## Monday, 14 December 2009

### Box Test

The log-ANOVA test was proposed by Box (1953). In this procedure, sub-samples are created out of the observations in the ith sample (where i=1,...,K). Each of the sub-samples hence contains separate observations where,

And

(F 2.18)

Where,

And is defined as

In the event that all values of are equal (or extremely close to being equal), the Box statistic () can be defined as:

(F 2.19)

The statistic approximates an F-distribution with (K-1) and () degrees of freedom. However, where the values diverge (thus they are not equal), a generalisation developed by Scheffe (1959) can be used to obtain the statistic:

(F 2.20)

In this equation, is defined as

Hence it can also be demonstrated that

that

The statistic also approximates an F-distribution with (K-1) and () degrees of freedom. Other modifications of the Box method such as the Bargmann modification (Gartside, 1972) of the Box test have been proposed remove bias and to improve the approximation to the homogeneity condition of ANOVA.