Laundered Shop Towels: 4- The red bar and the "three sigma" rule

In my last post I looked at how the concentration of heavy metals used to determine the Load value used in the calculation was derived.

Using the mean concentration derived from highly variable data (Standard Deviation is higher than the mean) biases the "exceedance ratios" to look higher than they really are.

Using the maximum contaminant levels detected to derive an "exceedance ratio" presents a situation that is near impossible to reproduce.  The maximum values they used create exceedance ratios that would never be found in the real world - you know - the world in which the worker holds the baby and is asked "why take the risk?"  That world.

Let's start at the beginning....

The equation Gradient uses to calculate these "exceedance ratios" assumes the following:

The worker will use 12 towels per day, five days a week, for 49 weeks in a year, for 40 years for a total of 117,600 laundered towels.

Source: Leach Presentation at 2011 AHMP conference

Let's assume that Gradient's assumption is reasonable, that a worker could, indeed, come in contact with 117,600 laundered towels over their working lifetime of 40 years.

Let's assume also that each time they use one of these 12 laundered shop towels per day, they place their hand to their mouth and the contaminant on their hand is transferred to their mouth - just like in Gradient's graphic below:

From: Gradient 2011 Paper

Regarding presenting data using the "maximum" level of metals found, the question that should have been asked by the authors is; can we reasonably assume that every one of these 117,600 towels could contain the maximum concentration of contaminants that was detected on the 23 sets of laundered shop towels analyzed?

The answer is unequivocally "no" - you cannot assume that.  It is so astronomically small a chance as to be impossible for this situation to ever take place (would probably have a better chance of getting hit by a falling satellite).  The three authors and Gradient should have recognized this and left it out of their study.  Instead they report it and Kimberly-Clark puts a bow on it and parades it out for all the world's workers to see:

Source

But let's say for the sake of discussion, that the towels could contain, for example, a maximum concentration of lead - reported by Gradient to be as high as 600 mg/kg.  What would be the chance of that happening, based on the mean value and Standard Deviation they reported for lead?

Statistically speaking, if the mean is the average concentration for the population (laundered shop towels), and if the data is normally distributed (bell curve), we would assume that 99.73% of the lead concentrations (low to high) found on a laundered shop towel would fall within three Standard Deviations from the mean ("three sigma" or "3 x SD").

Let's look at the maximum values Gradient reported:

From: Data entered into spreadsheet from Gradient 2011 Study

Notice the values in red?  Those values are more than three times the Standard Deviation from the mean.  These values - statistically - would appear only 0.27% of the time a laundered shop towel is sampled.

A more scientifically valid description of those red maximum values would have been to call them "outliers."  Gradient indicates that they removed outliers, but they used them to calculate the maximum intake values.

Why does this matter?  Well for one thing, statistics play into the equation and model Gradient developed for their Study.  If you are going to use a mean, then you need to use everything related to how that mean was calculated and what the mean states.  This brings forth the concept of the "three-sigma" rule.

Why is that important?  Because if the mean of the population of laundered shop towels is X, then the probability of finding a shop towel with a concentration slightly higher than three times the Standard Deviation becomes less than 3 in 1000 (0.99730).

How would this probability work out in the methodology Gradient has set forth in their model and calculation?

Out of 117,600 laundered shop towels, 352 towels could be encountered in a 40 year span of time with a heavy metal concentration at the maximum just above the concentration at the mean plus 3 x SD.  The further from the mean the lower the probability of seeing that value becomes.

Source

Which brings up the heavy metal contaminant: lead.

Lead is the one heavy metal that Gradient and Kimberly-Clark claim presents an intake risk that is; "3,600 times higher than agency exposure guidelines."

The maximum concentration value Gradient used in their equation to determine the Load is 600 mg/kg.  That concentration is just shy of 4 x SD, which tells us that it has a probability of occurring around one (1) time for every 15,000 towels used - or 8 times in a 40 year time period.

What Gradient and Kimberly-Clark want you to accept as a real risk is that with odds of 1 in 15,000, you - the worker - could reasonably come in contact with a laundered shop towel that exposes you to 600 mg/kg of lead each and every time you pick up a laundered shop towel.   They want the worker to accept that this can be done 117,600 times in a row, for 40 years, to give you a 3,600 times higher exposure to lead than acceptable under California's Proposition 65 lead MADL.

In order to obtain an intake exposure to more than 3,600 times the "toxicity criteria" for lead, a laundered shop towel must contain 600 mg/kg of lead each time it is picked up.  Statistically, with a mean of 100 and a Standard Deviation of 139, the chance of getting a towel with that concentration of 600 mg/kg is 1 in 15,000, unless you don't want to believe their mean and Standard Deviation reported.

Was this a blunder on their part?

Rule Number 2: Always look at the data used.

This maximum intake situation is not probable, not possible, not statistically valid.  And all we have looked at is just the data used to calculate the "load" portion in their equation.

Once again, we could stop right here and hold the Gradient findings presented in the study up as invalid.    Right now, the use of incorrect mean and maximum Load values relegates this paper to inaccurate, misleading, and heavily biased towards a conclusion of elevated risk.

But once again, where's the fun in stopping now?  There is more to influence the calculation of "intake" than just heavy metal concentrations they report are in/on the laundered shop towels.

No wonder Kimberly-Clark and the The Association of the Nonwovens Fabrics Industry (INDA) love this paper.

To reiterate....

• Rule Number 1: Always read the report the findings/recommendations were based on.
• Rule Number 2: Always look at the data used.
• Rule Number 3: Always check the assumptions used to derive the model that drives the conclusion.
• Rule Number 4: Compare apples with apples and oranges with oranges.
• Rule Number 5: Always make sure the model and equations reflect reality.

Next post: Laundered Shop Towels: That's quite a load


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