Wednesday, 16 December 2009

BF and Modified Brown-Forsythe Tests

The Brown-Forsythe (BF) test approximates an F variable with (K-1) of freedom. It takes the following form:

clip_image002

In this, the Sattertwaite approximation (Sattertwaite, 1941) is used to obtain the value for F. Here it is defined by

clip_image004

in which

clip_image006

The Brown-Forsythe (BF) test is implemented with the numerator degrees of freedom equal to K-1. This was modified by Mehrota (1997) using a Box (Box, 1954) approximation in order to obtain the value for the degrees of freedom in the numerator (vl) and the denominator (v). This variable, vl is defines as follows:

clip_image008

Likewise, the variable v is defined as:

clip_image010

Here, the modified Brown-Forsythe test takes the following form:

clip_image012

When under the Null hypothesis (Ho), clip_image014 approximates an F distribution with vl and v degrees of freedom respectively (Mehrota, 1997).

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