(( )) Analysis of variance of the model general linear multivariate approved ((form balanced)) error retailers analyze the contrast of the model general linear single variable-based.. /... / / ] B ( / ) A ( / ) [ ( / ) ( / ) /. ( ). ( ) Pillais trace, Wilkes Lambda, ) Hotel ling s trace Lawley Hotelling Trace).statigraph " Abstract " Collected data from panels agricultural pilot in the Faculty of Agriculture - University of Baghdad singled to study two types of fertilizer, measured (Tun / h) represents the first factor A, and the measurement (kg / h) and a second factor B, and predict [ number of plants - measured Weight (Ton / h) - Weight (kg / h)], was conducted from the Factor experience of grades ( staff ) and three dates and four replications.
The research aims to diagnose an error in the retail phenomena, multidimensional analysis of variables based general linear model-based single - variable and vice versa. The theoretical side of the single-variable analysis of variance theory based (the balanced design) with repeaters, and multivariate analysis of variance-based methods (Wilkes Lambda, Pillais trace, Lawley Hotelling Trace) and has been approved method of (Hotel ling's trace) in the application by statigraph program. The results of tests of the moral influence of workers and their interaction at different levels of confidence between single and multiple, which requires a formula to make sure the design data according to the fractional began phenomenon as the "choice based on the assumption of the wrong statistical method in accordance with the requirements of practical. : :- ( ANOVA) ( Random) (Fixed) (GLM) ( Mixed ) (GLM _ Univariate Procedure) ( Blanced ) ( Contrast) ( Interaction) GLM-Multivariate ) ( ". Procedure []. " :- " ( Scalar) []. σ
Univariate. ( ) Multivariate ) :-3. ( :-4 B -. - ( / ). -3 ( / ) A ( / ) ].[( / ) -: :- ( ) (GLM _ ANOVA) : (Categories) (Assignable Factors) ( ) ( ) [3]. F ( Post-hoc). [8] -: ( Cross) : 3
Y ijk = µ + α i + β j + (α β ) ij + e (ij)k.. () i =,,, r j =,,..., s k=,,..., n -: y :. i α. j µ : i α β : j β. β j α i : ) ij β α ( [6] -: Y ijk = µ + α i + β (i)j + e (ij)k.. (). k : e (ij)k ( Nested) S. O. V. (α ) ( β ) :() Expected Mean Squares for Cross-Classified Models for Blanked Data :. d.f. MS Fixed E(MS) Effects Random Effects (α Fixed,β Random)* α r- MSα σ + α i sn να r i= s σ +nσ αβ + r α i sn να i= σ +nσ αβ +snσ α β s- MSβ σ + βj rn νβ σ +rn σ β νσ +n σ α β +rn σ β j= αβ (r-)(s-) MSαβ σ + n e rs(n-) r i= s j= ( αβ) ij ναβ σ + n σ αβ σ + n σ αβ MSe σ σ σ for α Random and β Fixed the term ( nσ αβ ) appears in E(MSβ ) but in E((MSα ). See Hocking (973)and Kim and Carter (973)for distribution of controversy on this point. 4
N ( µ σ ) e ij ~ NID (0 σ Y ij 's ). (e (i) j ) ( t i ) : - : E (i)j 's - - -3 -: ( GLM-MANOVA) :... ( Scalar) ( SSCP) Sum Square for Cross Product [0]. [4] -: () Expected Mean Squares table (MANOVA) ( Cross) S.O.V. d.f. S.S. M.S. E(M.S.) Term ab- S.S t S.S t / ab- σ + n (y ij ÿ) / ab- iα a- S.Sa S.Sa/ a- σ + nb A i /a- jβ b- S.Sb S.Sb/ b- σ + na Bj / b- ijαβ ( a-)( b-) S.Sab S.Sab/( a-)( b-) σ + n(ab ij ) /(a-)(b-) )αβ S( ab(n-) S.Sw SSw/ ab(n-) σ ε Note: Expect Mean Squares for the Balanced Frequency Case. F (Lawley ( Pillai's trace) (Wilkes Lambda). Hotelling's trace). F 5
e h.( Hotelling) :-3.. =.. E. [9]. ( Seber 984. [5] H P ) - - -3-4 : -4 E H E( E + H ) H E H ( E + H ) λ i φ i -: θ i = - λ i = φ i ( + φ i ) ϑ i ø i = θ i - θ i = - λ i λ i λ i = - θ i = ( + ø i ) ( Wilk's Lambda ) :- 4- -: Λ P, h,e = E E + H p = ( ϑj) j= : e p : F F Ph, f t-g = ( ft g )( Λ / t ) f = e / ( p h + ) Ρ h Λ / t : 6
g = ( Ph - ) [( p h 4) ( p + h -5)] if p + h -5 > o t = other wise. h p : ( Pillai's Trace ) :- 4 - -: s ν (s) ( Pillai's Trace ) ν (s) = ϑ j = tr [ H (E + H ) - ] j= S = min ( p,h). F F s (m + S + ), s (m + S + ) = ( n + S + ) ν (s) (m + S + )(s- ν (s) ) S= min (P,h) m = ( P h - ) n = ( e p ) : Lawley Hotelling Trace :- 4 - -: T g 3 s T g = e j= φ j S = min ( P, h ) -: F F a, b = T g c e 7
a = P h b = 4 + ( a + ) ( B ) c = a ( b ) b ( e P ) B = ( e + h P ) ( e ) ( e P 3 ) ( e P ) Application : :3 - ( ) ( / ) A ( / ) ( / ) ] B. [( / ) + A ) [7]. ( B. Classes) : :4 Univariate ANOVA : : / (3) (Periods* Classes) (Periods) /. ( Test between subjects effect :(3) S.O.V. Type ш Sum df Mean F Sig. of Squares Square Corrected Model 57.39 5.478 3.790.004 Intercept 67.460 67.460 0.944.000 CLASSES 3.94 3.94.30 0.57 PERIODS 0.4 0.07 0.068 0.934 CLASSES* PERIODS 5.80 6.4 8.76 0.000 ERROR 7.6 90 3.09 Total 647.00 96 Corrected Total 330.00 95 R Square = 0.74 (Adjusted R Square = o.8 ) 8
(Periods) (Class). ( / ) : (4) (Periods* Classes) ( Classes ) (Periods). ( Test between subjects effect / ) :(4) S.O.V. Type ш Sum df Mean F Sig. of Squares Square Corrected Model 3.069 5 0.64.970 0.06 Intercept 446.606 446.606 60.543 0.000 CLASSES.4.4 6.004 0.06 PERIODS.5 0.608.940 0.053 CLASSES* PERIODS 0.6 0.306.480 0.33 ERROR 8.604 90 0.07 Total 469.303 96 Corrected Total.673 95 R Square = 0.74 (Adjusted R Square = o.094 ) (Periods) (Classes ). ( / ) : (5) (Periods* Classes) ( Classes ) (Periods). ( Test between subjects effect / ) :(5) S.O.V. Type ш Sum df Mean F Sig. of Squares Square Corrected Model 8645497.08 5 79099.46.88 0.06 Intercept 836087. 836087. 958.68 0.000 CLASSES 4036734.4 4036734.4 5.09 0.06 PERIODS 785059.9 869997.433.0 0.337 CLASSES* PERIODS 785059.9 3959.966.76 ERROR 794.6 90 790.696 Total 968370.5 96 Corrected Total 79756539.7 95 R Square = 0.08 (Adjusted R Square = o.059 ) 9
(Periods) (Classes ). / Multivariate MANOVA : : ) []. / (6) : ( / / (Hotelling Trace :(6). - - (Hotelling Trace ) ) Effect Value F Hypothesis Error Sig. d.f. d.f. Intercept 44.893 36.875 3 88 0.000 Classes 0.6 3.698 3 88 0.05 Periods 0.04.50 6 74 0.80 Interaction 0.54 3.689 6 74 0.00 (Periods) ( Classes ). S.O.V. ANOVA. : :(7) ANOVA ANOVA MANOVA Classes 0.57 0.06 0.06 0.05 Periods 0.934 0.053 0.337 0.80 Interaction 0.000 0.33 0.77 0.00 0
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