# Modernization Data Analysis and Visualization for Food Safety Research Outcomes
## 3 Descriptive Statistics
### Issues in Microbiological Counts
#### 3.7.2 Zeros, Limits of Detection, and Limits of Quantification  
When describing microbial populations on a certain product or surface, concentrations are estimated by counting the number of colony-forming units in a finite sample portion that later will be evaluated against a concentration-based criterion to make a decision. While enumerating, zero counts or non-results will come up frequently and usually will be reported as \"zero\" or \"below the limit of quantification\" (LOQ). LOQ in microbiology stands for the lowest concentration that can be determined in a specific analytical procedure [12; 17]. The use of zeros or \"below the LOQ\" has been widely implemented and usually provides results with a biased mean concentration estimate (depending on the number of observations reported). Approaches for handling this type of problem can be implemented in a data set in the following way:  
1. The simplest way to deal with values < LOQ is by ignoring non-quantifiable observations or setting \(\log_{10}\) to zero (0 Log). Both alternatives will bias the mean because setting observations below LOQ will decrease the mean, and if ignored, the mean will increase. 2. As mentioned before, if the microbial counts are \(\log_{10}\)-transformed, the presence of zero counts in a data set can cause an issue, as the \(\log_{10}\) of zero will give a non-determined number. One of the options to deal with this issue is by transforming microbial counts with a \(\log_{10}\) of the observation plus one \([log_{10}(x+1)]\)[32]. This transformation will change all zero counts to 1, and the \(\log_{10}\) transformation can be applied without any problem. Moreover, this correction is usually insignificant in terms of microbial counts; however, it should be considered when back-transforming the data and interpreting a biased mean. 3. Another simplistic approach consists of setting all values < LOQ to one half the limit of quantification [41]. Then the \(\log_{10}\) transformation is applied, and estimates will be obtained. An implicit assumption for this method is that a distribution below the limit of quantification follows a uniform distribution. If the data collected follow a lognormal distribution, then this method would give acceptable estimates; however, if the lognormal assumption is nearly correct some limitations may be encountered [42]. 4. To overcome the limitation previously mentioned, it is suggested to set all values < LOQ to \(LOQ/\sqrt{2}\) and then \(\log_{10}\) the observations to obtain the estimates [42]. When the data are not highly skewed, the replacement of values below the LOQ using this method would produce good estimates [42]. 5. The last and most accurate method to deal with values below the LOQ takes advantage of the normal distribution to extrapolate it back from the LOQ to estimate maximum likelihood estimates of the mean and standard deviation [12; 17; 42]. While this method is very accurate, it is laborious and understanding of it is somewhat limited among researchers. Despite the existence of these solutions to overcome values below the LOQ, when more than half of the data are not quantifiable, it is impossible to obtain an accurate estimate without biasing the results [42]. Moreover, in this type of case, reporting mean and standard deviation is questionable, so other estimates should be presented, such as the percentage of samples below the limit of detection and the range of the samples that were quantifiable [42]. Generally, two measurements are analyzed in food microbiology: (1) the occurrence of a microorganism, characterized in terms of presence or absence (proportion of food contaminated) and (2) the concentration of the microorganism in a food unit. Presence or absence is determined by detection methods, while concentrations can be determined by quantitative enumeration methods. Although they are determined separately, they are closely related, as higher concentrations are more likely at higher presence levels [17].