The Use of Orthogonal Polynomials for Trend Analysis

One of the methods of data analysis available to educational researchers and psychologists is trend analysis within the statistical framework of analysis of variance. In particular, if the set of treatments administered to different groups of subjects can be ordered along a continuum by means of a numerical measure, it may be substantively important to investigate the exact trend or relationship between this measure and the dependent variable. A typical example would be in experimentally manipulating the amount of study time on a particular topic and measuring the effect on retention. Within a larger context the discussion given below can be related directly to Mood's article (1971) on partitioning variance in regression models, even though the problem mentioned here is much more narrowly defined; some of the same concerns of orthogonality that arise in his presentation are relevant here as well.