The number of degrees of freedom DF can be partitioned in a similar way: one of these components (that for error) specifies a chi-squared distribution which describes the associated sum of squares, while the same is true for "treatments" if there is no treatment effect.
ðə nˈʌmbɚɹ ʌv dᵻɡɹˈiːz ʌv fɹˈiːdəm dˌiːˈɛf kæn biː pɑːɹtˈɪʃənd ɪn ɐ sˈɪmɪlɚ wˈeɪ: wˈʌn ʌv ðiːz kəmpˈoʊnənts ðæt fɔːɹ ˈɛɹɚ spˈɛsᵻfˌaɪz ɐ kˈaɪskwˈɛɹd dˌɪstɹɪbjˈuːʃən wˌɪtʃ dᵻskɹˈaɪbz ðɪ ɐsˈoʊsɪˌeɪɾᵻd sˈʌm ʌv skwˈɛɹz, wˌaɪl ðə sˈeɪm ɪz tɹˈuː fɔːɹ "tɹˈiːtmənts" ɪf ðɛɹ ɪz nˈoʊ tɹˈiːtmənt ɪfˈɛkt.