Table 2 Summary of Kolmogorov–Smirnov and χ2-GOF testsa.

From: Developing probability distributions for transfer efficiencies for dermal exposure

Chemical Surface Data sets used Kruskal–Wallis P-value n Distribution Parameters Kolmogorov–Smirnov P-value χ2-test P-value
Chlorpyrifos Carpet 12, 13, 15, 16, 110, 22, 23, 41, 0.089 95 Normal μ̂=0.0162, ς̂=0.009 0.2817 0.1469
   43, 93, 94, 95    Lognormal μ̂=−4.26, ς̂=0.54 0.9282 0.4936
      Exponential β̂=0.0162 0 0
      Gamma α̂=3.759, β̂=0.004 0.9979 0.6247
      Beta α̂1=0.85, α̂2=42.126 0 0
      Weibull α̂=2.008, β̂=0.018 0.6784 0.5715
      Uniform â=0.003, =0.045 0 0
  Vinyl 127,128, 32, 33, 34 0.0879 42 Normal μ̂=0.052, ς̂=0.050 0.1372 0.0002
      Lognormal μ̂=−3.301, ς̂=0.845 0.97 0.5809
      Exponential β̂=0.052 0.2559 0.4439
      Gamma α̂=1.647, β̂=0.031 0.8751 0.5256
      Beta α̂1=2.898, α̂2=45.901 0.0069 0.0044
      Weibull α̂=1.25, β̂=0.06 0.5567 0.1509
      Uniform â=0.005, =0.242 0 0
  Foil 111, 61, 62 0.1975 24 Normal μ̂=0.866, ς̂=0.066 0.2478 0.1562
      Lognormal μ̂=−0.147, ς̂=0.076 0.2488 0.3766
      Exponential β̂=0.886 0 0
      Gamma α̂=25.166, β̂=0.034 0.0099 0.0022
      Beta α̂1=8.277, α̂2=1.374 0.1778 0.0022
      Weibull α̂=14, β̂=0.89 0.1832 0.0068
      Uniform â=0.769, =0.965 0.2323 0.1562
  Turf 51, 52 0.004   None of the data sets were large enough to fit a distribution
Pyrethrins I Carpet 124, 125, 24, 26, 44, 46 0.0547 66 Normal μ̂=0.027, ς̂=0.020 0.0035 0
      Lognormal μ̂=−3.864, ς̂=0.675 0.3931 0.265
      Exponential β̂=0.027 0.0019 0.0012
      Gamma α̂=2.253, β̂=0.012 0.0976 0.0038
      Beta α̂1=0.85, α̂2=42.126 0 0
      Weibull α̂=1.47, β̂=0.03 0.1162 0.0011
      Uniform â=0.006, =0.086 0 0
  Vinyl 134, 35, 38 0.147 30 Normal μ̂=0.037, ς̂=0.030 0.437 0.197
      Lognormal μ̂=−3.66, ς̂=0.964 0.9554 0.5304
      Exponential β̂=0.037 0.4695 0.3397
      Gamma α̂=1.546, β̂=0.024 0.975 0.6083
      Beta α̂1=0.407, α̂2=8.232 0.0044 0.0001
      Weibull α̂=1.28, β̂=0.04 0.9629 0.6083
      Uniform â=0.002, =0.130 0.0001 0.0004
  Foil 112, 63, 64 0.4241 24 Normal μ̂=0.831, ς̂=0.079 0.7014 0.0584
      Lognormal μ̂=−0.188, ς̂=0.096 0.7271 0.0584
      Exponential β̂=0.831 0 0
      Gamma α̂=25.166, β̂=0.033 0.0984 0.0204
      Beta α̂1=42.104, α̂2=7.908 0.0827 0.0022
      Weibull α̂=12, β̂=0.87 0.561 0.0584
      Uniform â=0.710, =0.942 0.3686 0.0584
Piperonyl Carpet 122, 27, 28, 47, 49 0.0539 60 Normal μ̂=0.021, ς̂=0.012 0.0961 0.0081
butoxide      Lognormal μ̂=−4.001, ς̂=0.513 0.9528 0.6472
      Exponential β̂=0.021 0.0001 0
      Gamma α̂=3.809, β̂=0.006 0.1239 0.0233
      Beta α̂1=0.85, α̂2=42.126 0 0
      Weibull α̂=1.85, β̂=0.02 0.0812 0.0899
      Uniform â=0.007, =0.065 0 0
  Vinyl 131, 39, 310, 311, 312 0.1437 42 Normal μ̂=0.036, ς̂=0.026 0.0994 0.0001
      Lognormal μ̂=−3.625, ς̂=0.808 0.944 0.8604
      Exponential β̂=0.036 0.3156 0.4439
      Gamma α̂=1.849, β̂=0.019 0.8262 0.2952
      Beta α̂1=0.407, α̂2=8.232 0.0009 0
      Weibull α̂=1.41, β̂=0.04 0.5669 0.4729
      Uniform â=0.005, =0.091 0.001 0.0015
  1. aParameter calculations and notations for each distribution are summarized in Table S-1 (Supplementary Material).