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. 2010 Mar 12;76(9):2815–2822. doi: 10.1128/AEM.02714-09

TABLE 1.

Symbols and functions used in the detection probability modela

Definition Symbol/function
Nominal spiking concn at level l λl0
Standard deviation of logarithmized spiking level [ln(λ)] sd
True spiking level at level l, repetition k λlk = exp{Normal[ln(λl0)],sd}
Recovery in material m rm
Avg no. of detectable units per replicate in repetition k, material m, level l λmlk = rm × exp{Normal[ln(λl)],sd}
No. of detectable units in repetition k, material m, level l, replicate i λmlki = Poissonmlk)
Probability for at least one detectable unit in replicate mlki Pmlki = 1 − Poisson(0|λmlk) = 1 − exp(−λmlk)
No. of positive replicates, matrix m, repetition k, level l posmlk = Binomial{5|[1 − exp(−λmlk)]}
a

exp(a), ea; Normal(a,b), random number from the normal distribution, where a is the mean and b is the sd; Poisson(a), random number from normal distribution, where a is the mean; Poisson(b|a), probability that the Poisson distribution with a mean of a returns b; Binomial(a|b), random number from binomial distribution with a trials and probability b.