This study investigates error sources and the effects of each error source to determine optimal weights of the composite score of teacher recommendation letters and self-introduction letters using multivariate generalizability theory. Data were collected from the science education institute for the gifted attached to the university located within in a capital city in Korea. The results were as follows. First, error sources for the students were relatively large suggesting that the score variances explained the differences in giftedness among the students. Second, based on the maximum generalizability coefficient for teacher recommendation letters and self-introduction letters, the optimal weight ratio should adjust to 0.7:0.3 from 0.5:0.5 in the original institution weights. These results are specific to the selection assessment instruments considered in this study; however, the methodology applied can be utilized in other selection instruments developed by many institutions.