Student Placement Utilizing Incomplete Data Records

Abstract

A method is proposed for the construction of a classification rule based on both complete and incomplete data records. This method incorporates the Hocking-Smith estimation procedure to find estimates of the mean vectors and variance-covariance matrices from samples which may contain incomplete data vectors. The resulting estimates are used to construct a discriminant function. We will demonstrate that these incomplete observation vectors contain information relevant to classification and should not be discarded. The proposed method is applied to the placement of students into one of two college algebra courses at Tarleton State University. The standard procedure that ignores incomplete observation vectors in the construction of a classification rule is also applied to the same data, and comparisons are made between the two methods. The proposed method that utilizes the incomplete observation vectors correctly classifies a higher percentage of students than does the standard method.EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT 1978, 38 RECENT research has been conducted on prediction of success in first year college mathematics courses. The majority of the research concerns itself with the relationships between success in first year college mathematics and indicators of prior attainment, e.g., high school grades, placement tests, various achievement tests, psychological-type tests, and attitude test scores (or a combination of these variables).Discriminant analysis is a statistical technique that has been beneficial in classification of students as potentially &dquo;successful&dquo; or &dquo;unsuccessful&dquo; in mathematics courses. For example, Morgan (1970) uses the