Levene's test for homogeneity of variance

Tests for differences in variance between different subsets of data.

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