Quantities and Measurements in Research

We have noted that in the process of answering the question, How many? (when relevant), we need counting, and that count­ing, besides being a measurement by itself, is the basis of all other measurements. When we measure the height of a person who is, let us say, 5’10”, we are in effect counting the number of one- inch-long pieces, placed end to end, that cover the entire length of the person while he is standing erect, from the bottom of his foot to the top of his head, which comes to be seventy in number. The height scale against which he was made to stand, and on which his height was “read,” simply served the purpose of a refer­ence, conforming to the first rule of counting, namely,

If A = C and B = C, then A = B

where A is the height of the person in inches, B is the number of one-inch-long pieces required for the purpose, and C is the height read on the scale. (Instead of having individual one-inch pieces separately in a bunch, we have such lengths imprinted on the height scale for convenience).

Now, let us say that a person’s weight needs to be found and that we have a conventional weighing balance for the purpose. Placing the person on one pan, the required number of one- pound weights are placed on the other pan until neither of the two pans sinks. Then, the weight of the person is obtained by counting the number of one-pound weights required for the purpose. If instead of all one-pound weights, we used one hun­dred-pound weight, one fifty-pound weight, two ten-pound weights, and three one-pound weights, we do the simple addi- tion—(1 x 100) + (1 x 50) + (2 x 10) + (3 x 1)—and obtain the weight of the person as the sum: 173 pounds.

Another “property” of the person can be so measured: the per­son’s age, which is the number of years elapsed since the person was born. Here the counting is even more direct. Suppose on the first birthday of a person a marble were placed in a pouch, and at the end of another year, another marble were placed into the same pouch, and another marble after another year, and so on, until now. If we now want to know the age of the person, we need only open the pouch and count the number of marbles in it. The same result is obtained if we do the arithmetic of subtract­ing the year of birth from the current year (which indeed is the way age is most often found). Age, counted in years, is the mea­sure of elapsed time. If the time elapsed for an event requires less time, say the timing of a 100-meter sprinter, we count in seconds and decimals of seconds with an appropriate stopwatch. The above three properties of the person, height (in terms of length), weight (mass, to be more precise), and age (in terms of time), being measurable, are “quantified.” These also happen to be three of the most fundamental qualities directly measurable in the physical world. It is necessary to note that the inch, pound, and year (or second) are arbitrarily defined units. We may count the length, the weight, and the time equally well in any other unit. When so done, the numbers arrived at will be different, but with no change in the rule (or principle) of measurement.

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