Shapiro-wilk Website Links For
Test 		 

Information About

Shapiro-wilk
  CATEGORIES ABOUT SHAPIRO-WILK TEST
   
statistical tests
   
APPAREL
BABY
BEAUTY
BOOKS
CAR TOYS
CELL PHONES
DVD'S
ELECTRONICS
GOURMET FOOD
GROCERIES
HEALTH & PERSONAL
HOME & GARDEN
JEWELRY
MUSIC
MUSIC INSTRUMENTS
OFFICE PRODUCTS
SOFTWARE
SPORTING GOODS
TOOLS & HARDWARE
TOYS
VIDEO GAMES
SHOPPING HOME
MORE SHOPPING...



:W = {\left(\sum_{i=1}^n a_i x_{(i)} ight)^2 \over \sum_{i=1}^n (x_i-\overline{x})^2}

where

  • ''x''(''i'') (with parentheses enclosing the subscript index ''i'') is the ''i''th Order Statistic , i.e., the ''i''th-smallest number in the sample;

  • \overline{x}=(x_1+\cdots+x_n)/n\, is the sample mean;

  • the constants ''a''''i'' are given by


::(a_1,\dots,a_n) = {m^ op V^{-1} \over m^ op V^{-1}V^{-1}m}

:where

::m = (m_1,\dots,m_n)^ op\,

:and ''m''1, ..., ''m''''n'' are the Expected Value s of the Order Statistic s of an Iid sample from the standard normal distribution, and ''V'' is the Covariance Matrix of those order statistics.

The test rejects the null hypothesis if ''W'' is too small.


REFERENCES


  • Shapiro, S. S. and Wilk, M. B. (1965). "An analysis of variance test for normality (complete samples)", ''Biometrika'', 52, 3 and 4, pages 591-611.