Cognitive diagnostic assessment (CDA) is a new theoretical framework for psychological and educational testing that is designed to provide detailed information about examinees' strengths and weaknesses in specific knowledge structures and processing skills. During the last three decades, more than a dozen psychometric models have been developed for CDA, which are also called cognitive diagnosis models (CDM). Although they have successfully provided useful diagnostic information about the examinee, most CDMs are complex due to a large number of parameters in proportion to the number of skills (attributes) to be measured in an item. The large number of parameters causes heavy computational demands for the estimation. Also, a variety of specific software applications is needed depending on the chosen models. Purpose of this study was to propose a simple and effective method for CDA without heavy computational demand using a user-friendly software application. Bayesian inference for binomial proportion (BIBP) was applied to CDA because of the following fact: When we have binomial observations such as item responses (right/wrong), using a" beta" distribution as a prior of a parameter to estimate (i.e., attribute-mastery probability) makes it very simple to find the "beta" posterior of the parameter without any integration. The application of BIBP to CDA can be flexible depending on the test item-attribute design and examinees' attribute-mastery patterns. In this study, effective ways of applying the BIBP method was explored using real data studies and simulation studies. Also, other preexisting diagnosis models such as DINA and LCDM were compared to the BIBP method in their diagnosis results. In real data studies, the BIBP method was applied to a test data using two different item designs: four and ten attributes. Also, the BIBP method was compared with DINA and LCDM in their diagnosis result using the same four-attribute data set. There were slight differences in the attribute mastery probability estimate ([Special characters omitted.]) among the three model (DINA, LCDM, BIBP), which could result in different diagnosis results for attribute mastery pattern (alpha[subscript k]). Simulation studies were conducted to (1) evaluate general accuracy of the BIBP parameter estimation, (2) examinee the impact of various factors such as attribute correlation (no, low, medium, and high), attribute difficulty (easy, medium, and hard) and sample size (100, 300, and 500) on the consistency of the parameter estimation of BIBP, and (3) compare the BIBP method with the DINA model in the accuracy of recovering true parameters. It was found that the general accuracy of the BIBP method in the true parameter estimation was relatively high. The DINA estimation showed slightly higher overall correct classification rate but the bigger overall biases and estimation errors than the BIBP estimation. The three simulation variables (Attribute Correlation, Attribute Difficulty, and Sample Size) showed significant impacts on the parameter estimations of both models. However, they affected differently the two models: Harder attributes showed the higher accuracy of attribute mastery classification in the BIBP estimation whereas easier attributes were associated with the higher accuracy of the DINA estimation. In conclusion, BIBP appears an effective method for CDA with the advantage of easy and fast computation and a relatively high accuracy of parameter estimation. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]