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Table 1 Performance of simulations with PV = 0.01 (small effects) for 4 sample sizes and 4 quantitative traits (normal, left-skew, right-skew, bimodal) transformed using logarithm (log), inverse-logarithm (ilog), Box-Cox, and rank-based.

From: Effects of normalization on quantitative traits in association test

  True Positive Rate False Positive Rate Displacement
  1000 2000 4000 8000 1000 2000 4000 8000 1000 2000 4000 8000
Normal 4.27 18.26 43.59 50.86 0.03 0.11 0.10 0.21 24.03 17.11 15.06 10.04
Left-skew 5.98 18.26 47.86 53.45 0.09 0.07 0.16 0.17 23.45 15.25 14.24 9.01
Right-skew 3.42 20.00 41.88 51.72 0.04 0.11 0.10 0.22 24.16 17.57 15.15 10.28
Bimodal 2.56 10.43 35.04 44.83 0.03 0.09 0.09 0.17 26.32 19.16 16.14 11.31
Normal - Log 5.98 18.26 47.86 53.45 0.09 0.07 0.16 0.17 23.45 15.25 14.24 9.01
Normal - ilog 7.69 27.83 50.43 57.76 0.17 0.21 0.18 0.37 21.91 15.87 13.51 9.55
Normal - boxcox 5.13 18.26 44.44 50.86 0.04 0.10 0.12 0.20 23.73 16.87 14.81 10.02
Normal - rank 14.53 36.52 57.27 65.52 0.08 0.17 0.24 0.44 18.97 12.50 11.65 6.65
Left-skew - log 7.69 22.61 50.43 56.03 0.10 0.07 0.22 0.20 23.08 14.50 13.44 8.16
Left-skew - ilog 5.13 19.13 45.3 54.31 0.05 0.09 0.15 0.19 23.46 16.08 14.43 9.58
Left-skew - boxcox 5.13 18.26 43.59 50.00 0.05 0.08 0.11 0.17 23.97 16.87 14.71 10.06
Left-skew - rank 14.53 36.52 57.27 65.52 0.08 0.17 0.24 0.44 18.97 12.50 11.65 6.65
Right-skew - log 5.13 16.52 41.88 49.14 0.04 0.08 0.12 0.17 23.99 17.09 14.83 10.21
Right-skew - ilog 3.42 22.61 43.59 51.72 0.05 0.11 0.10 0.23 23.98 17.63 15.17 10.41
Right-skew - boxcox 4.27 16.52 41.88 50.86 0.03 0.09 0.10 0.21 24.2 17.23 15.11 10.13
Right-skew - rank 14.53 36.52 57.27 65.52 0.08 0.17 0.24 0.44 18.97 12.50 11.65 6.65
Bimodal - log 4.27 13.91 41.88 47.41 0.08 0.05 0.13 0.15 25.32 16.84 14.91 10.35
Bimodal - ilog 2.56 11.30 35.90 45.69 0.04 0.10 0.08 0.19 26.25 19.35 16.26 11.35
Bimodal - boxcox 2.56 12.17 36.75 44.83 0.04 0.08 0.08 0.17 25.71 18.07 15.48 10.8
Bimodal - rank 14.53 36.52 57.27 65.52 0.08 0.17 0.24 0.44 18.97 12.50 11.65 6.65