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:    G_j < G_UL(α,ν_j,ν_total,L)

   One-sided lower limit test:    G_LL(α,ν_j,ν_total,L) < G_j

   Two-sided test:                    G_LL(α/2,ν_j,ν_total,L) < G_j < G_UL(α/2,ν_j,ν_total,L)

2.3  Computing critical G values

The critical G values G_UL and G_LL are calculated from:

The equations to calculate G_UL and G_LL are exact.  The accuracy of G_UL and G_LL only depends on the accuracy of the input value F_c.  F_c can be read from tables, but can also be obtained using the FINV function in Excel: F_c = 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.