298 REPORTS ON THE STATE OF SCIENCE, ETC. 



(5) The Significance of a Mean. 



(a) Population variance known, or estimated from a large sample. 



The test consists in entering the tables of the Normal Probability Function with 

 the ratio of (a), the deviation of the sample mean from the population mean, to (b), the 

 standard error of the mean. 



(A) pp. 415-416. (B) pp. 101-103. (C) pp. 82-83. (D) pp. 344-345. 

 Tables. ' Tables for Statisticians and Biometricians,' Cambridge University 

 Press. Table II. 



(B) Table I. (C) Appendix C. 



(b) Sample variance only known. 



Here the ratio of (i) the deviation of the sample mean from the population mean 

 to (ii) the estimated standard error of the mean is taken, and the tables of the 

 ' t '-distribution are used. 



For large samples this test becomes the same as (a) for all practical purposes. 



(B) pp. 106-108. 

 Tables : (B) Table IV. Metron, vol. v, 3, 1925. 



(6) The Significance of the Difference between the Means of Two Samples. 



The procedure is to enter the appropriate probability tables with the ratio of the 

 difference between the means to the standard error, or estimated standard error, of 

 that difference. 



(a) Test applicable in the case of large samples from two populations hi which 

 the variance may differ. 



(B) pp. 103-105. (D) pp. 345-346. Tables as for 5 (a). 



(b) Test, sensitive for difference between the means, as to whether two samples 

 can be regarded as drawn from the same population, accurate for small samples. 



(B) pp. 109-113. Tables as for 5 (b). 



(7) The Significance of the Difference between the Variance of Two Samples. 



Test whether two samples can be regarded as drawn from populations of equal 

 variance. 



(B) pp. 192-200. Table VI., p. 210. 



(8) The x 2 Test for Goodness of Fit. 



(a) Comparison of the observed frequencies with those expected theoretically in 

 the corresponding groups or classes. 



(A) pp. 426-433. (B) pp. 77-84. (C) pp. 370-387. 

 Tables. 'Tables for Statisticians and Biometricians.' Table XII. 

 (B) Table III. 



(b) Analogous test of agreement between two or more observed frequency series. 



,'B) pp. 94-95. Biometrika, vol. viii, pp. 250-254. 

 Tables as for 8 (a). 



