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Table 4 Additivity and Tukey's correction factor γ

From: The ChQoL questionnaire: an Italian translation with preliminary psychometric results for female oncological patients

   untransformed scores transformed scores
Facet n. of items Friedman's χ 2 p γ using γ by Facet using γ by Domain using constant γ = 1.5
Complexion 4 4.07 0.04 1.782 0.80 0.47 0.45
Sleep 3 0.81 0.37 2.090 0.71 0.93 0.91
Stamina 6 9.82 0.00 1.598 0.23 0.16 0.14
Appetite 4 0.39 0.54 1.327 0.80 0.94 0.93
Climate 3 0.21 0.64 1.143 0.88 0.59 0.61
Consciousness 3 1.23 0.27 1.737 0.55 0.59 0.44
Thinking 5 2.07 0.15 1.386 0.99 0.24 0.72
Spirit 2 3.01 0.09 2.401 0.49 0.29 0.20
Verbal Expr. 2 7.44 0.01 2.740 0.26 0.07 0.04
Joy 4 48.81 0.00 2.465 0.00 0.00 0.00
Anger 5 14.93 0.00 1.946 0.10 0.00 0.01
Depression 6 12.63 0.00 0.586 0.29 0.00 0.00
Fear & Anx. 3 0.56 0.46 0.665 0.65 0.39 0.27
Domain        
Physical form 20 13.81 0.00 1.522 0.35 0.35 0.30
Vitality & Sp. 12 9.60 0.00 1.811 0.83 0.83 0.26
Emotion 18 1.51 0.22 1.156 0.52 0.52 0.64
  1. The Tukey's test for non-additivity is applied by Facet and by Domain, on the original untransformed score. Non-additivity is found in 6 out of 13 Facets and 2 out of 3 Domains (p-level 0.05). The three last columns show the p-level from the same test, but applied on scores transformed with different corrective factors γ. Third last column: uses γ from the previous column, same row; penultimate column: γ from the previous column, but by Domain (last three rows); last column: flat constant γ = 1.5.