Simple Cross-Over Design Experiment by Dr. Wuttigrai Boonkum

1. Simple Cross – over Design(แผนการทดลองแบบเปลี่ยนสลับอย่างง่าย) By Dr.WuttigraiBoonkum Dept.Animal Science, Fac. Agriculture KKU

2. 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.

3. 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.

4. 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

5. Statistical model

6. Hypothesis setting • Look like Latin Square Design such as: • Trt = 2, hypothesis is:

7. Lay out A1 A2 A3 A5 A6 A4 Period1 Transition period Period2 Resting period 12 EU.; A = Animal Period1 Period2

8. 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

9. SAS output

10. ANOVATable Interpretation is likely LSD P-value > 0.05 non-significant; ns P-value < 0.05 significant; * P-value < 0.01 highly significant; **

11. Advantages • Have efficiency more than CRD • Good for budget limitation • Increase precision for Experimental design

12. 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.

13. A B A B A B Example Sequence A  B  A Sequence B  A  B

14. 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

15. Statistical model

16. + - = 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 + - =

17. ANOVA Note: Animal(sq) = Animal within sequence error; P = Period (is regression)

18. 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;

19. SAS output

20. 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

21. Advantages • Precision morn than cross-over design • Appropriate for time period traits

22. 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”.

23. Replicated Latin Square Design 3 type of Replicated Latin Square 1. Type I: originally animal set, time difference.

24. 2. Type II: new animal set, same time.

25. 3. Type III: new animal set, time difference.

26. 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

27. Orthogonal or balanced square Example : A, B, C, D and E are treatments A A A A A

28. Statistical model and ANOVA

29. Statistical model and ANOVA

30. Statistical model and ANOVA

31. 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;

32. SAS code • Type C: Proc anova data = ……….; class sq anim period trt; model Y = sq anim(sq) period(sq) trt; means trt /BON; Run;

33. SAS outputType A

34. SAS outputType B

35. SAS outputType C

36. 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.

37. 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

38. SAS code Proc GLM data =……….; class sq anim period trt resid; model milk = sq anim(sq) period(sq) trt resid; Run;

39. Graeco Latin Square Design • Researcher can separate a variable later (greek letter) • Level of effects equal row effect, column effect and treatment effect.

40. Statistical model

41. Lay out

42. 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;

43. ANOVAof Graeco Latin Square Design

44. The End Next time I will lecture about … Incomplete block design