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# FKtest

### Antonio Trujillo-Ortiz (view profile)

15 Aug 2009 (Updated )

Fligner-Killeen test for homogeneity of variances.

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Description

There are several tests for homogeneity of variances. Fligner and Killeen (1976) suggest ranking (i) the |x_ij - mean| as normal type scores (a) by (0.5 + i/2(N+1)). Where i is the group and j the observation. The replacement of the mean by the median, a modification, is an attempt to improve the robustness of the test. From these scores is formulated a statistic based on a Chi-squared or a F distribution.

According to Conover et al. (1981), the Fligner-Killeen test by median is one of the best tests to use on the basis of robustness and power. Also, by several simulations, the Type I error rate and power is slightly larger when F approximation was used than when the Chi-squared approximation was used. Some of these tests are very sensitive to outliers, but Fligner test is not. Fligner test is the most robust against departures from normality.

Syntax: function FKtest(X,o)

Inputs:
X - Data matrix; Data=column 1, Group=column 2
o - By median=1 (default), mean=2

Outputs:
Complete analysis of the homogeneity of variances test by a Chi-squared and F approximation

Required Products Statistics and Machine Learning Toolbox
MATLAB release MATLAB 7 (R14)
16 Jul 2012 Alexander

### Alexander (view profile)

I just verified this using fligner.test in R (used the data provided by the author in the commments).

One issue I had was the line of code:

A = [a' X(:,2)];

A = [a X(:,2)];

To avoid an error with concatenation

31 Aug 2011 James

### James (view profile)

Antonio: have you validated your code by comparing the results between yours and those given by R fligner.test?

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