WILKS SHAPIRO NORMALITY TEST

WILKS SHAPIRO NORMALITY TEST

Analysis Command

Perform a Wilks Shapiro test for normality.

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, ... , w_n) 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 w_i. The w_i are approximately proportional to the normal scores M_i. 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.

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.

WILKS SHAPIRO NORMALITY TEST Y1
WILKS SHAPIRO NORMALITY TEST Y1 SUBSET TAG > 2

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.

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).

None

The following are synonyms for the WILKS SHAPIRO NORMALITY TEST.
WILKS SHAPIRO TEST Y
WILKS SHAPIRO Y

ANDERSON DARLING TEST	= Compute the Anderson-Darling test for normality.
CHI-SQUARE GOODNES OF FIT	= Compute the Chi-Square goodness of fit test.
KOLMOGOROV-SMIRNOV GOODNES OF FIT	= Compute the Kolmogorov-Smirnov goodness of fit test.
PROBABILITY PLOT	= Generates a probability plot.
PPCC PLOT	= Generates a ppcc plot.

Shapiro, S. S. and Wilk, M. B. (1965). Biometrika, 52, 591-611.

Distributional Fitting, Assumption Testing

2000/1

 
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