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Dataplot Vol 1 Vol 2

WILKS SHAPIRO NORMALITY TEST

Name:
    WILKS SHAPIRO NORMALITY TEST
Type:
    Analysis Command
Purpose:
    Perform a Wilks Shapiro test for normality.
Description:
    The Wilks Shapiro test statistic is defined as:

      \( W = \frac{(\sum_{i=1}^{n}{w_iX'_i})^2} {\sum_{i=1}^{n}{(X_i - \bar{X})^2}} \)

    where the summation is from 1 to n and n is the number of observations. The array X contains the original data, X' are the ordered data, \( \bar{X} \) is the sample mean of the data, and w'=(w1, w2, ... , wn) or

      \( w' = MV^{-1}[(M'V^{-1})(V^{-1}M)]^{-1/2} \)

    M denotes the expected values of standard normal order statistics for a sample of size n and V is the corresponding covariance matrix.

    W may be thought of as the squared correlation coefficient between the ordered sample values (X') and the wi. The wi are approximately proportional to the normal scores Mi. W is a measure of the straightness of the normal probability plot, and small values indicate departures from normality. Note that the Dataplot PPCC PLOT command is based on a similar concept.

    Monte Carlo simulations studies have indicated that the Wilks-Shapiro test has good power properties for a wide range of alternative distributions.

Syntax:
    WILKS SHAPIRO NORMALITY TEST <y>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y> is the response variable being tested;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    WILKS SHAPIRO NORMALITY TEST Y1
    WILKS SHAPIRO NORMALITY TEST Y1 SUBSET TAG > 2
Note:
    Dataplot uses Algorithm AS R94 (SWILK sub routine) from the Applied Statistics Journal, 1995, Vol. 44, No. 4. This routine should produce accurate critical values for N <= 5,000.
Note:
    The following statistics are also supported:

      LET A = WILK SHAPIRO TEST Y
      LET A = WILK SHAPIRO TEST PVALUE Y

    In addition to the above LET command, built-in statistics are supported for about 20+ different commands (enter HELP STATISTICS for details).

Default:
    None
Synonyms:
    The following are synonyms for the WILKS SHAPIRO NORMALITY TEST.

      WILKS SHAPIRO TEST Y
      WILKS SHAPIRO Y
Related Commands: Reference:
    Shapiro, S. S. and Wilk, M. B. (1965). Biometrika, 52, 591-611.
Applications:
    Distributional Fitting, Assumption Testing
Implementation Date:
    2000/1
Program:
     
    SKIP 25
    READ ZARR13.DAT Y
    SET WRITE DECIMALS 5
    WILKS SHAPIRO NORMALITY TEST Y
        
    The following outpout is generated:
                 Wilk-Shapiro Test for Normality
      
     Response Variable: Y
      
     H0: The Data Are Normally Distributed
     Ha: The Data Are Not Normally Distributed
      
     Summary Statistics:
     Total Number of Observations:             195
     Sample Mean:                              9.26146
     Sample Standard Deviation:                0.02279
     Sample Minimum:                           9.19685
     Sample Maximum:                           9.32797
      
     Test Statistic Value:                     0.99827
     P-Value:                                  0.99923
      
      
                 Conclusions
      
     ------------------------------------------------------------
                                   Null Hypothesis           Null
             Null     Confidence        Acceptance     Hypothesis
       Hypothesis          Level          Interval     Conclusion
     ------------------------------------------------------------
           Normal          50.0%         (0.500,1)         ACCEPT
           Normal          80.0%         (0.200,1)         ACCEPT
           Normal          90.0%         (0.100,1)         ACCEPT
           Normal          95.0%         (0.050,1)         ACCEPT
           Normal          97.5%         (0.025,1)         ACCEPT
           Normal          99.0%         (0.010,1)         ACCEPT
           Normal          99.9%         (0.001,1)         ACCEPT
      
        

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Date created: 6/5/2001
Last updated: 10/29/2015

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