Testing Independence in Two-Way Contingency Tables with Data Subject to Misclassification

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Abstract
The misclassification process is represented by a stochastic matrix containing the probabilities that an individual who belongs in one cell is counted as belonging to another (or perhaps the same) cell. These probabilities are supposed known. If misclassification in the row direction is independent of that along the column variable then the size of the usual chi-square test is unchanged. It is shown how to calculate loss of power in this case and also how to calculate the change in size of the test if the errors are not independent. A modified test criterion is suggested when errors are not independent and a numerical example is included.