ASSESSMENT OF NON-NORMALITY IN PRETEST-POSTTEST RESEARCH UNDER SCREENING OF THE PRETEST SCORE

• Published in: Journal of the Japanese Society of Computational Statistics Vol. 21; no. 1; pp. 31 - 44
• Main Authors: Iwasaki, Manabu, Kawata, Yuichi
• Format: Journal Article
• Language: English
• Published: Japanese Society of Computational Statistics 2008; 日本計算機統計学会
• Subjects: Bivariate normal distribution; Kullback-Leibler divergence; Kurtosis; Screening; Skewness
• ISSN: 0915-2350; 1881-1337
• DOI: 10.5183/jjscs1988.21.31

Pretest-posttest research designs are frequently employed in various research fields to eliminate individual variability so as to precisely assess treatment effects. In pretest-posttest designs, screening is often performed on the baseline values to determine whether subjects are to be enrolled to the study. To assess the effectiveness of the treatment considered, the t test or the analysis of variance is often employed. Such procedures require normality of the underlying distribution. Even if the pretest and posttest scores jointly follow a bivariate normal distribution, screening of the pretest score will unquestionably depart from the normality assumption. Little research, however, has been done to assess the extent of non-normality under such a situation. The present paper examines the extent of non-normality caused by screening of the pretest scores. Under a bivariate normal distribution for pretest and posttest scores, the degree of departure from normality is assessed in terms of Kullback-Leibler divergence, skewness, and kurtosis of distributions for several types of screening schemes. Situations of maximum departure from normality will be identified. It is shown that, even at such a maximum departure from normality, the extent of departure is not so large, and hence our use of the t test and the analysis of variance can be validated from the viewpoint of robustness.