The Research About Influencing Factors Of Using Estimation Formula To Estimate Variance Compoents Under Sparse Data Matrix

China has always been a country of test since ancient times. There exists a variety of tests at present, which we can meet in different situations such as getting employed, having a promotion or getting a qualification certificate. As we all know, college entrance test is most focused because it can determine numbers of students' fate. So it is worthy to research and control its fairness and accuracy. Among the numerous methods, Generalizability Theory(be called GT for short) can provide a better optimization and prediction.GT, proposed by Cronbach,Gleser and Rajaranam in 1963, is one of three modern test theories of psychology and education. It can be applied to analyze different fields of test, such as test content, test reliability and talent assessment, etc. GT is based on the random sampling which is also the foundation of the classical test theory(CTT). CTT can only provide a general error for each test, while GT can decompose the error of a test, find out different sources of error and calculate the value of different errors. In this way not only can we get the generalizability coefficient and reliability coefficient, also we can change the initial measure design according to our research purposes, thus having optimization and prediction for a test. Therefore, GT is more suitable for the analysis of educational tests and talent assessments and it is getting more and more attention. But the current data analysis softwares, such as GENOVA and mGENOVA cannot directly handle sparse datas, which include missing data. To solve this issue, the author derived the estimation formulas for estimating variance components of sparse data matrixs under p*r*i two facets crossed design, which were based on the formula method proposed by Brennan (2001). Later the author discussed various factors that influence the estimation precision of variance components.The results of this research are listed below:1. The derived estimation formulas can give a better estimation for variance components of sparse data.2. Main effects of sparse structure(S), examinee quantity(P), item quantity(I), and variance components(VC) can reach statistical significance. Twice interaction effects of P*S,I*S,I*VC and S*VC can reach statistical significance. Triple interaction effect of I*S*VC can reach statistical significance.3. The factor that had greatest impact on estimation precision is item quantity.4. Estimation formulas have their applicative limitation.