Prediction is Not the Only Measure of a Plan: A Response to Marston

Abstract

Prediction Is Not the Only Measure of a Plan: A Response to Marston Recently Marston (1988) attempted to demonstrate the predictive usefulness of two graphing methods, arithmetic and logarithmic, in helping practitioners choose the most technically adequate graph for measuring progress on individual educational plans (IEPs). Marston analyzed each charting procedure in terms of its predictive accuracy at various points in time. Specifically, Marston obtained various 1-minute (min) timed performance measures of reading and written expression (words read correctly, incorrectly, and words written correctly and incorrectly) of 83 low-achieving students in Grades 3-6. Data were collected weekly for 10 weeks; and, using computer simulation, after 7 weeks, regression equations were determined for each measure. Subsequently, the slope of each student's performance over the initial 7-week period was used to predict performance in terms of expected frequencies at Weeks 8, 9, and 10. Slopes were calculated using simulated charting on equal-interval and semilogarithmic graphs. Deviations between students' actual performance and predicted performance for each type of chart were determined. Results indicated statistically significant differences favoring the equal-interval scale on a number of comparisons made at Weeks 8, 9, and 10. Marston found that the equal-interval chart produced more accurate predictions than did the logarithmic chart (specifically, the Standard Behavior Chart [Pennypacker, Koenig, & Lindsley, 1972]). Marston asserted that the likelihood of using repeated measurement for educational planning, for interventions, and for assessments by special educators may be related to teacher graph preference. He concluded that the research favoring equal-interval graphs provides an empirical basis for making the appropriate choice of graphs. We believe that Marston has unfairly dismissed the usefulness of the Standard Behavior Chart (SBC) as a technically adequate measurement tool. This article provides discussion of conceptual and practical issues raised by Marston's study. These issues require attention when practitioners consider the adequacy of a particular graphing approach. CONCEPTUAL ISSUES Importance of the Predictive Function According to Marston, proponents of the SBC have maintained that a significant characteristic of the chart is the ability to better predict student performance. Regarding the trend line or slope used for prediction, White and Haring (1980) stated, The real purpose of the line is to provide a basis for timely program change decisions (p. 259). marston asserts that a significant characteristic of the chart, according to SBC proponents, is its better prediction of student performance. This assertion is an overstatement. Actually, proponents more often list as advantages the SBC's consistent and orderly display of data, the extended range of the chart's scale (permitting a wide range of behaviors to be recorded>, and the use of a real time (calendar day) X axis (an improvement over informal graphs that display data by sessions only) (White, 1986; White & Haring, 1980). Marston appears to be concerned about the capability of various charts to produce the most exact prediction, and he feels that the acid test is a minimal degree of error in prediction. An important parameter of prediction, however, is the degree of confidence that one has about the prediction. Predicting future student performance from current performance data is impossible to do with great precision. Consequently, teachers trained to use the SBC attempt to establish range of days within which a predicted value can be expected to occur with some degree of confidence. This is done by drawing lines above and below the data display, parallel with the trend line that has already been drawn centrally through the data points. These parallel lines border the data at the lower and uppermost boundaries. …