An Application of Generalizability Theory to Self-introduction Letter and Teacher's Recommendation Letter Used in Identification of Mathematical Gifted Students by Observations and Nominations

Abstract

The purpose of this study is: 1) to determine error sources and the effects of each error source, 2) to investigate optimal measuring conditions from holistic and analytic scoring methods, and 3) to compare the value of reliability between Cronbach's alpha and the generalizability coefficient in self-introduction letter and teacher's recommendation letter based on the generalizability theory in identification of mathematical gifted students by observations and nominations. Data of this study were collected from the science education institute for the gifted attached to the university located within in a capital city for the 2011 academic year. Scores form two raters using holistic and analytic scoring methods in both assessment types were used. The results of this study were as follows. First, as to both assessment types, error sources for people were relatively large regardless of scoring methods. However, error sources for raters in holistic scoring methods had a more significant impact than those of analytic scoring methods. Second, to set optimal measuring conditions in the self-introduction letter and teacher's recommendation letter, if we fixed the number of raters into 2 based on holistic scoring methods, at least 5 and 10 content domains were needed, respectively. In addition, the number of items in teacher's recommendation letter should be more than 3 when we fixed the number of content domains into 4, and the number of items in self-introduction letter should be more than 8 when we fixed the number of content domains into 6 using analytic scoring methods. Third, Cronbach's alpha having only a single source of errors was higher than the generalizability coefficient regardless of assessment types and scoring methods. Hence we recommend that generalizability coefficient based on various error sources such as raters, content domains, and items should be considered to keep a satisfactory level of reliability in both assessment types.