In setting the cut-scores on National Curriculum tests it is important to maintain standards. In the process of test development, both within and across years, changes are made to the style of the questions in order to increase their "accessibility". This raises the question of whether a more accessible test should have higher cut-scores. Purely statistical definitions of equating are blind to differences between "accessibility" and "easiness" and cut-scores derived from statistical equating methods will be higher for a more accessible test. Arguments about the increased validity of the more accessible test are sometimes used to justify not raising the cut-scores as much as would be indicated by statistical methods. These arguments are shown to be equivalent to postulating that changing the accessibility is changing the construct measured by the test. Using a statistical measurement model can provide a rational basis for understanding accessibility and identifying types of question where accessibility issues are causing a measurement problem.