Statistical Techniques for Quality Control

Basic summary statistics and graphical assessments of the data distributions are often invaluable to this initial examination. For example. Table 3.1 shows summary statistics for the distribution of protein expression levels measured in a proteomics experiment involving the three patients sampled before and after a chemotherapeutic treatment (Cho et al., 2007). 

These summary statistics can already provide several important observations on the data. For example, the maximum values are very high compared with the rest of 

TABLE 3.1 Summary Statistics of Protein Expression Levels 

As the logarithm fails to produce numeric results for values less than or equal to zero and produces negative numbers for values less than 1, transformed datasets may contain undefined values or other values that behave poorly in subsequent statistical analyses. To exclude such values from the transformed dataset, it may be necessary to set all values below a certain threshold equal to that threshold value. This is called thresholding and is commonly performed with a threshold value of unity, so that all extremely small values become zero. 

Although the logarithm is often a good choice for transforming the distribution of a dataset, more refined methods may also be used. The Box-Cox transformation (Box and Cox, 1964) can be used to improve the linear fit of two variables x and y by transforming x according to the following  

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Ad-hoc approaches—Methods of estimating should be borrowed from other problems whenever applicable. For example, statistical techniques for quality control theory can probably be applied to chemicals by viewing discharges as "faulty" production. 

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