Assessing ICV Precision and Accuracy

Precision can be evaluated for replicate measurement of the ICV following establishment of the multipoint calibration by calculating the confidence interval for the interpolated value for the ICV concentration. Triplicate injection of an ICV (L = 3) with a concentration well within the linear region of the calibration range enables a mean concentration for the ICV to be calculated. A standard deviation s can be calculated. One ICV reference standard can be prepared closer to the low end of the calibration range, and a second ICV reference standard can be prepared closer to the high end of this range. A confidence interval for the mean of both ICVs can then be found as follows:

A relative standard deviation, for the /th component, expressed as a percent (%RSD), also called the coefficient of variation, can be calculated based on the ICV instrument responses according to

where s. is the standard deviation in the interpolated concentration for the /'th-targeted component based on a multipoint calibration and x is the mean concentration from replicate measurements. For example, one can expect a precision for replicate injection into a GC to have a coefficient of variation of about 2%. As another example, one can expect a precision for replicate solid-phase extractions to have a coefficient of variation of between 10 and 20%. The coefficient of variation itself is independent of the magnitude of the amount or concentration of analyte / measured, whereas reporting a mean ICV (along with a confidence interval at a level of significance) can only be viewed in terms of the amount or concentration measured. The coefficient of variation is thus a more appropriate parameter when comparing the precision between methods.

Accuracy can be evaluated based on a determination of the present relative error provided that a known value is available. A certified reference standard for at least one analyte or for a mix of analytes constitutes such a standard. Accuracy is calculated and reported in terms of a percent relative error according to

Statements of precision and accuracy should be established for the ICV, and as long as subsequent measurements of the ICV remain within the established confidence limits, no new calibration curve needs to be generated.

Assessing Sample Results

Following the establishment of a calibration and the evaluation of the precision and accuracy for one or more ICVs, we can apply additional statistical assessments on a batch of replicate analytical results from real samples. The Q test can be applied to identify any outliers within a series of sample results. The rejection quotient Q is defined as a ratio of the gap (difference between the questionable value and its nearest neighbor) to the range (difference between questionable value and lowest value in series), (p. 57)32 For L replicate samples where L = 8 to 10, we have (p. 32):

If we have an even larger number of replicate samples such as L = 11 to 13, a different equation for Q is used, as shown below:

where xn is a questionable result in the set x},xy ..., xn that are arranged in order of increasing value such that x, < a, < x . x , designates a result that is nearest x , and x , is a result second nearest x . x, and are results furthest and second furthest from x . Q , is compared to Q ... . at

/I 1 2 /1 ^calc f ^critical

the 90% confidence level. If Q . exceeds Q ... „ then the result is considered an outlier and can be eliminated from the results. A table of Q values is found in Appendix F.

An initial statistical assessment of replicate samples can be accomplished by calculating a mean analyte concentration from L replicate samples and a standard deviation using previously stated equations found in this chapter.

For two separate batches of replicate sample results, assumed free of systematic error and drawn from the sample population,

The /’-test can be used to compare variance from both sets. The F value is calculated according to

Fcalc is compared to Fcn( from a tabulated list. Refer to the F table in Appendix F. The number of degrees of freedom for each variance is used to locate the specific F ... If F , < F then there is no significant difference in two variances.

If a theoretical or established reference whose mean g is known, we can proceed to find a mean x (average) drawn from L replicate observations and df= L - I degrees of freedom such that

Depending on the outcome of the F-test, two independent means can be compared. There are two approaches to this. If the F-test finds both variances not to be significantly different, then we have

where s is a pooled standard deviation from both sets and is calculated according to Also,

If the F-test finds both variances to be significantly different, then we have where df is computed as shown below:

where дс and x are means from respective batches of replicate sample results for L; replicates having a variance of and for L, replicates having a variance of fca|c is compared to tcrit values from a tabulated array of Student’s t values. Selective values for Student’s t are found in the Appendix. Both df and the confidence level are necessary when obtaining a value for fcrj|. In both cases, if f,a|t < fcri|, then both means that are being compared are not significantly different.

Our journey across the “jungle” of data reduction and interpretation has been completed. Topics whose underlying principles also relate to data reduction and interpretation are now introduced. These include: [1]

Having discussed what constitutes GLP in terms of QA and QC, let us introduce the very important and not to be neglected people factor in all of this.

  • [1] The nature of a trace analysis laboratory • From analog transducer to spreadsheet • Chromatographic software peak integration • Sampling for enviro-health and enviro-chemical trace quantitative analysis.
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