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Simple Cross – over Design(แผนการทดลองแบบเปลี่ยนสลับอย่างง่าย) By Dr.WuttigraiBoonkum Dept.Animal Science, Fac. Agriculture KKU
Simple Cross-Over Design • Other name “Simple Change-over Design” or “Reversal design” • Look like Repeated Measurement Exp. • About 3 factors are treatments, Animal and time. • Researcher must change – over all treatments in each animal. • Response measured of treatment effect in each animal and each time.
Objective • To compare between cross-over design and switch-back design. • Can calculated statistic parameters in cross-over design and switch-back design. • Can interpretation and conclusion of results from SAS program. • Tell differentiate of Type of Replicated Latin Square.
Step by Step of Cross-over Design Classify Factors Consideration of number of Animal, Treatment and Time Statistical model, Hypothesis setting, Lay out ANOVA analysis using SAS program Interpretation and Conclusion
Hypothesis setting • Look like Latin Square Design such as: • Trt = 2, hypothesis is:
Lay out A1 A2 A3 A5 A6 A4 Period1 Transition period Period2 Resting period 12 EU.; A = Animal Period1 Period2
SAS code Data……; input row col trt y; Cards; x x x x x x x x x x x x ; Proc anova data =………….; class row col trt; model y = row col trt; means trt /duncan; Run; Like Latin square design
ANOVATable Interpretation is likely LSD P-value > 0.05 non-significant; ns P-value < 0.05 significant; * P-value < 0.01 highly significant; **
Advantages • Have efficiency more than CRD • Good for budget limitation • Increase precision for Experimental design
Switch-back Design • Look like cross-over design. • But turn around 1st treatment when cross-over each treatments. • This design is appropriate for high effect of time on treatment • The example this design such as: lactation trait, growth trait, traits about time period etc.
A B A B A B Example Sequence A B A Sequence B A B
Lay out Animal 1 Animal 2 Animal 3 Animal 4 Animal 6 Animal 5 Period1 Period2 Period3 18 EU. Sequence A B A This lay out have 2 sequence: Sequence B A B
+ - = H : ( B B ) / 2 A 0 H : ( A A ) / 2 B 0 0 0 + - ¹ + - ¹ H : ( B B ) / 2 A 0 H : ( A A ) / 2 B 0 A A or or - = - = H : B 2 ( A ) 0 H : A 2 ( B ) 0 0 0 - ¹ - ¹ H : B 2 ( A ) 0 H : A 2 ( B ) 0 A A Hypothesis setting • Look like Cross-over Design such as: • Trt = 2, hypothesis is: Sequence B A B Sequence A B A + - =
ANOVA Note: Animal(sq) = Animal within sequence error; P = Period (is regression)
SAS code Data……; input row col trt observ; If cow = 1 or cow = 2 or cow = 3 THEN seq = 1 ELSE seq = 2; P = period; Cards; x x x x x x x x x x x x ; Proc GLM data =………….; class seq cow period trt ; model observ = seq cow(seq) period p*seq p*cow(seq) trt /SS1; Test H = period p*seq E = p*cow(seq); Test H = seq E = cow(seq); Lsmeans trt ; Run;
Interpretation Check P-value of adjusted p * sequence interaction Check P-value of adjusted period and sequence respectively Check P-value of treatment effect ns * , ** conclusion Treatment mean analysis
Advantages • Precision morn than cross-over design • Appropriate for time period traits
Replicated Latin Square Design • Use case more than 2 treatment • Researcher want to change-over trt. • To decrease error of sequence so must have a square. • Each square must difference of sequence so may be called “balanced square” or “orthogonal square”.
Replicated Latin Square Design 3 type of Replicated Latin Square 1. Type I: originally animal set, time difference.
Orthogonal or balanced square Example : A, B, C and D are treatments A B C D B C D A D A B C B C D A
Orthogonal or balanced square Example : A, B, C, D and E are treatments A A A A A
SAS code • Type A: Proc anova data = ……….; class sq anim period trt; model Y = sq anim period(sq) trt; means trt /Duncan; Run; • Type B: • Proc anova data = ……….; • class sq anim period trt; • model Y = sq anim(sq) period trt; • means trt /Duncan; • Run;
SAS code • Type C: Proc anova data = ……….; class sq anim period trt; model Y = sq anim(sq) period(sq) trt; means trt /BON; Run;
Latin square Design to Estimate Residual Effects • Transition period limited. • Some treatments may have residual effects. • Sometime Researcher interested in residual effects. • Example residual effects such as antibiotic, hormones etc.
SAS data set X Data; input sq anim period trt $ milk Resid; Cards; 1 1 1 A 38 X 1 1 2 B 25 A 1 1 3 C 15 B 1 2 1 B 109 X 1 2 2 C 86 B 1 2 3 A 39 C 1 3 1 C 124 X 1 3 2 A 72 C 1 3 3 B 27 A 2 4 4 A 86 X 2 4 5 C 76 A 2 4 6 B 46 C 2 5 4 B 75 X 2 5 5 A 35 B 2 5 6 C 34 A 2 6 4 C 101 X 2 6 5 B 63 C 2 6 6 A 1 B ; A B
SAS code Proc GLM data =……….; class sq anim period trt resid; model milk = sq anim(sq) period(sq) trt resid; Run;
Graeco Latin Square Design • Researcher can separate a variable later (greek letter) • Level of effects equal row effect, column effect and treatment effect.
SAS code Data…………; input row col trt $ greek $ observe; Cards; x x x x x x x x x x x x x x x x x x x x ; Proc anova data =…..; class row col greek trt; model observe = row col greek trt; means trt / duncan; Run;
The End Next time I will lecture about … Incomplete block design