[Comparison of several expressions of two-way ANOVA for a latent factor: analysis of the relation between music and mood]

The purpose of this research is to provide a two-way analysis of variance (ANOVA) model for a latent factor. Typical psychological studies measure mental states with questionnaires and analyze the variance of the measures into the portions attributable to various sources. This type of research, when conducted under regular ANOVA designs, uses total score as the dependent measures. However, this method is based on the unrealistic presumption that every item on the questionnaire has the same factor loading on the attribute being measured. In this research, we incorporated factor analysis model, and used a latent factor instead of total score as the dependent measure, thereby applying ANOVA under a more realistic assumption. Structural Equation Modeling (SEM) was used to express statistical models. This paper also examined a relation between music and mood, which is a quite popular area of research in psychology of music. To study the possible effects of tonality and key-signature on mood, music was chosen to represent tonality and key-signature conditions.