rv.i-2 



APPENDIX 



Samples 

 R S T 



A. Actual Data 



B. Expected Data 



C. Difference (A-BI 



C Squared 

 Expected 



figure A-5. 3X4 contingency 

 table. 



ginal totals, which must be the same in B 

 as in A. Accordingly, there is only one 

 degree of freedom (one variable) in the 2X2 

 contingency table formed. Difference table 

 C is then constructed, the values of which 

 are identical in crisscross position and 

 always total zero. Each of the values in C 

 is made less extreme (closer to zero) by 3^, 

 to comply with Yates' correction. This is 

 shown in D. Each of the corrected differ- 

 ences in D is squared and divided by the 

 corresponding expected value shown in B. 

 The sum of the four values obtained 

 (1/2 + i/6 + |/4 + J/12) is chi-square. 

 In the present case chi-square is less than 

 1 (but more than 0.004) and has a prob- 

 ability greater than 10%. The null hy- 



pothesis is thus accepted, namely, that the 

 two samples are not statistically different 

 at the 5% level of significance. 



2. Involving Two or More Variables 



Contingency table approach to the chi- 

 square test. Sometimes the data in a 

 sample fall into more than two classes or 

 outcomes, and more than two such samples 

 are to be compared. This involves "num- 

 ber of classes — 1" variables as well as 

 "number of samples — 1" variables. The 

 total number of variables equals the prod- 

 uct of these two sources of variability. The 

 number of degrees of freedom is equal to the 

 total number of variables, which is always 



