Exact tests for some latent traits

Item response theory is one of the modern test theory with many applications in the educational and psychological testing field. Recent developments made it possible to characterize some desired latent properties in terms of a collection of manifest ones, so that hypothesis tests on these latent traits can, in principle, be performed. But the existing test methodology is based on asymptotic approximation, which is impractical in most applications since the required sample sizes are often unrealistically huge. In this paper, we study a class of tests for making exact statistical inference about four manifest properties (CSN, MM, CA, and VCD). One major advantage is that these exact tests do not require large sample sizes and hence can be routinely adopted in empirical studies. Some numerical examples with applications of the exact tests are also provided.