CHIS VQ11/ In an experiment to study the effect of different doses of vitamin C (0.100...

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CHIS VQ11/ In an experiment to study the effect of different doses of vitamin C (0.100 and 0.200 mg) on patients having cold flu, it's believed that the age of patients affects the recovery from the flu. If the dose is given to 3 patients, the results as follows: Syy = 1000.Sxy = 200,Sxx = 900, Eyy = 500, Exy = 200, Exx = 150 Test if there are differences between the 3 doses of vitamin C. Comment? 12 Analysis of Covariance for a Single-Factor Experiment with One Covariate Sums of Squares Adjusted for Regression and Products Source of Variation Degrees of Freedom x y y Degrees of Freedom Mean Square Treatments a-1 T TAV Tw Error a(n-1) E Ex E SSE = Eyy - (Ex)-IE. a(n-1)-1 MSE = SSE a(n-1)- Total an 1 Sxx SAY Syy SSE = Syy - (S)/Sxx an 2 SS-SSE SSE - SSE a-1 a-1 Adjusted Treatments Because of the presence of the covariate variable, we must adjust Syy and Eyy for the regression of y on x. If there were no concomitant variable, we would have Sxy = Sxx = Exy = Exx = 0. 9 Notation: S Pyy = a n an - - i=1 j=1 a Sxx a n Sxy Txy n = i=1 j=1 a n -x) = i=1 j=1 i=1 j=1 a n (xi) - x) (y ij - 1) = xijij i=1 j=1 = n Tyy = n Txx = n i=1 a i=1 a i=1 - = 1 i=1 j=1 a i=1 a i=1 a N x * ( xi. x.) (Ft. - v.) = = = xij vij - n i=1 y2 an an an an (x) (y.) an (x) (y..) an 10 an Eyy = (Vij Vi.) = Syy Tyy i=1 j=1 a n (xij - xi.) = Sxx - Txx Exx = i=1 a n Exy = (xij .)(Yij i.) = Sxy Txy i=1 j=1 - - CHIS VQ11/ In an experiment to study the effect of different doses of vitamin C (0.100 and 0.200 mg) on patients having cold flu, it's believed that the age of patients affects the recovery from the flu. If the dose is given to 3 patients, the results as follows: Syy = 1000.Sxy = 200,Sxx = 900, Eyy = 500, Exy = 200, Exx = 150 Test if there are differences between the 3 doses of vitamin C. Comment? 12 Analysis of Covariance for a Single-Factor Experiment with One Covariate Sums of Squares Adjusted for Regression and Products Source of Variation Degrees of Freedom x y y Degrees of Freedom Mean Square Treatments a-1 T TAV Tw Error a(n-1) E Ex E SSE = Eyy - (Ex)-IE. a(n-1)-1 MSE = SSE a(n-1)- Total an 1 Sxx SAY Syy SSE = Syy - (S)/Sxx an 2 SS-SSE SSE - SSE a-1 a-1 Adjusted Treatments Because of the presence of the covariate variable, we must adjust Syy and Eyy for the regression of y on x. If there were no concomitant variable, we would have Sxy = Sxx = Exy = Exx = 0. 9 Notation: S Pyy = a n an - - i=1 j=1 a Sxx a n Sxy Txy n = i=1 j=1 a n -x) = i=1 j=1 i=1 j=1 a n (xi) - x) (y ij - 1) = xijij i=1 j=1 = n Tyy = n Txx = n i=1 a i=1 a i=1 - = 1 i=1 j=1 a i=1 a i=1 a N x * ( xi. x.) (Ft. - v.) = = = xij vij - n i=1 y2 an an an an (x) (y.) an (x) (y..) an 10 an Eyy = (Vij Vi.) = Syy Tyy i=1 j=1 a n (xij - xi.) = Sxx - Txx Exx = i=1 a n Exy = (xij .)(Yij i.) = Sxy Txy i=1 j=1 - -