Abstract ] [ Lawley Hotelling Trace).statigraph. Hotel ling s trace

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1 (( )) 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.

2 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

3 Univariate. ( ) Multivariate ) :-3. ( :-4 B -. - ( / ). -3 ( / ) A ( / ) ].[( / ) -: :- ( ) (GLM _ ANOVA) : (Categories) (Assignable Factors) ( ) ( ) [3]. F ( Post-hoc). [8] -: ( Cross) : 3

4 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

5 N ( µ σ ) e ij ~ NID (0 σ Y ij 's ). (e (i) j ) ( t i ) : - : E (i)j 's : ( 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

6 e h.( Hotelling) :-3.. =.. E. [9]. ( Seber 984. [5] H P ) : -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

7 g = ( Ph - ) [( p h 4) ( p + h -5)] if p + h -5 > o t = other wise. h p : ( Pillai's Trace ) : : 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 : : T g 3 s T g = e j= φ j S = min ( P, h ) -: F F a, b = T g c e 7

8 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 Intercept CLASSES PERIODS CLASSES* PERIODS ERROR Total Corrected Total R Square = 0.74 (Adjusted R Square = o.8 ) 8

9 (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 Intercept CLASSES PERIODS CLASSES* PERIODS ERROR Total Corrected Total 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 Intercept CLASSES PERIODS CLASSES* PERIODS ERROR Total Corrected Total R Square = 0.08 (Adjusted R Square = o.059 ) 9

10 (Periods) (Classes ). / Multivariate MANOVA : : ) []. / (6) : ( / / (Hotelling Trace :(6). - - (Hotelling Trace ) ) Effect Value F Hypothesis Error Sig. d.f. d.f. Intercept Classes Periods Interaction (Periods) ( Classes ). S.O.V. ANOVA. : :(7) ANOVA ANOVA MANOVA Classes Periods Interaction

11 )) ((. :5 )) (( )). (( Reference. B. j. Winer ( 97). Statistical Principles in Experimental Design Second Edition. McGraw Hill.. D.C. Montgomery (99).Design and Analysis of Experiment, Third Edition. john Wiley & Sone. 3. D. Morrison ( 967). Multivariate Statistical Methods McGraw Hill. 4. J.C. Hsu (996). Multiple Comparisons, Theory and methods. Chapman & Hall. 5. Jerry L. Hintze, Kaysville, Utah Copyright (007). Published by NCSS, NCSS help System. 6. Lawson, john. (987). Basic Industrial Experimental Design Strategies Center for Statistical. 7. R. Johnson and D. Wichern (99). Applied Multivariate Statistical Methods, Third Edition.. Prentice Hall. 8. Scheffe, H. (959) The Analysis of Variance. Wiley, New York. 9. Seber, G.A.F.(984) Multivariate Observations. John Wiley & Sone. New York. 0. S.R. Searle, G. Casella, and C.E. McCulloch (99). Variance Components. John Wiley & Sone.. Y. HOCHBERG and A.C. Tamhane (987). Multiple Comparison Procedures. John Wiley & Sone.

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