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R.D. Fritz et al. / Food Chemistry 216 (2017) 170–175

1.00

y = 0.0002x 2 - 0.0317x + 1.1777 R² = 0.973

0.90

Danger Range: Avg. >= 20 ppm with >= .05 prob. of single .25g test result <20 ppm (20 - 60ppm avg. in sample)

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0.70

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Compliant (< 20ppm average in sample)

0.30

Non-Compliant with low prob. of single .25g test result <20 ppm (> 60ppm average in sample)

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Prob. of .25g Test Result <20 ppm

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0

10

20

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60

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Avg. Gluten (ppm) due to Kernel Based ContaminaƟon in 50g sample

Fig. 2. Probability that a 0.25 g test result reads <20 ppm for various average contamination rates in the host sample.

concentrated in fewer and fewer 0.25-g test amounts. Since additional observations is a costly way to deal with this, finding a solution to the non-homogeneity issue itself appears the more prudent alternative.

of incorrectly deeming it compliant (i.e., <20) via a single reading. However for samples whose true gluten average spans from 20 ppm to 60 ppm, a ‘danger zone’ presents itself where the chance of incorrectly dispositioning it as compliant is above the often used 5% risk maximum. An equation relating the probability of a single test reading being <20 ppm (i.e., compliant) relative to true sample average gluten content (for up to 60 ppm gluten) could then be defined as Y = 0.000214X 2 0.0317X + 1.1777, where Y = probability of getting a compliant reading (i.e., <20 ppm) via a single test out- come, and X = True average gluten in the sample. According to this equation, if the true sample average is 20 ppm, analysis with a single 0.25-g will have 63% chance of getting a <20 ppm reading. So, when a gluten kernel exists and provides an overall average of 20 ppm gluten, roughly two out of three observations will end up less than 20 ppm (due to the non-homogenous grind and resultant skewed distribution characterized herein). Additional tests per sample could improve the ability to accu- rately characterize a ‘ground sample’, but highly skewed distribu- tions like this require a good amount of effort to get an ‘accurate enough’ estimate of the sample mean (compared to symmetrical ones like normally distributed data ( Olsson, 2005 )). For example, assuming we have a conforming sample that is log-normally dis- tributed with a non-transformed average = 11.4 ppm and standard deviation = 4.0 ppm, it would take 10 observations to gain 95% confidence the average of this sample does not exceed 20 ppm. This assessment was done via simulation, employing the Modified Cox Method for estimating confidence intervals for the mean of a lognormal distribution ( Olsson, 2005 ). Consequently, relatively large numbers of tests would tend to be needed to accurately assess gluten content given the non- homogeneity discovered in this research. And the poorer the grind, the worse this situation becomes since the contamination is then

4. Conclusion

Our research has looked into the use of a single 0.25 g test amount to assess the gluten content of ground groats when a gluten-containing kernel is in a sample. The results indicate that a homogenous grind is difficult to attain and that resultant 0.25 g test results tend to be log-normally distributed. It appears this phenomenon is at play in finished goods as well (i.e., where whole grains have been cut and flaked), as our repetitive tests on ‘gluten positive’ servings from our ‘in-market survey’ suggest. The log-normal distribution of gluten outcomes complicates the assessment task since a single observation (or even a number of them) may not accurately represent the rest of the sample (since a substantial range of outcomes is inherent in skewed distributions like this). Consequently, conventional use of a single 0.25 g test should be treated with caution, particularly when a positive compliant gluten reading has been obtained with that first reading. Since it may be impractical in terms of cost to improve gluten assessment accuracy with multiple tests per sample, solving the non-homogenous grinding circumstance uncovered here is needed. Our research is underway in that direction. Parallel efforts from oat industry or GF industry should be encouraged.

Disclosure of competing interests

The authors declare that they have no competing interests. Ronald D. Fritz, Yumin Chen, and Veronica Contreras are salaried