10.6 \(2\times 2\) Contingency Table in Principle

The table below is similar to the Table 1 in Matthew and Sandip (2018), which plays a key role in estimating classification accuracy.

\(p_{00}\) is the probability that a randomly selected student who does not master attribute \(k\) is estimated to be absence of attribute \(k\) given his or her responses \(Y\).

\(p_{11}\) is the probabbility that a randomy selected student who has attribute \(k\) is estimated to master attribute \(k\) given his or her responses \(Y\).

More generally, we have

\(P_{ab}= P(\alpha_k = a, \hat{\alpha}_k=b)\)

This is for a single attribute and it is clear that the accuracy can be calculated as \(p_{00}+p_{11}\).