中文摘要：

通常认为由属性和项目关联阵（即Q矩阵）的列对应的项目充任认知诊断测验中行为样本,其实这种做法不能有效防止理想反应模式的误判。如在测验之前便可确定欲测之属性及层级关系,找到可达阵,可证明可达阵的各个列对应的项目类在认知诊断测验中必不可少,否则在理想反应模式下就一定有一些被试会被误判。本文给出充分必要Q矩阵的概念,以区别Tatsuoka（1995,2009）讨论过的充分Q矩阵概念。充分必要Q矩阵才能有效指导测验的编制。

英文摘要：

Researchers such as Tatsuoka,Leighton and Gierl,just to name a few,maintain that the Qr matrix can be interpreted as a cognitive blueprint or cognitive test specification.But when there are so many attributes involved in the diagnostic test and their dependence is weaker,the number of the columns in Qr matrix is too large to be included in the test blueprint.Tatsuoka pointed out that it is clear that a set of attribute mastery patterns（knowledge states） and a set of ideal item-response patterns do not have a one-to-one correspondence.Several attribute-mastery patterns correspond to a single ideal item-response pattern.If a knowledge state corresponds to an ideal response pattern,the knowledge state is grouped into an equivalent class.If several attribute-mastery patterns correspond to a single ideal item-response pattern,it is called the mismatch of the attribute mastery pattern,and is harmful to classification accuracy.Some researches noticed this phenomenon,but found no effective solution to it. In this paper a theorem on the design of cognitive diagnostic test blueprints is listed as follows.As suggested by Leighton and Gierl,a clear exploration of the attributes and their hierarchy has to be done according to the logical order of design before the formation of cognitive diagnostic tests.Only under the condition of one bijective between the set of knowledge states and the set of ideal response patterns can the test specification（Q matrix） contain all columns of the reachabliity matrix.This is benefitial to the construct of tests for the cognitive diagnosis purpose.There are some examples to explain the theorem.A Monte Carlo simulation study is implemented and the results strongly support the theorem. This theorem for developing cognitive diagnostic tests could be applied to the construct of the item selection strategy of computerized adaptive testing with cognitive diagnosis（CD-CAT） and employed to guide the construct of an item pool for cognitive diagnostic tests.