A Note on the Bias in the Multi-nomial Classification

다항분류상 편의에 관한 연구

If two inspectors classify items in a lot into m classes, it is possible that each of them makes wrong classification in some cases, thus causing bias. Expressions have been obtained for the limits of this bias in estimating the proportion of the different classes. From the results of the classification they obtained limit for the estimates of Proportions have been worked out, based on assumption regarding the magnitudes of probabilities of misclassification. Now we suppose that $P_{ti}{\;}(t=1.2)$ is the probability that t the inspector classifies correctly an item in class $A_i$ and $q_{tji}$ is the probability that he misclassifies in $A_j$ an item actually belonging to $A_i$, therefor, $P_{ti}+ \sum\limits_{j{\neq}i}q_{tji}=1$ An estimate for the proportion $P_k$ of the class $A_k$ in the lot would be $\hat{P}_k=r_{kk}+(\frac{1}{2})\sum\limits_{j{\neq}k}r_{kj}+r_{jk}$ The % Bias in proportion $\hat{P}_k$ is $\frac{E(\hat{P}_k)-P_k}{P_k}{\times}100$