James 



days are sufficient observations obtained to prepare \iseful analyses. 



Table I gives the mean absolute error for each of the smal- 

 yses discussed above plus a value for 30 percent of data. At 100 

 percent of data the error is obviously zero since the fit is assumed 

 perfect. 



TABLE I» ACCURACY OF MAMUAL AHALYSES 

 FOR AREA A 



Percent Data Mean Absolute Error (^) 



100 0.00 



30 0.if3 



10 1.30 



5 l.TO 



35 1.89 



2 2.95 



As expected the mean absolute error decreases with the in- 

 creasing availability of data. Thus, by doubling the data input 

 from 2 percent to k percent the analysis error is reduced by 39 per- 

 cent. Tripling the 2 percent input reduces the error by 50 percent 

 but above this point the increase of data does not produce noteable 

 improvements in analysis reliability. For instance, although the 

 error is reduced by half if the data is tripled it vould take 12 

 times as much data to reduce the error by half again. Table 1 pro- 

 vides information concerning the quantity of data required to ensure 

 specified analysis accTiracies, assuming perfect data. Since the 

 present data used for synoptic charts are far from perfect the mean 

 absolute errors must be recalculated using data typical of that pres- 

 ently available. This was done in the second series of tests. 



(1) Error Functions 



For the second series of tests for Area A the perfect 

 data were modified by introducing errors similar to those fovmd in 

 present ship injection temperatures. Two error functions were 

 assumed; one for accxiracy of temperature and the other for accjiracy 

 of ship position. The errors of the inptrt ten^ratures were 

 assumed to average 2°F, with a range of +7^, and follow somewhat 

 a noriml probability distribution. With this error distribution 

 applied to 10 percent of data, for example, there would be 6 perfect 

 observations, 10 with +1.0°F errors, 8 with +2.0'^ error, 6 with 

 +3.0°F errors, k with +2.0°F errors, and 2 each of +5, +6, and +7 F 

 error. 



133 



