A notable exception to this rule occurs when the bucket or injection tempera- 

 ture shows no variation whatsoever over a period of time. This is not an indication of 

 a good instrument, but rather it is an indication that no readings were made, and 

 the value of the last reading taken was repeated over and over. Contrary to the rule 

 of low randomness, this indicates a very unreliable bucket or injection thermometer 

 reading, and the average values should be relied upon. 



9.1.2. Comparison of Standard Deviations 



When the average value is calculated for a series of zero depth values, and a 

 corresponding average is obtained for the injection or bucket thermometer values, 

 their standard deviations from this average can also be obtained. 



With reliable instruments, both standard deviations should be approximately 

 equal, representing for the most part the variations in the ocean. (See Section 4.3, 

 Equation 3). If the two standard deviations are not similar, either one of two con- 

 ditions is prevalent : (1) the one with the larger standard deviation has less ac- 

 curacy and reliability; (2) the one with the smaller deviation represents a case of 

 repeated readings rather than measured ones. The latter case can be quickly de- 

 termined from the individual values. 



9.1.3. Evaluation of Variability Data by the Coefficient of Correlation 



The extent to which the data represent true ocean variability as opposed to 

 the random errors of the two measuring instruments can be obtained through the 

 coefficient of correlation. For any two independent measurements, the extent to 

 which one measurement is dependent upon the other, i.e., Y is a function of X, 

 is given by the correlation coefficient. 



If the coefficient of correlation is high, then the variations of the readings of 

 both instruments are a measure of variations in the ocean itself. If the coefficient of 

 correlation is low, then the variations of both instruments are random variations and 

 no conclusions about ocean variability should be attempted. 



The coefficient of correlation may be derived mathematically as follows : 



^ Nil, (-^;-) (^o^) (1) 



Where r = coefficient of correlation 



N = number of readings ^ 



X = arithmetic average of the raw score, or 1^1= ^i 

 xi = each individual reading 



■y and yi are defined asX and xi (specifically applied, xi and x are the 

 individual and average bucket temperatures, while yi and y are 

 the corresponding individual and average zero depth values of 

 the Bathythermogram. 

 (T>i = standard deviation of :<i 

 cry = standard deviation of n 



The coefficient of correlation of two sets of variates, expressed in their standard 

 deviation as units, is the arithmetic mean of the products of deviations of correspond- 

 ing sets of values from their respective means. 



Since a» and or are constant; 



.E(x - x) (y - y) 



^ (2) 



<'x<'y 



27 



