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:

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, is the sample mean of the data, and w'=(w1, w2, ... , wn) or

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.

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
WILKS SHAPIRO NORMALITY TEST Y


The following outpout is generated:

               WILKS SHAPIRO TEST FOR NORMALITY
  
 1. STATISTICS:
       NUMBER OF OBSERVATIONS                =      195
       LOCATION PARAMETER                    =    9.261460
       SCALE PARAMETER                       =   0.2278881E-01
  
       WILKS SHAPIRO TEST STATISTIC VALUE =   0.9982718
  
 2. CRITICAL VALUES:
       P-VALUE      =   0.9992256
  
 3. CONCLUSIONS:
       AT THE 90% LEVEL, WE ACCEPT THE NORMALITY ASSUMPTION.
       AT THE 95% LEVEL, WE ACCEPT THE NORMALITY ASSUMPTION.
       AT THE 97.5% LEVEL, WE ACCEPT THE NORMALITY ASSUMPTION.
       AT THE 99% LEVEL, WE ACCEPT THE NORMALITY ASSUMPTION.