Terminal Digit Preference
Numbers that end in zero motivate and energize people. Recall Y2K, when the world celebrated on January 1, 2000. The irresistibility of zeros resulted in everyone celebrating on the wrong date: the new millennium started on January 1, 2001, not 2000. The first year of the Julian calendar in the Common Era started on January 1, 0001, not 0000, and the first decade ended on December 31, 0010. The first millennium started on January 1, 0001, the second on January 1, 1001, and the third (under the Gregorian adjustment of the Julian calendar) on January 1, 2001, not 2000. The celebration was a year early but the attraction of the zeros was irresistible.
Terminal even numbers are preferred over odd numbers. The United States Census Bureau began to calculate age from birth dates because respondents rounded their ages to the nearest even number, giving a saw-toothed appearance to the curves. Even terminal digits are ten times more frequent than odd terminal digits in manual blood pressure measurements. Many decision points in medicine are arbitrarily set at a terminal digit that is zero or five. In hematopathology, if the marrow blast cell count is 20% myeloblasts, one has acute myelogenous leukemia; technically, if less than 20% one does not. I know of no evidence for this boundary.(1,2) It had been 30%, but was changed to 20% without any data to support either decision. If one is treated for acute myelogenous leukemia and has a residual of 5% myeloblasts in the marrow, one has failed treatment, but with 4% myeloblasts, one is in remission, all other things being equal.(1,2) But the normal myeloblast count in the marrow is less than 2%. This approach, unqualified, is what I call “thalamic medicine”: the cerebral cortex is not involved. Fortunately, most physicians can rationally deal with such silliness. This artificial and arbitrary boundary has important implications because clinical trials may require a marrow myeloblast count of 20% for entry, depriving persons with acute myelogenous leukemia by all other measures of participation, if they do not meet this criterion. Nevertheless, selecting an odd number other than five for a boundary is very unusual.
Figure 1. There are three types of sphygmomanometer; mercury, aneroid, and digital. This figure is of a manual aneroid sphygmomanometer. The rubber pump is used to raise the cuff pressure above the patient’s systolic pressure and then the pressure is released by unscrewing slowly the small valve at the base of the rubber bulb. The operator has to read the pressure indicator of a rapidly descending needle to coincide with the pulse sound at the antecubital fossa (crease of the arm) heard through a stethoscope. One has to coordinate the appearance and disappearance of the pulse sounds heard through the stethoscope with the location of the descending needle on the gauge. This ear-eye coordination is usually done hurriedly and perfunctorily by many observers making the blood pressure an approximation. The scale on the gauge, highlighting intervals of 20 mm of pressure, e.g. 100, 80, 60, etc. usually results in rounding to zeros or five, if that number seems closer to the appearance or disappearance of the Korotkoff sound, as the needle passes by the numbers. Based on the studies cited(3) and personal experience, approximation is usually represented by an even number or zero or five, usually zero.(3)
We celebrate anniversary years ending in zero exuberantly, but not those that end in three or seven. An anniversary of an event at fifty years is called a jubilee. Imagine holding a jubilee after fifty-nine years. It would never happen, even though it is more impressive in duration by nearly twenty percent than is fifty years. The word “jubilee” is from the Hebrew, yōbel, pronounced yovel, meaning the year at the end of seven cycles of schmita (sabbatical year). According to biblical instructions, it had a particular impact on land ownership and management in ancient Israel. Thus, every seven cycles of seven years was forty-nine (or fifty) years, depending on how one counted. In some places in scripture, a jubilee is said to occur every fifty years, during which slaves and prisoners are freed, debts forgiven, and the mercies of the Lord would be manifest. (Apparently, our forbearers drifted from forty-nine to fifty at times, also.) In the Book of Joshua, “yōbel” refers to a ram’s horn (shofar): “Seven priests shall bear seven trumpets of ram’s horns before the ark.” There are many references to “jubilee” in the Hebrew Bible.
The potential computer software catastrophe from the approach of the year 2000 was real and would have been disastrous. Most computer software programs had been designed to have a field holding the last two digits of the year to save memory space. One knew that “89” meant 1989. But we were about to have a year 00. That designation would represent a date earlier than 1901, possibly 1900. It was felt that the “millennium bug,” as it was nicknamed, would cause chaos in government records, banking systems, insurance companies, and utility systems, among others. So software had to be reconfigured or replaced to use a four-digit year; in many software programs there was not space for that conversion. Other systems such as elevators, medical equipment, and temperature control of large buildings could be at risk as well. Major concern was expressed about the U.S. government’s ability to get the job done in time. President Bill Clinton signed a bill passed by Congress, the Year 2000 Information and Readiness Act, to spur the work on the systems at risk and to encourage sharing of best practices among U.S. companies. European and Asian countries and the United Nations were also working feverishly to avert disaster through a huge, worldwide, logistical, and costly effort to replace software programs to hold a four-digit year field.
It is unclear why zeros (and fives) make such an imprint on our minds. Some have argued that it is the impact of our monetary denominations. With the exception of the penny and dollar, coinage and all denominations of paper money, except for the now discontinued two-dollar bill, are functions of five and ten. Thomas Jefferson was assigned the task by George Washington to propose to Congress a system of currency, weights, and measures that would make standard those items in all thirteen states. The dollar was accepted as the basic unit of coinage in 1785, followed by a complete decimal system the next year.(3)
Figure 1B. A digital blood pressure measurement instrument. Note that the terminal digit on the readout is not an approximation but an actual number with the terminal digits representing a more precise measurement of blood pressure. Here the blood pressure is 127 over 63 and the pulse 62 beats per minute. The expected probability of a terminal digit of 0, 1, 2, 3 . . . through 9 is approximately 10% in each case, if recorded digitally.(3)
Terminal digit preference had been the norm in blood pressure measurement when a manual method was used, not a digital recorder. In a large, carefully analyzed study of blood pressure measurements in the United States obtained from electronic medical records, approximately half of the values of both systolic and diastolic pressure ended in zero when a manual method was used.(4) The expectation is that ten percent would end in zero, which is seen when providers use a digital device. With a manual device, a terminal digit of 3, 7, or 9 occurred in 0.3% of measurements or 0.9% in the aggregate, when one would expect each to be present in approximately 10% (or 30% for the aggregate of all three), since the probability of a terminal digit is one in ten or 10%. This normal expectation was approximated when a digital device was used. Rounding to a pleasing terminal digit was shown to affect the diagnosis of hypertension at the margins and the use of antihypertensive agents in patients in whom terminal digit preference was applied.(4) The consequences of minor variations in blood pressure, given the millions of measurements taken in the United States every day, is consequential.(5) Similar issues have been noted in pathologists reporting measurement of tumor size.(6) Efforts to avoid these problems have been made. The point of mentioning them is to add weight to the universality of terminal digit preference.
Perhaps the supposition about coinage and bills is reversed; that is, our preference for zeros and fives led to the monetary denominations, rather than vice versa. In any case, terminal digit preference for zeros and fives is a deeply embedded bias in human behavior. This is why normal blood pressure is often designated as 120 over 80 (121 over 81 or 119 over 79 are equally indicative, but dysphoric).
How would we react to speed limits of 33 or 37 mph rather than 35; 63 or 67 mph rather than 65? Dysphoria! Perhaps the exploration by neuroscientists and experimental psychologists of what is so compelling about zeros and fives, or even versus odd numbers, might uncover explanations for other deeply held biases. Are ingrained feelings about evenness and oddness akin to our feelings about similarity and difference? Do our deeply ingrained biases about differences in skin color and ethnicity parallel our attitudes toward odd numbers?
References
Lichtman MA. Does a Diagnosis of Myelogenous Leukemia Require 20% Marrow Myeloblasts, and Does <5% Marrow Myeloblasts Represent a Remission? The History and Ambiguity of Arbitrary Diagnostic Boundaries in the Understanding of Myelodysplasia. Oncologist 2013;18:973-980.
Lichtman, M.A. The classification and clinical manifestations of the clonal myeloid diseases. In: Kaushansky K, Lichtman MA, Prchal JT, Levi MM. Burns LJ, eds. Williams Hematology 10th ed. New York, NY: McGraw-Hill Education; 2021:1341-60.
Crease RP. World in the Balance: the historic quest for an absolute system of measurement. W.W. Norton Co. Inc., New York, 2011. Pp. 1-317
Nietert PJ et al. Effect of terminal digit preference on blood pressure measurement and treatment in primary care. Am J Hypertension 2006;19:147-152.
National High Blood Pressure Education Program. National Herat Lung and Blood Institute and American Heart Association Working Meeting on Blood Pressure Measurement. April, 2002. nhlbi.nih.gov/files/docs/resources/heart/bpmeasu.pdf
Hayes, SJ. Terminal digit preference occurs in pathology reporting, irrespective of patient management implications. J Clin Pathol 2008;61:1070-1071.
Image Credit
Fig 1: Image by succo from Pixabay
Fig 1B: Photo by the author
Written October 2020