No. 589] NOTES AND LITERATURE 57 



from the tables. Whether the methods used in such cases by 

 Harris 16 will prove the best available remains to be seen. 



Considerable attention has recently been given to the probable 

 error of the correlation coefficient. 



If the number of observations upon which r is based is large 

 and if it does not approach too closely either of its limiting 

 values of + 1 or — 1, the use of the formula of Pearson and 

 Filon, 



E r = .6745 



readily evaluated by the use of the tables of 1 — r a given by 

 Soper 17 used in connection with the x u of Miss Gibson's Tables 18 

 or approximated by the Abac of Heron, 19 is quite legitimate. 

 But when either of these conditions is not realized the value of r 

 found from a single sample will probably not be the true corre- 

 lation for the population under consideration. 



Chemists, agriculturists, physiologists and many others often 

 must necessarily reason from a relatively small number of obser- 

 vations. It is therefore of very real importance that some valid 

 measure of the statistical trustworthiness of such coefficients be 

 known. Some of the problems concerning the probable error of r 

 when it approaches its numerical limits or when the number of 

 cases upon which it is based is small are discussed mathematically 

 hy Soper 20 as they have been attacked experimentally by "Stu- 

 dent. ' ' 21 Further contributions to the subject are those of Fisher 22 

 and of Pearson, 23 who summarizes the series of studies and gives a 

 table to facilitate the interpretation of correlation coefficients 

 based on small samples. He says : 



16 Harris, J. Arthur, "On the Significance of Variety Tests," Science, 

 N. S., 36: 318-320, 1912, and BiometriTca, I. c. 



"Soper, H. E., In "Tables for Statisticians and Biometricians. " 



is BiometriTca, 4: 385-392, 1906. Also in Pearson's Tables. 



"Heron, D., "An Abac for Determining the Probable Errors of Corre- 

 lation Coefficients," BiometriTca, 7: 411, 1910. Also in Pearson's Tables. 



20 Soper, H. E., "On the Probable Error of a Correlation Coefficient to a 

 Second Approximation," BiometriTca, 9: 91-115, 1913. 



21 "Student," "Probable Error of a Correlation Coefficient," BiometriTca, 

 6: 302-310, 1908. 



"Fisher, R. A., "Frequency Distribution of the Values of the Correla- 

 tion Coefficient in Samples from an Indefinitely Large Population," Bio- 

 metriTca, 10: 507-521, 1915. 



23 Pearson, K, "On the Distribution of Small Samples"; Appendix I to 

 papers by "Student" and R. A. Fisher, BiometriTca, 10: 522-529, 1915. 



