### Use of CRM in method validation – a worked example

This worked example illustrates the use of a certified wheat flour reference material to evaluate analytical bias (recovery) of a Kjeldahl nitrogen method for its crude protein content expressed as K-N.

Those analysts familiar with the Kjeldahl method can testify that it is quite a tedious and lengthy method. It consists of three major steps, starting from strong acid digestion of the test sample with concentrated sulfuric acid and a catalyst to form ammonium sulfate, followed by addition of sodium hydroxide to make it into an alkaline solution, evolving a lot of steam and ammonia during the process, and lastly subject to steam distillation before titrating the excess standard boric solution after reaction with the distilled ammonia gas at the steam distillate collector.

During these processes, there is always a chance to lose some nitrogen content of the sample due to volatility of reactions during the processing, and one can therefore expect to find lower K-N content in the sample than expected. Of course, many modern digestion/distillation systems sold in the market have minimized such losses through apparatus design but some significantly low recoveries do happen, depending on the technical competence and the extent of precautions taken by the laboratory concerned.

In here, a certified wheat flour reference material with a N- value of 1.851 g/100g + 0.017 g/100g was used. It was subject to duplicate analysis by four analysts in different days, using the same digestion/distillation set of the laboratory. The test data were summarized below and the pooled standard deviation of the exercise was calculated together with its overall mean value:

Although 97.3% recovery of the K-N content in the certified reference material looks reasonably close to 100%, we still have to ask if the grand mean value of 1.802 g/100g was significantly different from the certified value of 1.851 g/100g. If it were significantly different, we could conclude that the average test result in this exercise was bias.

A significance (hypothesis) testing using Student’s *t*-test statistic was carried out as described below:

Let H_{o} : Grand observed mean value = certified value (1.851 g/100g)

H_{1} : Grand observed mean value ≠ certified value

By calculation, *t*-value was found to be 3.532 whilst *t* -critical value obtained by MS Excel® function “=T.INV.2T(0.05,3)” was 3.182. Since 3.532 > 3.182, the Null Hypothesis H_{o} was rejected, indicating the difference between the observed mean value and the certified value was significant. We can also use Excel function “=T.DIST.2T(3.532,3)” to calculate the probability *p*-value, giving *p* = 0.039 which was less than 0.05. Values below 0.05 indicate significance (at the 95% level).

Now, you have to exercise your professional judgement if you would wish to make a correction to your routine wheat flour sample analyses posted within the validity of your CRM checks by multiplying test results of actual samples by a correction factor of 1/0.973 or 1.027.

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