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This study has two principal aims. It explores the relationships between the results of various formats of paper-and-pencil classroom assessments of Chemistry. It also investigates the performance of pupils in different formats of assessment in relation to their cognitive style, personal preferences, and intellectual development. The study was conducted mainly in Greece with the participation of first year upper secondary public school pupils (Lykeio, Grade 10, age 15-16) in two stages. The convergent/divergent characteristic correlated with pupils’ performance in assessment where language was an important factor. However, in algorithmic type of questions or in questions where there is more use of symbols and less use of words, the convergent/divergent characteristic did not relate to pupils’ performance. The short answer or open ended questions favour divergent pupils more than objective questions because in short answer questions pupils need to articulate their thoughts, and divergent pupils were the ones more able to do it. In objective testing, if a question needs reading skill in order to elaborate and interpret a text given, then again the convergent/divergent style is a very important factor for success. It seems that, in relation to the convergent/divergent characteristic, the chemistry content is a factor affecting the type of questions being asked. Field independent pupils surpassed field dependent pupils in all the tests, and in almost all the formats of assessment. It seems that the field dependent/independent characteristic is a very important factor for pupils in order to perform well in almost all types of assessments, irrespective of the content of the question. The short answer questions favour more field independent pupils than the objective questions in some of the chemistry tests. It is a matter of concern that performance in a chemistry test is so strongly related to these particular psychological parameters, control over which is outside the individual pupil. This raises an important ethical issue about assessment. Are we testing chemical knowledge and understanding or cognition?