From the face expressions of participants attending my measurement uncertainty courses, I could tell that some of them had yet to grasp the important point of calculating the combined uncertainty from a series of uncertainty components. I hope the following notes can bring more clarity to this issue….
Calculation techniques in combining uncertainties
Microbiological counting is normally done after incubating a portion of prepared sample on a sterilized culture medium at stipulated temperature over time. Very often, microbial growth rate data are heteroscedatic, or non-normally distributed. The heteroscedatic data tend to have unequal variability (scatter) across a set of independent or predictor variables. The presence of such data can be demonstrated graphically as following some kind of cone shape on a scatter graph, as in Figure 1 below:
The outcome of data analysis would be seriously flawed if we were to directly take the counts for statistical evaluation like what we would normally do for a set of chemical analysis data.
To overcome this, we may consider microbial growth data as being log-normally distributed to cater for the physiological or biochemical based mechanism involved.
Many microbiologists in their recovery studies would have noticed that the % recoveries can never be found satisfactory after dividing the experimental colony counts with the known inoculated number of bacteria. They tend to be in the region of 70% or so. However, once the data are logarithmic transformed to the base of 10, the relative standard deviation RSD’s obtained are more acceptable, as shown in the figure below:
Figure 2: The % recoveries of colony forming units (cfu)/ml
The limit of detection (LOD) is an important characteristic of a test method involving trace analysis but its concept has been, and still is, one of the most controversial in analytical chemistry. Read more … Controversies on Limit of Detection