교육연구에 있어서 분산분석의 일반적 적용에 관한 연구 = A Study of the General Application of Analysis of Variance for Educational Research

다국어 초록 (Multilingual Abstract)

The major purpose of this study is to explain the general cases of two way analysis of variances with unbalanced cell size and/or missing cells. In the statistical text book contains only special cases of a research, for example, which all research group sizes are equal. Of course, in that cases all computational procedures can be performed manually. But in the real data from research field, the data for ANOVA are not balanced. Hence it is extremely difficult to compute statistics by hand. Of course, SPSS or SAS, a famous commercial statistical packages, can easily compute the statistics but the algorithm is not easy for social scientist, who are not familiar with mathematics or statistics, to understand. Therefore, the general cases of ANOVA can be explained by GLM (General Linear Model) effectively. There are three different examples were utilized: (1) balanced, (2) unbalanced and (3) unbalanced with missing cell. Each example contains a fictitious data set, matrix notations and step by step computational procedure. Based on the GLM algorithms, a FORTRAN program were made for the analysis of some general cases of ANOVA. And this research can be extended the multivariate analysis of variance.