTOSIS PLOT Y1 Y2 X  
    

Dataplot generated the following output.

       ********************************************
       **  LET A = DIFFERENCE OF KURTOSIS Y1 Y2  **
       ********************************************
  
  
 THE COMPUTED VALUE OF THE CONSTANT A             = -0.74951410E+00
  
  
       ***********************************************
       **  TABULATE DIFFERENCE OF KURTOSIS Y1 Y2 X  **
       ***********************************************
  
  
                 *    Y1       AND Y2
     X           *    DIFFERENCE OF KURTOSIS
 **********************************************
     1.00000     *    -1.06819
     2.00000     *   -0.147545
     3.00000     *   -0.595553
  
       GROUP-ID AND STATISTIC WRITTEN TO FILE DPST1F.DAT