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Levene's test for homogeneity of variance

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21 Nov 2013 (Updated )

Tests for differences in variance between different subsets of data.

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Description

  function [p,atab] = levenes(data,grp)
 
  Implements Levene's test for the mogeneity of variance.
  Can be used on any data suitable for an n-way ANOVA.
 
  Parameters:
    data and grp are identical to the first two parameters passed to
    MatLab's anovan function. Type 'help anovan' for details.
    
    data should be a vector with measurement data (the dependent variable).
    grp should be a 1 x nVar cell array, where nVar is the number of
    variables (or factors). Each cell of grp should be a vector of same size
    as data used as a grouping variable (as in anovan.m).
 
  Returns:
    p and atab are the same as the first two values returned from anovan.
    p is the probability of a difference in variance among the different
    cells in the data matrix greater than or equal to the one in data.
    atab is the usual information from an ANOVA, eg.:
    
     'Source' 'Sum Sq.' 'd.f.' 'Singular?' 'Mean Sq.' 'F' 'Prob>F'
     'X1' [ 0.0416] [ 3] [ 0] [ 0.0139] [0.2797] [0.8400]
     'Error' [30.3020] [ 612] [ 0] [ 0.0495] [] []
     'Total' [30.3436] [ 615] [ 0] [] [] []
 
  Notes:
    The solution here is based on the fact that Levene's test is equivalent
    to the following:
       Let D = abs(y(i,j) - y_hat(.,j))
       Where i is the data index and j indexes cell membership, and y_hat
       is the within-cell mean ("cell" here referring to the cells of a data
       matrix of).
       
       Then perform a one-way ANOVA with D as the dependent variable.

    * Requires MatLab's statistics toolbox.
 
  Aaron Schurger
  June 2007

Required Products Statistics Toolbox
MATLAB
MATLAB release MATLAB 7.4 (R2007a)
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Updates
22 Nov 2013

Some editing of the comments.

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