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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
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.
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
y = 0.0002x
2
- 0.0317x + 1.1777
R² = 0.973
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0
10
20
30
40
50
60
70
80
90
100
110
Non-Compliant with low prob. of
single .25g test result <20 ppm
(> 60ppm average in sample)
Prob. of .25g Test Result <20 ppm
Avg. Gluten (ppm) due to Kernel Based ContaminaƟon in 50g sample
Compliant
(< 20ppm
average in
sample)
Danger Range:
Avg. >= 20 ppm with >=
.05 prob. of single .25g
test result <20 ppm
(20 - 60ppm avg. in sample)
Fig. 2.
Probability that a 0.25 g test result reads <20 ppm for various average contamination rates in the host sample.
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R.D. Fritz et al. / Food Chemistry 216 (2017) 170–175