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For isolated word recognisers   , we can define a more specific measure than the various contributions to the error rate  alone. The class of substitution s can be divided into all possible confusions between words. The confusion tex2html_wrap_inline46759 is defined as the probability that word i is recognised as word j. (Incidentally, the value tex2html_wrap_inline46765 is the fraction of times word i is correctly recognised.) These probabilities can be estimated from a large test sample in the same manner the basic error rates  are measured, by measuring the number of times the confusion took place:
where tex2html_wrap_inline46769 is the number of times word j was recognised on the input word i.

The confusion matrix  gives more detailed information than the error rates , but has much worse statistics, as the numbers involved are normally low. If we want to include insertions  and deletion s in this matrix, a null word i=0 should be added (formally not in the vocabulary ), so that the row tex2html_wrap_inline46777 contains false alarms , the column tex2html_wrap_inline46779 the deletions,   and tex2html_wrap_inline46781. From this expanded confusion matrix , the error rate  can be calculated from the diagonal of the matrix, i.e. tex2html_wrap_inline46783. The elements tex2html_wrap_inline46759 for tex2html_wrap_inline46787 are called the off-diagonal elements .  

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