DESIGN AND STATISTICAL ANALYSIS OF SCIENTIFIC EXPERIMENTS : Email: falnakhlawi@kau.edu.sa ( or) dr_nakhlawy@hotmail.comwww.kau.edu.sa\falnakhlawiTel. Office :64159Mobile :0504453978

OBSERVATION

TESTED HYPOTHESIS

STATISTICAL INFERANCE

PREDICTION WITH NEW PROBLEMS

. () . . . .

. ( ). . . . . . . . . .

Experimental Unit : . Treatment : . Replication : . Experimental Error : Efficiency of experiment : Efficiency of Experiment = 1\Error Variance .

: 1- .Replication 2- .Randomization 3- Local Control.

1- REPLICATION

:1- . 2 - : S2x- = / . S2x- = S2\r 3- .4- .

2- Randomization . : 1- .2- .3- .

3- Local Control :1- Optimum Sample size 2- Optimum no. of Replicates . 3- . 4- .

Experimental Error :1- .2- .3- .4- . :1- .2- . 3- .4- . 5- .

1- : . 2- : (c.v. ).3- : . 4- : . 5- : 0.05 0.01

EXPERIMENTAL DESIGNS1- .CRD 2- .GROUP EXPS.2-1- .COMPLETE B.D. 2-1-1- .R.C.B.D. 2-1-2- .LATIN SQUARE 2-1-3- .GREECO L.S.2-2- .INCOMPLETE 2-2-1- .FACTORIAL EXPS. 2-2-1-1- .SPLIT PLOT DESIGN 2-2-1-2- .SPLIT BLOCK DESIGN 2-2-1-3- .BOXS DESIGN 2-2-1-4- .CONFOUNDING EXPS. 2-2 -2- .PSEUDO FACTORIAL 2-2-2-1- .LATTICE DESIGNS 2-2-2-2- .YOUDEN SQUARE DESIGNS 2-2-2-3- POLY EXPERIMENTS.

:1- : ....2 .3 .4 .5 ( ) .

: SIMPLE EXPERIMENT DESIGNS : . : . . . . . .

DESIGNS USED IN THE SIMPLE EXPERIMENTS : Completely Randomized Design ( CRD ) Randomized Complete Block Design ( RCBD ) Lattin Square design

COMPLETELY RANDOMIZED DESIGN(CRD) . : - - - :

CRD CRD:1- t.2- n.3- r.4- n.5- T1 Tt.6- . 7- ( )Layout.

Example : 3 . : 3 :A ,B &C . (t=3). : 15 . (n=15). : r=15/3=5. : CRD.

: CRD (1-15). : 14-2-3-13-11-7- 4 - 9 - 12-6 -1-10-8-5- 15 . : : 3 1 2 . : C :14-2-3-13-11. A :7-4-9-12-6 . B :1-10-8-5- 15 .

CRD ( )Layout of the Experiment.

Statistical Analysis : Analysis Of Variance . :1- .Additively Of The Main Effects . 2- .Independence Of Errors . 3- .Homogeneity Of Errors . 4- .Normality Of Errors .

TRANSFORMATION OF DATA

:

TRANSFORMATION OF DATA1- LOG TRANSFORMATION. (SDs of samples are roughly proportional to the means and the evidence of multiplicative rather than additive main effects).2- SQUARE ROOT TRANSFORMATION . (Rare events, the data follow a Poisson distribution).3- ARCSINE TRANSFORMATION. (Data based on counts expressed as percentages or proportions of the total sample and followed the Binomial Distribution :variances are related to the means).

ANALYSIS OF VARIANCE : : Correction Factor (C.F.) C.F.=(X)2/n Total S.S. Total S.S. = X2-C.F. Treatments S.S. Treat's S.S.=[(T1)2+(T2)2++(Tt)2]/r-C.F. Error S.S. Error S.S.=Total S.S. Treatments S.S.

ANOVA

Test of Significance F F F F . F > F .

Randomized Complete block Design (RCBD) . . :1- .2- . : 8 .

RCBD ()Blocks (Replicates) : : . : ...... . Panel Tests : . : . : ( ) . : .

RCBD :1- t .2- n .3- ( ) r .4- . : ( )Layout Of Experiment.

RCBD ) ) : 6 : A,B,C,D,E & F 24 . 10 5 . : RCBD t = 6 F &A,B,C,D,E n=24 () r=24/6=4

RCBD : 6 ( = 4 ) . : R1 : 3-4-6-1-5-2 R2 : 5-2-1-4-6-3 R3 : 1-2-3-6-4-5 R4 : 6-3-2-5-1-4 :

R1

R2

R3

R4

RCBD : :Total S.S. = X2- CF BlockSS=](R1)2+(R2)2++(Rr)2/[t -CFTreatSS=](T1)2+(T2)2++(Tt)2 / r-CFError S.S.=Total S.S.-Block S.S.-Treat S.S ANOVA .

ANOVA

F F F : F : .

ANOVA Table I : Analysis of variance of (character or characters) as affected by (treatments)._________________________________________ Source of df Mean Squares __variation_______________ch1______ch2_______ch3___Replicates 3 NS NS NSTreatments 5 114.23** 25.56 NS 12.32*Error 15 8.34 14.65 3.10 _____________ ______________________df: degrees of freedom.NS: not significant at 0.05 level of probability.*,**: significant differences at 0.05 and0.01 levels of probability,respectively.

Means comparison :Least Significant Difference (LSD)LSD=t (p,Error df)2MSError/r LSD LSD . LSD .

FACTORIAL EXPERIMENTS . :1- Main Effect . 2- Interaction . : CRD RCBD . =(P)(q)(c) p : . q . c . 4 .

: A B . A = 2 : a1 , a2 B = 3 : b1,b2,b3 RCBD r=4 . t=p x q t=2x3=6 (n) :n=r x t=4 x6=24

Total S.S=X2-CF Rep.S.S.= [R12+ +Rr2]/t - CF .Treat S.S.= [T12+ +Tt2]/r - CF . A S.S.= [a12+a22]/rq - CF. B S.S.= [b12+b22+ b32]/rp - CF. AB S.S.=Treat S.S.-A S.S.- B.S.S.Error SS=Total SS- Rep SS- Treat SS

ANOVA

F ANOVA : NS . * ** .

LSD 1- A :LSD= t (P,Error df) 2MS Error/rq2- B :LSD= t (P,Error df) 2MS Error/rp 3- AB :LSD= t (P,Error df) 2MS Error/r

SPLIT PLOT DESIGN :1- . : . . . . . . .

2- .3- 4- .

Split Plot design :1- ( ).Main Plot Treatments (A).2- = p 3- .Sub-plot Treatments (B) .4- = q 5- = r 6- = n=p x q x r

:

Split plot Design7- (A) : a1, a2 , a3ai .8- (B) : b1, b2, b3 , b4bj A . : ( )

Split Plot Design : A : p =3 :a1 ,a2 ,a3 B : q= 4 :b1,b2,b3,b4 r=3 n=3x4x3=36 experimental units =12 .

Split Plot Design : R1 : a1-a3-a2 R2 : a2-a3-a1 R3 : a3-a1-a2 : R1 :a1 : b2-b1-b4-b3 R1 :a3 : b1-b4-b3-b2 R1 :a2 : b3-b1-b4-b2 R2 :a2 : b3-b2-b4-b1 R2 :a3 : b4-b3-b1-b2 R2 :a1 : b2-b4-b1-b3 R3 :a3 : b2-b4-b1-b3 R3 :a1 : b1-b3-b2-b4 R3 :a2 : b4-b3-b2-b1

R1

Split Plot Design Analysis of Variance1-Total S.S.=X2- CF2-Main(Whole) Plot S.S.=[W112+ W122 ++ Wwr2] /q CF3-Rep.SS=[R12++ Rr2 ]/pq- CF4-A SS.=[a12++ ap2 ]/rq CF5-Error a SS=Main SS-Rep SS-A SS6-B SS.= [b12++ bq2 ]/rp CF7-AB SS.= [a1b12++ apbq2 ]/rCF-A SS-B SS8-Error b SS.=Total SS-Main SS-B SS-AB SS

ANOVASplit Plot