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

ANOVA (analysis of variance) in the quantum linguistic formulation of statistics