CORRECTION OF DATA TOR ERRORS 309 



used instead of eciuations, and, because of this rather popular pre- 

 sentation, many readers may want to consult, as the original sources, 

 the intensely interesting mathematical contributions of "Student",' 

 Professor Karl Pearson,'- and R. A. Fisher.-^ 



Case Whkre Customary Theory Applies 



We start, as in customary error theory, with the assumption that 

 the probability distribution of errors is normal. This simply means 

 that the probability of the occurrence of an error within any range is 

 assumed to be equal to the area under the so-called normal curve^ 

 (such a curve is shown in Fig. 1) between the limits of the same range. 



Fig. 1 — Customarily assumed law of error curve — normal law 



50.00000% of area within 0± .674-i9(r 

 68 . 26894% of area within =fc la 

 95 . 44998% of area within =t 2<t 

 99 . 73002% of area within ± 3a 



The total area under the curve is, of course, unity. This curve is 

 plotted with the origin at the true value and with the errors measured 

 in units of the root mean square error <x. The fractions of the area 

 bounded by certain multiples of the root mean square error are shown 

 for reference. 



Let us make an experiment and see how far customary error theory 



1 Biometrika, Vol. VI, 1908, pp. 1-15. Vol. XI, 1917, pp. 416-417. 



' Biometrika, Vol. X, 1915, pp. 522-529. 



3 Biometrika, Vol. X, 1915, pp. 507-521. Proc. Camb. Phil. Soc, Vol. XXI, 1923, 

 pp. 655-658. 



■» The equation for this has recently been traced back to Abraham De Moivre (1733) 

 by Professor Pearson. See Biometrika, Vol. XVI, 1924, pp. 402-404. 



