Table 2. Options for interpreting non-detect data.^a.

Technique	Percent of observations below detection limits	General description	Advantages	Disadvantages	Source
Discard non-detect entries	NA	Entries with a non-detect value are eliminated.	This approach is simple.	Analysis of results that have been reported as not detected is not possible. The data set may be distorted.	Levine113
Substitution of a value in place of the non-detect value	<15%	Substitute non-detects with zero; half the LOQ or LOD; at the LOQ or LOD; or at the LOQ/√2. Substitution with ½ the LOD has been used frequently in the past for chemical assessments.	Substitution is simple. Treating non-detects as zero reduces overestimation while treating non-detects as the LOD avoids underestimation.	Use of this method could cause the data set to become skewed. Underestimation (with treating non-detects as zero) and overestimation (with treating non-detects at the ½ the DL and at the DL) is possible.	EPA;17 EPA;115 Levine113
Atchison's method	<15%	The mean and variance are adjusted to assume non-detects are zero. Assumption is that microbial data is log normally distributed.	Assumes data below the LOD were actually present, but could not be recorded.	May result in overestimation.	EPA;115 Levine113
Cohen's method	<20%	Uses a maximum likelihood estimation approach to fit a lognormal distribution to the data. Assumes the data follow a normal distribution.	Accounts for data below the LOD.	As the number of observations falling below the LOD increases, the statistical power decreases, and the true significance level increases. observations >20 are required for consistent results. Do not use if >50% of observations are non-detect. The LOD must be the same for all entries.	EPA;115 Levine;113 Helsel116
Kaplan–Meier	<50%	Non-parametric method. Estimates a cumulative distribution function for data that has multiple LODs to compute descriptive statistics.	Does not require a distribution to be specified. Can account for multiple censoring limits.	Used primarily for data with “greater thans”.	Helsel;116 Helsel120
ROS	50–80%	Imputation method (censored or missing observations are given a value, but not all non-detects are given the same value) which uses probability plot of detects to fill in the non-detect values.	Can be used for data with multiple LODs. Performs better on small sample sizes than MLE and substitution methods or for data that do not fit a distribution.	None given in the cited sources.	Helsel;116 Helsel;120 Wong108
Modern MLE	50–80%	Uses less-than values (censored values) and detected observations to provide adjusted estimates of the mean and SD that were likely to have produced both detected and non-detected data. Assumes data follow a normal or lognormal distribution.	Accounts for data below the detection level.	Must have an n >50 to use this method.	EPA;115 Helsel;116 Helsel120
Test of proportions	>50%	Non-parametric method. Requires at least 10% of the data be quantified.	Can be used for categorical data (presence/absence).	May not be applicable for composite samples.	EPA;115 Levine113
Log-probit analysis	NA??	Distributional method. Assumed data has a lognormal probability distribution. Detected values are plotted and percentages of non-detects are accounted for.	More accurate and less biased than substitution.	Requires data to have enough detected observations to define the distribution function with confidence.	EPA17

Abbreviations: EPA, U.S. Environmental Protection Agency; LOD, limit of detection; LOQ, limit of quantitation; NA, not applicable; ROS, regression on order statistic.

^aAdapted from Levine¹¹³ and EPA.¹¹⁵