A Brief Report on How Impossible Scores Affect Smoothing and Equating

Abstract

Equating under the external anchor design is frequently conducted using scaled scores on the anchor test. However, scaled scores often lead to the unique problem of creating zero frequencies in the score distribution because there may not always be a one-to-one correspondence between raw and scaled scores. For example, raw scores of 17 and 18 may correspond to scaled scores of 150 and 153, thereby creating zero frequencies for scaled scores of 151 and 152. These gaps in the frequency distribution may adversely affect smoothing and equating. This study examines the effect of these zero frequencies on log-linear smoothing of score distributions and final equating results. Results suggest that although smoothing is significantly affected by the presence of these zero frequencies, the impact on the actual equating results is minimal.