ANOVA is based on the law of total variance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation.
ænˈoʊvə ɪz bˈeɪst ɔnðə lˈɔː ʌv tˈoʊɾəl vˈɛɹiəns, wˌɛɹ ðɪ əbzˈɜːvd vˈɛɹiəns ɪn ɐ pɚtˈɪkjʊlɚ vˈɛɹɪəbəl ɪz pɑːɹtˈɪʃənd ˌɪntʊ kəmpˈoʊnənts ɐtɹˈɪbjuːɾəbəl tə dˈɪfɹənt sˈoːɹsᵻz ʌv vˌɛɹɪˈeɪʃən.