© 2018, Springer Nature B.V. Analysis of variance (ANOVA) is tailored for independent observations. Recently, there has been considerable demand for ANOVA of high-dimensional and dependent observations in many fields. For example, it is important to analyze differences among industry averages of financial data. However, ANOVA for these types of observations has been inadequately developed. In this paper, we thus present a study of ANOVA for high-dimensional and dependent observations. Specifically, we present the asymptotics of classical test statistics proposed for independent observations and provide a sufficient condition for them to be asymptotically normal. Numerical examples for simulated and radioactive data are presented as applications of these results.