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Table 3 Increments (positive values) and decrements (negative values) of power (%) for ANCOVA, ANOVA and CSA relative to a nominal power of 80% and conditional upon levels of baseline imbalance and ZY correlation

From: Bias, precision and statistical power of analysis of covariance in the analysis of randomized trials with baseline imbalance: a simulation study

  Z′ T –Z′ C Treatment effect
  0.2 0.5 0.8
ZYcorrelation ZYcorrelation ZYcorrelation
Analysis   0 0.1 0.3 0.5 0.7 0.9 0 0.1 0.3 0.5 0.7 0.9 0 0.1 0.3 0.5 0.7 0.9
ANCOVA −1.96 −1.00 5.10 13.60 >19.9 >19.9 >19.9 −1.70 4.10 14.90 18.60 >19.9 >19.9 −1.40 1.20 10.00 16.40 19.90 >19.9
  −1.64 −1.00 4.50 11.90 19.90 >19.9 >19.9 −0.90 3.80 13.90 18.40 >19.9 >19.9 –.80 .70 9.50 15.80 19.90 >19.9
  −1.28 −0.70 3.60 10.40 18.90 >19.9 >19.9 −0.90 3.10 12.10 17.30 >19.9 >19.9 –.10 .90 8.80 15.30 19.90 >19.9
  0.00 −0.40 0.60 2.00 10.50 17.20 >19.9 −0.10 −0.30 4.10 9.90 17.40 >19.9 .00 −1.30 1.20 7.60 14.10 >19.9
  1.28 −0.50 −1.80 −6.30 −7.00 −2.90 15.10 −0.20 −4.30 −8.50 −10.20 −4.30 16.10 −1.50 −6.30 −11.00 −12.40 −7.50 13.20
  1.64 −0.70 −2.80 −11.10 −14.80 −15.20 3.80 −0.50 −6.00 −12.30 −16.90 −15.60 5.40 −2.30 −7.90 −17.10 −21.40 −20.30 4.10
  1.96 −0.70 −3.70 −15.40 −21.20 −26.50 −12.90 −0.80 −7.30 −15.30 −23.70 −28.00 −13.30 −3.60 −9.90 −21.00 −28.30 −31.90 −16.30
CSA −1.96 11.50 14.70 17.70 >19.9 >19.9 >19.90 10.90 17.10 19.10 19.60 >19.9 >19.9 12.80 13.70 16.00 19.90 >19.9 >19.9
  −1.64 7.70 11.40 15.80 >19.9 >19.9 >19.90 7.30 9.70 16.80 19.00 >19.9 >19.9 9.40 10.60 14.20 19.80 19.90 >19.9
  −1.28 2.40 6.50 12.50 19.90 >19.9 >19.90 1.10 4.80 13.40 18.50 >19.9 >19.9 3.10 5.50 11.80 16.00 19.90 >19.9
  0.00 −26.60 −22.20 −11.60 2.00 15.40 >19.90 −27.70 −23.50 −13.10 –.30 15.10 >19.9 −28.50 −26.40 −15.80 −1.40 12.00 >19.9
  1.28 −60.00 −58.30 −52.90 −44.30 −26.60 10.30 −59.20 −57.70 −52.30 −45.40 −28.80 12.80 −58.40 −57.60 −54.30 −46.80 −30.20 11.40
  1.64 −67.20 −65.30 −62.60 −56.50 −46.90 −6.10 −65.70 −64.50 −61.00 −56.00 −45.50 −6.00 −65.40 −65.20 −61.80 −57.30 −47.10 −5.60
  1.96 −71.40 −71.00 −68.70 −66.20 −59.30 −29.50 −69.60 −68.90 −67.30 −64.50 −57.60 −31.60 −69.80 −69.40 −67.90 −64.60 −59.00 −29.80
ANOVA −1.96 −0.60 −0.80 0.20 −1.30 −0.30 0.80 −0.30 0.30 −0.70 0.20 0.10 0.10 2.00 1.00 1.70 1.90 2.80 2.60
  −1.64 −0.60 −0.80 0.20 −1.30 −0.30 0.80 −0.30 0.30 −0.70 0.20 0.10 0.10 2.00 1.00 1.70 1.90 2.80 2.60
  −1.28 −0.60 −0.80 0.20 −1.30 −0.30 0.80 −0.30 0.30 −0.70 0.20 0.10 0.10 2.00 1.00 1.70 1.90 2.80 2.60
  0.00 −0.60 −0.80 0.20 −1.30 −0.30 0.80 −0.30 0.30 −0.70 0.20 0.10 0.10 2.00 1.00 1.70 1.90 2.80 2.60
  1.28 −0.60 −0.80 0.20 −1.30 −0.30 0.80 −0.30 0.30 −0.70 0.20 0.10 0.10 2.00 1.00 1.70 1.90 2.80 2.60
  1.64 −0.60 −0.80 0.20 −1.30 −0.30 0.80 −0.30 0.30 −0.70 0.20 0.10 0.10 2.00 1.00 1.70 1.90 2.80 2.60
  1.96 −0.60 −0.80 0.20 −1.30 −0.30 0.80 −0.30 0.30 −0.70 0.20 0.10 0.10 2.00 1.00 1.70 1.90 2.80 2.60
  1. Maximum increment is given as >19.9 since this would represent a conditional power in excess of 99.9%. Increments/decrements in power for ANOVA are due to random variation of the simulated dataset around the nominal 80% power.