IX. On the Probable Error of Mean-Square Contingency

1906 Biometrika  
Let there be any contingency table and tip be the total frequency in the pth row, n, in the gth column, tip, the frequency of the constituent common to the jrth row and gth column, N the total frequency dealt with in the table. Then it is known* that the total mean square contingency <£* of the table is given by: the sum being for all values of p and q. Let (^w be the contribution to p* be the contribution to * from a single row, and ^>, J from a single column, i.e. since Thus: and similarly:
more » ... s: and similarly: It follows that: Let us write Then: (v) (vi) We shall now proceed to find the probable error of » M . We state the following preliminary propositions t, where a denotes the standard deviation of random sampling: -\-.(viii) .
doi:10.1093/biomet/5.1-2.191 fatcat:yk5ab7nyibeljdkzvcguv7do3y