Much
Alfred A. Brooks
OREJC Approval
Background
The catchy title is all this paper has in common with Shakespeare's comedy. This paper attempts to explain the cause of common misunderstandings in the presentation of risk assessment and dose assessment. Dose assessment has a great deal in common with risk assessment and the two are treated the same. The author apologizes for the mathematics but the problem is not understandable without a few mathematical constructs. The assessments may be statistical or point value in nature but this in no way eliminates the causes of the misunderstanding.
The concepts of "nothing" and the associated number "zero" have been a problem to the human race since time immemorial. "Zero" was introduced as a number by the Arabians in the 7-th century. Mathematics and logic now accommodate them well but the general public still treats it special case; for instance, writing "0 or 1 or more" rather that "0 or more". Except for division there is little that is special to zero.
The problem is compounded by the fact the scientific terminology comprises lay terms with special limited definitions. This combined with the use of a scientific term and its corresponding lay term in the same sentence leads to confusion and misunderstanding. For instance, the sentence "I will work late tonight replacing the work term in the equation" contains the word "work" in two different contexts: 1) the first "work" is a lay term meaning "I will apply myself to a task" and 2) the second "work" is a scientific term meaning the product of a "force" and a "distance". (Notice the word "product" also has dual meanings.) The use of a scientific term carries with it all the characteristics and conditions belonging to the underlying concept and thus is a very important tool for the communication of ideas.
Ambiguous Statements in Risk
Assessment
One of the ambiguities in public risk assessment presentation lies in the undefined, descriptive terms uses to describe small risks: small, not substantial, vanishingly small, negligible, of no interest, insignificant, no risk, almost zero, essentially zero, and yes even zero to mean very, very small. The problem is that these terms are not defined terms and hence are subject to misinterpretation by the recipient. Some listeners may believe that a risk of 0.1 is small while another may claim 0.001 is large depending upon the circumstances and the emotional status of the individual. A discussion carried out using undefined terms having lay meanings cannot be considered a scientific nor unambiguous. It is the responsibility of the presenter to avoid these semantic traps.
Statistical Computations
Statistical computations start with distribution functions for the input variables. This gives one the ability to say something about the reliability of the resulting answers.
Risks are probabilities and by definition always lie between 0 and 1. The probability of a distributed variable having a precise value is zero. The larger lifetime, health risks (cancer, stroke and heart attack) are about 0.1 to 0.3. For some purposes 0.001 or 0.0001 may be considered small; most reasonable persons would consider 0.000001 as small. The personal perception of the magnitude of a risk is a very subjective thing but very real to the observer. In a technical sense large and small risks are comparative to some other known related risk or to 1.
One of the most frequent misunderstandings is the use of "zero" to mean "essentially zero" or "negligible" and this would be understood by most fellow scientists. The public often takes this to mean "precisely zero" and they know that such a statement is, under the circumstances impossible and hence false. The result is an increase in the level distrust. The proper resolution of this problem is to use "zero" only in its correct meaning and to carefully define and explain the meaning of "almost zero", using it only in its defined sense.
Other misunderstandings come from the belief that statistics cannot prove a negative or that statistics cannot prove that a distributed continuous variable is precisely zero. The statements may be true (depending on circumstances) but they are not germane to the proper interpretation of data. Statistics does not predict specific precise values but enables calculation of estimates of distributed variables with an estimate of its confidence interval at some level of confidence. If zero lies within the confidence interval at a high level of confidence we say that "the variable does not differ from zero" or informally "the variable is zero". The shorthand statement is not strictly true and leads to misunderstanding and should be avoided.
Non-statistical Computations
Non-statistical computations follow the same principles as their statistical equivalent but do not have the benefit of uncertainty estimation. Nothing about the possible range of the variable can be determined from the computation but can be crudely estimated by assuming discrete errors in the input data followed by error propagation. The same confusion about "zero" and "almost zero" exists and the same caveats apply. While there is no apparent problem in calculating a "zero" risk it is still there; buried in the assumption that the input data was exact when it was not. Again the presenter must make it clear what is meant by the terminology used and what it is: an estimate of unknown certainty.