18 THE SYSTEMS CONCEPT 



distribution in what is being measured. Measuring the length of a room 

 with a 12-in. ruler will result in a fairly wide error, and although the mean 

 value of a number of observations should be close to fact, there may be a 

 large uncertainty in an individual measurement. Besides such random errors, 

 there may exist also constant errors which are sometimes very important but 

 too rarely recognized. Suppose the ruler has been made 1/16 in. too short at 

 the factory. If the room were 32 ft long, in addition to the random errors, 

 every measurement would have been 2 in. short: even the mean value cannot 

 be trusted in the presence of a constant error! It is revealing to read the 

 temperatures on several of the thermometers in the laboratory thermometer 

 drawer! Constant errors and the need for calibration become quite obvious. 

 Even under the most carefully controlled experimental conditions, unknown 

 constant errors creep in. In addition, personal bias is always with us, in 

 reality if not in principle. 



The variation in the quantity being measured is often called "biological 

 variance." Consider the height of 80 people at a lecture — it usually has a 

 distribution from about 5 ft, in. to 6 ft, 3 in., with the average approxi- 

 mately 5 ft, 7 in. Deviations from 5 ft, 7 in., however, could hardly be con- 

 sidered as errors or abnormalities! 



Constant errors are deadly and can result in gross misinterpretations. 

 Analytical chemistry done without proper calibrations is an example. It 

 has been shown to be prevalent even in routine analyses done day in and 

 day out in the hospitals, with large variations in mean values being reported 

 between them — each hospital apparently having its own constant errors! 

 This is embarrassing, but it is a fact. Under these conditions, diagnoses 

 made with reference to some published work from another hospital could 

 easily be wrong. It is necessary continually to be on the alert against con- 

 stant errors, or "biased [not personal] observations," as they are sometimes 

 called. 



Random errors and natural distribution in the variable measured can 

 both be treated with statistical methods. The most reliable methods, and in 

 fact the only reliable method in constant use, presuppose that the observa- 

 tions distribute themselves about a mean or average value such that the 

 density of points is greatest at the mean and progressively less and less as the 

 deviation from the mean becomes larger. That is, it presumes a "normal" 

 distribution in the observations. Figure 1-7 shows the normal distribution 

 curve. It can be interpreted two ways: 



(1) P represents the number of observations, N, which are Ax units less 

 than the mean; 



(2) P represents the probability that any measurement now being made 

 will have a deviation less than Ax from the mean. 



