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The least squares distance method of cognitive diagnosis (LSDM; Dimitrov, 2007; Dimitrov & Atanasov, 2012) provides information about the probabilities for correct processing of cognitive attributes that govern the responses of examinees on test items given the examinees’ locations on the IRT logit scale. The input for using the LSDM are estimates of item parameters obtained through an appropriate IRT or Rasch calibration. This study offers an approach to testing for differential functioning of cognitive attributes and comparison of groups on their performance on cognitive attributes in the framework of the LSDM. Applications of the proposed approach can provide useful feedback to educators for cognitive-based learning, curriculum development and assessment.