  Recently, we proposed quantum language (or, measurement theory), which is
characterized as the linguistic turn of the Copenhagen interpretation of
quantum mechanics. We believe that this language has a great powet of
description, and therefore, even statistics can be described by quantum
language. In this paper, we show that ANOVA (analysis of variance (one-way and
two-way)) can be formulated in quantum language. Since quantum language is
suited for theoretical arguments, we believe that our results are visible and
understandable. For example, we can answer the question "What kind of role does
Kolmogorov's probability theory play in ANOVA?" That is, the readers find that
Kolmogorov's probability theory is merely used in order to calculate
multi-dimenstional Gauss integrals, and thus, they can avoid to confuse the
relation between Kolmogorov's probability theory and statistics.
