The research has included 96 Roma elementary-school pupils from the first grade, 7 years and 6 months old on average, and 78 pre-school children, (6 years and 1 month old on average), out of which number there were 37 Roma pupils and 41 non-Roma pupils. The cognitive functioning has been tested with a battery consisted of 5 tests, which was based on the (adapted) Wechsler’s scales and the linguistic competence test. The results have shown a significant lagging of Roma children behind the control group and test norms. The Analyses of Covariance have pointed to a significant influence of the father’s educational background on the test score, but the difference between groups remained notable even when that variable was kept under control. However, the Item Analyses revealed a number of items that turned out to be evidently "unfair" toward Roma children, and their elimination contributed to the annulling of differences among groups in the Analyses of Covariance for a particular number of tests. The data has been interpreted by the authors as a proof of necessity and possibility to adapt tests for the needs of testing the educationally neglected children. The fact that the greatest differences have been noticed in the tests saturated with the factors of visual-motor coordination and memory has been justified by the authors with the Roma children’s lack of experience of manipulation with toys and possible attention deficit as a consequence of absence of stimulative environment.