The Use of Within-Group Slopes as Indices of Group Outcomes

The possibilities and problems in th euse of within-group slopes of outcomes on inputs as indicators of substantive group effects are considered. Slopes are proposed as outcome measures which may reflect within-group processes in between-group analyses of multilevel data. Research on aptitude × treatment interactions, contextual effects and school effects provide a theoretical rationale for the proposed methodology. Data from the IEA Six Subject Survey are used to illustrate how a group-level analysis with slopes as outcomes might look. Finally, the statistical, empirical, substantive, and communication problems that arise from the use of slopes as outcomes are discussed.