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Archive for September, 2018

Techniques used in combining uncertainties

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



What is least square difference?


Application of Least Significance Difference



Microbiological data transformation

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

Log Recovery

Controversy of LOD (Detection Limit)

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