Saturday, November 6, 2010

2. General summary of G test

2.1  Calculating a G ratio
The G test evaluates the ratio:
2.2  Conducting a G test
The G test can be run as a one-sided test upper-limit test, as a one-sided lower-limit test and as a two-sided test at any significance level α.  When running a G test, it is checked for each data set j if the corresponding inequality is met:
   One-sided upper limit test:    Gj < GUL(α,νjtotal,L)
   One-sided lower limit test:    GLL(α,νjtotal,L) < Gj
   Two-sided test:                    GLL(α/2,νjtotal,L) < Gj < GUL(α/2,νjtotal,L)

2.3  Computing critical G values
The critical G values GUL and GLL are calculated from:

The equations to calculate GUL and GLL are exact.  The accuracy of GUL and GLL only depends on the accuracy of the input value FcFc can be read from tables, but can also be obtained using the FINV function in Excel: Fc = FINV(probability, degrees of freedom 1, degrees of freedom 2).

2.4  Evaluating balanced and unbalanced designs
The G test can handle both balanced and unbalanced designs.  In case of balanced designs, all data sets have the same number of degrees of freedom.  Balanced designs are covered in § 3, unbalanced designs in § 4. 

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