To determine if a significant relationship exists between the conceptual systems of principals and academic achievement, nine hypotheses were formulated stating that there is no statistically significant relationship between student achievement and the complexity of school environment, emphasis on academic achievement, professional training levels, sex, age, and years of experience of principals, school size, location, and student expenditure with respect to the principal's conceptual system. Of 43 randomly selected principals in 9 school districts located in Harris and Fort Bend Counties in the metropolitan area of Houston, Texas, 40 participated in Paragraph Completion Method tests to determine their conceptual system. Academic Achievement at each school was determined by using the composite scores of the Iowa Tests of Basic Skills. An Analysis of Variance (ANOVA) was used to find any significance between the nine aforementioned variables and achievement. Based on the results, four of the nine hypotheses were not supported. Significant differences in achievement with respect to the principal's conceptual system were found in sex, school size, location, and student expenditure. Comprehensive explanations of procedures and results are included. (21 references) (EJS)