Table 1 Simulated replicates having added bias and noise of different distributions
From: A Multi-feature Reproducibility Assessment of Mass Spectral Data in Clinical Proteomic Studies
Data presented are median( P25,P75) | Parametric version | Non-parametric version | |||
|---|---|---|---|---|---|
Distribution of the systematic bias | Size of the samples and its replicates | Distribution of the permutated p values | Distribution of the test statistics | Distribution of the permutated p values | Distribution of the test statistics |
Normal | |||||
µ = 2 σ = 4 | 30 | 0.02 (0.01,0.06) | 3.76 (3.42,4.19) | – | – |
µ = 0 σ = 4 | 15 | 0.51 (0.30, 0.67) | 2.18 (1.95, 2.57) | 0.59 (0.41, 0.82) | 0.00 (−0.08, 0.08) |
µ = 2 σ = 2 | 0.02 (0.009, 0.04) | 4.01 (3.63, 4.65) | 0.001 (0.001, 0.001) | −0.84 (−0.96 ,−0.71) | |
µ = 2 σ = 4 | 0.15 (0.06, 0.34) | 2.94 (2.50, 3.47) | 0.005 (0.001, 0.03) | −0.42 (−0.48, −0.32) | |
µ = 0 σ = 4 | 8 | 0.36 (0.13, 0.57) | 2.34 (1.92, 3.17) | 0.64 (0.42, 0.90) | 0.00 (−0.14,0.14) |
µ = 2 σ = 2 | 0.18 (0.10, 0.31) | 2.97 (2.42, 3.54) | 0.02 (0.004, 0.08) | −0.65 (−0.81, −0.50) | |
µ = 2 σ = 4 | 0.32 (0.19,0.53) | 2.50 (1.98, 3.01) | 0.50 (0.24, 0.64) | −0.21 (−0.35, −0.07) | |
Exponential | |||||
\( \lambda = 1\left( {\mu = \sigma = 1} \right) \) | 15 | 0.01 (0.005, 0.03) | 4.48 (3.88, 4.98) | 0.001 (0.001,0.001) | −1.03 (−1.14, −0.89) |
\( \lambda = 2\left( {\mu = \sigma = 0.5} \right) \) | 0.007 (0.002,0.02) | 4.70 (4.24, 5.37) | 0.001 (0.001, 0.001) | −1.17 (−1.29, −1.01) | |
\( \lambda = 1\left( {\mu = \sigma = 1} \right) \) | 8 | 0.12 (0.05, 0.19) | 3.21 (2.86, 4.22) | 0.01 (0.001, 0.03) | −0.73 (−1.01, −0.63) |
\( \lambda = {\text{2}}\left( {\mu = \sigma = 0.{\text{5}}} \right) \) | 0.07 (0.04, 0.13) | 3.61 (3.16, 4.56) | 0.002 (0.001, 0.005) | −0.98 (−1.17, −0.81) | |
Bimodal | |||||
\( \mu = 1,\sigma = 2\left( {m/z \leqslant 1,000} \right)\mu = 2,\sigma = 4\left( {m/z > 1,000} \right) \) | 30 | 0.03 (0.008, 0.08) | 3.68 (3.33, 4.27) | – | – |
\( \mu = 2,\sigma = 4\left( {m/z \leqslant 1,000} \right)\mu = 4,\sigma = 8\left( {m/z > 1,000} \right) \) | 0.03 (0.01, 0.08) | 3.68 (3.28, 4.02) | – | – | |
\( \mu = 1,\sigma = 1\left( {m/z \leqslant 1,000} \right)\mu = 2,\sigma = 2\left( {m/z > 1000} \right) \) | 15 | 0.03 (0.01, 0.08) | 3.68 (3.28, 4.02) | 0.001 (0.001, 0.001) | −0.96 (−1.08, −0.80) |
\( \mu = 1,\sigma = 2\left( {m/z \leqslant 1,000} \right)\mu = 2,\sigma = 4\left( {m/z > 1,000} \right) \) | 0.12 (0.06, 0.32) | 3.07 (2.55, 3.51) | 0.004 (0.001, 0.01) | −0.42 (−0.52, −0.34) | |
\( \mu = 2,\sigma = 4\left( {m/z \leqslant 1000} \right)\mu = 4,\sigma = 8\left( {m/z > 1,000} \right) \) | 0.14 (0.06, 0.29) | 3.00 (2.61, 3.48) | 0.005 (0.001, 0.03) | −0.40 (−0.50, −0.31) | |
\( \mu = 1,\sigma = 1\left( {m/z \leqslant 1,000} \right)\mu = 2,\sigma = 2\left( {m/z > 1,000} \right) \) | 8 | 0.18 (0.08, 0.37) | 2.88 (2.39, 3.56) | 0.02 (0.003, 0.14) | −0.65 (−0.81, −0.43) |
\( \mu = 1,\sigma = 2\left( {m/z \leqslant 1,000} \right)\mu = 2,\sigma = 4\left( {m/z > 1,000} \right) \) | 0.26 (0.14, 0.55) | 2.67 (1.95, 3.21) | 0.48 (0.23, 0.65) | −0.21 (−0.35, −0.07) | |
\( \mu = 2,\sigma = 4\left( {m/z \leqslant 1,000} \right)\mu = 4,\sigma = 8\left( {m/z > 1,000} \right) \) | 0.36 (0.19, 0.54) | 2.32 (2.03, 2.87) | 0.32 (0.23, 0.62) | −0.28 (−0.35, −0.14) | |