In scientific and engineering investigations a single measurement of an unknown quantity is seldom considered sufficient.
Two or more measurements are usually made in order to establish a check on instrumental errors, operator's errors in making readings, and the reliability of the sample. Thesemultiple measurements have two principal advantages: They reveal by their concordance the precision of the measuring process, and they make possible the use of an average of several measurements which will, in general, have a higher precision than one measurement alone. If three measurements are made, it is fairly commonpractice for students to take the "best two out of three" --averaging the two values closest together and discarding the other. Recently, however, Dr. W. J. Youden of the Statistical Engineering Laboratory at the National Bureau of Standards has shown that this procedure very often leadsto less precise results than the averaging of all three measurements together.
Experimental work frequently creates new situations in which the precision of the observations is not known in advance and must be determined from the same data that establish the estimated or average valueassigned to the quantity being measured. Whilea single measurement cannot yield any estimate of the reproducibility of the value, two measurements do give a primitiveindication of their precision.
But in an entirely new experimental situation, two measurements may not give a reliable estimate of the precision, since any marked disagreement between the two readings may be due either to the inherent crudeness and inaccuracy of the measurement process or to some accident, such as the gross misreading of an instrument scale, which makes at least one of the measurements greatly in error. With two discordant observations and no other information, it is impossible to decide between these alternative interpretations.
Three measurements is the minimum number that can conceivably reveal one of the measurements to be unreliable in a new experimental situation. Intuition suggests that if two of the three measurements are in close agreement while the third stands apart considerably removed from either of the others, then there may be groundsfor suspecting and perhaps rejecting the third value. In termsof the difference between the two in good agreement, how different may the third measurement be before it should be suspected? Since this problem is important to all * Communicated by the Director. 6~