Accuracy versus Approximation of the Research

Being accurate and being scientific are often taken to be synony­mous. And similarly, being approximate is taken to be contrary to being scientific. Neither of these beliefs is necessarily true. Imagine a piece of “scientific” information in which the distance between Boston and New York is mentioned as 221.8215 miles. The questions that should arise from such information are many:

  1. Where exactly are the two points known as Boston and New York?
  2. What path was followed between the two points?
  3. What measuring instrument and methods were used?
  4. How precise was the instrument?
  5. At what temperature was the measurement made, and was any correction made on that account?

And so on. All such questions are relevant because any one of the above factors, or any combination of them, is more than likely to affect the number given for distance, since it is so vul­nerable at the third and fourth places to the right of the decimal point. Even a very scientifically minded person will normally be satisfied if the distance is given as 222 miles and will likely feel no impulse to ask the kind of questions mentioned above.

Quite often, the temptation to be overly accurate is common not with the fundamental or primary quantities, such as distance, but with the derived quantities. For instance, if the distance is measured as 222 miles, and the time for travel is measured as 4 hours and 15 minutes, then the average speed is given by 222 + 4.25, which can be calculated to be 52.23529 . . . miles per hour, with the numbers after the decimal point continuing. At this point, all that can be seen are two numbers connected by the divi­sion sign. The tendency is to forget how the two numbers were obtained and to be carried away by the love of accuracy. The num­bers resulting from such calculations, when the source of data used is unknown, unseen, or ignored, are often treated with the kind of respect reserved for deities in temples, transcending the stone, metal, wood, plaster, or other materials they are made of. It is desirable on the part of the scientist not to be carried away by such unfettered, unquestioned devotion to numbers. A TV com­mercial presenting a smiling, good-looking woman with the state­ment that 77 percent of her facial wrinkles are gone because of the use of a certain miracle lotion does not tell us how the number seventy-seven was derived. If we ever get the primary data that yielded such a number, it is likely to be far from “scientific.”

Returning to the accuracy stated for speed, it cannot be more accurate than the accuracy of the “raw” information or the pri­mary data, namely, that of distance and that of time. The number for the distance has no numerals after the decimal point and that for time has two such numerals. It is quite adequate, and in fact proper, to round off the number for speed to only two places after the decimal point. Thus, giving speed as 52.23 miles per hour is the right thing to do, and for all practical purposes, to mention it as approximately 52 miles per hour is not inconsistent with being “scientific.” To compute and mention the speed as 52.23529 . . . miles per hour instead is not only a waste of time, but it is misleading. The saying, “The road to hell is paved with good intentions,” may in such cases acquire some relevance.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.

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