1 / 90

Experimental Design Summary

This summary explores different experimental design methods for genetic studies, including completely randomized block, randomized complete block, Latin square, lattice square, rectangular lattice, factorial, split-plot, and strip-plot designs. It discusses the advantages, disadvantages, and restraints of each method, along with examples and considerations for different genotypes and facilities.

pricketts
Download Presentation

Experimental Design Summary

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Experimental DesignSummary

  2. Completely Randomized Block Yij =  + gi + eij Average over the whole experiment Effect of ith genotype = + + Error jth replicate of the ith genotype

  3. Completely Randomized Block • Can be used with unbalanced replication of entries. • Genetic studies (i.e. F1, F2, BC1) • Simple to analyze. • Completely random. • Can fit into any area. • Unlikely to manage fertility gradients.

  4. Randomized Complete Block Yijk =  + ri +gj + eijk Average over the whole experiment Effect of ith replicate Effect of jth genotype = + + + Error ith genotype in the jth replicate block

  5. Randomized Complete Block • Layout is simple and can be adjusted to fit almost any shapes experimental area. • Simple and relatively robust to errors (say in planting). • Analyses is simple to carry out. • Block effects are often significant. • No restraints on entry numbers.

  6. Latin Square Yijk =  +gi + rj + ck + eijk Where Yijk is the performance of the ith genotype in the jth row and kth column;  in the overall mean; gi is the effect of the ith genotype; rj is the effect of the jth row; ck is the effect of the kth column; and eijk is the error term.

  7. Latin Square • Advantage of latin square designs is their accuracy and ability to remove gradients in two directions. • Disadvantage is that they require large levels of replication. A 10 entry experiment would require 100 experimental units. • Latin square analyses are intolerant to missing values.

  8. Lattice Square Yijk =  +gai + bak + rj + eijk Where Yijk is the performance of the ith genotype in the jth replicate and kth sub-block;  in the overall mean; gai is the effect of the ith genotype adjusted according to sub-blocks; bak is the effect of the kth sub-block adjusted according to the entries in that block; rj is the effect of the jth replicate; and eijk is the error term.

  9. Lattice Square • Lattice squares are usually more effective than RCB’s. • Have restraints on the number of entries and replicates. • Are not truly randomized. • Errors in plot arrangement (i.e. planting) renders them useless. • Lattice squares are resolvable.

  10. Rectangular Lattice Yijk =  +gai + bak + rj + eijk Where Yijk is the performance of the ith genotype in the jth replicate and kth sub-block;  in the overall mean; gai is the effect of the ith genotype adjusted according to sub-blocks; bak is the effect of the kth sub-block adjusted according to the entries in that block; rj is the effect of the jth replicate; and eijk is the error term.

  11. Rectangular Lattice • More flexible in entry and replicate number than square lattices. • Designs are resolvable. • Designed for statutory cultivar field testing.

  12. Interactions A B

  13. Factorial Experimental Design

  14. Factorial Experimental Design I II III

  15. Two-Factor Factorial Model Yijk =  + ri + dj + wk + dwjk + eijk Where Yijk is the performance of the the ith replicate, and the jth d factor and kth w factor;  in the overall mean; rj is the effect of the jth replicate; di is the effect of the ith d-factor; wk is the effect of the kth w-factor; dwjk is the interaction effect between dj and wk; and eijk is the error term.

  16. Factorial Experimental Designs • Can be used with any number of factors and factor levels. • Gives equal precision to estimating all factors and levels. • Greatest mistake by researchers is to include too many factors where interpretation of three-way interactions can be difficult.

  17. Split-Plot Design I II III IV 3 2 1 4 3 1 4 2 3 1 2 4 2 4 1 3 3 2 1 4 3 1 4 2 3 1 2 4 2 4 1 3

  18. Split-Plot Design Model Yijk =  + ri + gj + e(1)ij + tk + gtjk + e(2)ijk Where Yijk is the performance of the the ith replicate, and the jth main-plot and kth sub-plot;  in the overall mean; rj is the effect of the jth replicate; gi is the effect of the ith main-plot; e(1)ij is the main-plot error; tk is the effect of the kth sub-plot; gtjk is the interaction effect between gj and tk; and e(2)ijk is the sub-plot error term.

  19. Strip-Plot Design B A C A C B 1 1 2 2 I IV 4 4 3 3 B A C A C B 3 3 1 1 III II 2 2 4 4

  20. Strip-Plot Design Model Yijk = +ri+gj+e(g)ij+tk+e(t)ij+gtjk+e(gt)ijk Where Yijk is the performance of the the ith replicate, and the jth strip and kth strip;  in the overall mean; rj is the effect of the jth replicate; gi is the effect of the ith strip-plot; e(g)ij is the g-factor error; tk is the effect of the kth strip-plot; e(t)ij is the t-factor error; dwjk is the interaction effect between gj and tk; and e(gt)ijk is the sub-plot error term.

  21. Restraints

  22. Genotypes/Species

  23. Facilities • Glasshouse, Laboritory, Field, Growth rooms. • Types of data. • Time availability • Funding.

  24. Restraints Facilities, Data types, Timing, and Funding Factors, levels Replicates, Plot size

  25. Examples Scottish Summers Day

  26. Jeannie’s Oriental Mustard • Oriental mustard (Brassica juncea L.) is a new crop to the PNW • Growers have little experience growing the crop. • Design an experiment to determine the optimum growing conditions to maximize productivity.

  27. Jeannie’s Oriental Mustard Factors ?

  28. Jeannie’s Oriental Mustard • Four cultivars. • 2 oilseed and 2 condiment. • 2 planting dates. • 3 seeding rates. • 5 nitrogen levels. • 3 Replicates.

  29. Jeannie’s Oriental Mustard

  30. Jeannie’s Oriental Mustard I II III Late Planting Early Planting Early Planting Late Planting Late Planting Early Planting

  31. Jeannie’s Oriental Mustard Late Planting Early Planting

  32. Jeannie’s Oriental Mustard I II III I II III Late Planting Early Planting

  33. Jeannie’s Oriental Mustard I II III I II III Late Planting Early Planting

  34. Jeannie’s Oriental Mustard I II III I II III Late Planting Early Planting

  35. Jeannie’s Oriental Mustard 2 Arid 3 g Arid 5 g 1 Arid 4 g

  36. Jeannie’s Oriental Mustard 2 P. Gold 3 g Amulat 5 g Kodiak 5 g Kodiak 3 g Arid 3 g Arid 5 g 1 Kodiak 4 g Amulat 3 g Arid 4 g Amulat 4 g P. Gold 5 g P. Gold 4 g

  37. Jeannie’s Oriental Mustard 2 Arid 4 g Arid 5 g Arid 3 g 1

  38. Jeannie’s Oriental Mustard 2 Arid 4 g Arid 5 g Arid 3 g Kodiak 3 g Kodiak 5 g Kodiak 4 g 1 P. Gold 3 g Amulat 4 g Amulat 5 g Amulat 3 g P. Gold 4 g P. Gold 5 g

  39. Example 1 ~ #4 p79 • Soil erosion in PNW. • Normal barley/wheat rotation. • New crops canola and AWP. • Test erosion of new crops in no tillage, minimum tillage and conventional tillage.

  40. Example 1 ~ #4 p79 • As much land as needed. • Cultivators set to 20 feet. • Tradition drill at 10 feet and no tillage drill at 15 feet. • Design a suitable experiment.

  41. Example 1a ~ #4 p79 100’ 30’

  42. Example 1a ~ #4 p79

  43. Example 1a ~ #4 p79 AP Ba AP Ba Ca Ca Ca Ba AP Ba Ca AP AP Ba Ca Ca AP Ba

  44. Example 1a ~ #4 p79

  45. Example 1b ~ #4 p79

  46. Example 1b ~ #4 p79 AP Ba AP Ba Ca Ca Ca AP Ba Ba Ca AP AP Ba Ca Ca AP Ba

  47. Example 1a ~ #4 p79 Ba Ca AP AP Ba Ca Ca Ba AP Ba Ca AP Ba Ca AP Ca Ba AP

  48. Example 1a ~ #4 p79 Ba Ca AP AP Ba Ca Ca Ba AP Ba Ca AP Irrigate Ba Ca AP Ca Ba AP Buffer Ba Ca AP AP Ba Ca Not Irrigate Ca Ba AP Ba Ca AP Ba Ca AP Ca Ba AP

  49. Example 1b ~ #4 p79 Buffer Buffer Buffer Irrigate No Irrigate Irrigate No Irrigate

  50. Example 3 ~ #6 p.80 • Restrictions on insecticides on beans stop BMV. • Aphids max out at 5 weeks before harvest. • Apply 6” of water, one inch/4 weeks. • Reduced irrigation: early maturity, less cost.

More Related