Determining School Effectiveness Following a Regression Analysis

Abstract

Three methods that can be used subsequent to a regression analysis to determine the relative effectiveness of schools are Dyer’s performance indicators (PIs), Scheffé’s hyperbolic confidence bands, and Gafarian’s linear confidence bands. The purpose of this paper is to investigate the relative usefulness of the three methods under various conditions. The three methods were applied to hypothetical data from 54 schools randomly generated from a multivariate normal distribution using parameters from previous studies. Data points having PIs of 1 and 5 generally fell outside of the Scheffé confidence bands. The linear confidence bands were much wider than the Scheffé bands near the mean and slightly narrower at the extremes. The results indicated that extreme PIs seem to be appropriate for identifying schools which are achieving above and below expectation. Fine discriminations using PIs as defined by Dyer may not be warranted. Gafarian bands tend to be so wide as to limit their applicability to most settings. The choice of a particular technique to determine school effectiveness is dictated somewhat by the intent of the investigator. A conservative strategy would dictate employing the Scheffé technique with high confidence levels or adopting a decision rule of a difference of four PIs between two schools. Use of lower confidence levels or less stringent differences in PIs would result in a more liberal strategy.