TWO TYPES OF EXPERIMENTS
Presentation Title Goes Here Introductio Introduction n to Experimental Designs
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Violeta Bartolome Senior Associate Scientist-Biometrics Crop Research Informatics Laboratory International Rice Research Institute
• Single Factor Experiments - several several levels levels of of one one factor are being tested while keeping all other factors at a constant level. Example: Varietal trial - several varieties are tested under uniform management and cultural practices. • Multi-factor or factorial experiments - test test two two or more factors simultaneously. Example: Testing five five varieties under four four nitrogen rates.
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Experimental designs applicable to single-factor experiments • Comple Complete te Block Block Design Design (comp (complet letely ely rando randomiz mized, ed, randomized complete block and and latin square designs). generally used for experiments with a small number of treatments. blocks,, each of which contains o characterized by blocks the complete set of treatments. • Incomple Incomplete te Block Block Designs Designs (latti (lattices, ces, alpha-lat alpha-lattice tice,, and and group balanced block designs). o
o o
generally used for experiments with a large number of treatments. characterized by blocks, each of which contains
Completely Randomized Design (CRD) • Appropria Appropriate te only for experimen experiments ts with with no obvious obvious heterogeneity between experimental units. • Any differenc difference e among among experimen experimental tal units units receivi receiving ng the same treatment is considered as experimental error . • Trea Treatm tmen ents ts are are assi assign gned ed completely at random so that each experimental unit has the same chance of receiving each of the treatments.
A field experiment is to be conducted in CRD with 5 treatments and 4 replications replications.. How do you you make the layout ? Step1: Step1: Divide the area into 5 trts trts x 4 reps reps = 20 plots.
Near homogeneous area :: color, composition, and layout
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Step2: Step2: On 20 pieces of paper, write treatment numbers and put in box. Step3: Step3: Assign treatment on each plot by drawing lots.
In CRD, the treatments are assigned completely at random
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Randomized Complete Block Design (RCB) • When the exper experimen imental tal units units are are not not homogen homogeneou eous s and it is possible to group the experimental units into blocks such that experimental units within each block are more homogeneous than those between blocks. • The prese presence nce of of blocks, blocks, each each conta containi ining ng all all the treat treatmen ments, ts, is the primary distinguishing feature of the RCB design.
An experiment is to be conducted in RCB with 5 treatments and 4 replications. replications. How do you you make the layout? fertility gradient
fertility gradient T4
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First, divide the field into 4 equal parts, each part representing one block. Next, divide each block into 5 equal parts, each part representing one plot. Then randomly assign the 5 treatments to the 5 plots in each block. :: color, composition, and layout
Advantage of RCB Latin Square Block Variation
CRD ERROR RCBD ERROR
• Capaci Capacity ty to simu simulta ltaneo neousl usly y handle handle two two known known sources of variation. • A treatm treatmen entt appea appears rs only only once once in in each each row row or column. • To rando randomiz mize, e, use use basi basic c plans plans foun found d in some some statistics book. • Number Number of treatment treatments s should should be equal equal to numbe numberr of replications.
Experimental error is minimized by removing block variation from the error.
• Very Very seldo seldom m used used in agricu agricultu ltural ral expe experime riment. nt.
Example of LATIN SQUARE layout
Advantage of Latin Square
fertility gradient Column 1
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Block Row Variation Variation
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Latin Square Error RCBD ERROR
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FACTORIAL EXPERIMENTS
Experimental error is minimized by removing row and column variations :: color, composition, and layout from the error.
Advantages of factorial experiments
Two or more factors are tested simultaneously. • Provid Provide e for for exami examinat nation ion of inte interac ractio tion n among the various factors tested.
Example:
2 levels of Variety (V 1, V2) 3 levels of Land Preparation (L 1, L2, L3) The treatments are: V1L1
V1L2
V1L3
V2L1
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• Economica Economicall by by compa comparison rison to several several single single facto factor r experiments. • Broade Broadens ns appl applica icabil bility ity of of main main effe effect ct conclusions.
Designs Applicable To Factorial Experiments • Comp Comple lete tely ly Rand Random omiz ized ed Des Desig ign n • Random Randomize ized d Comple Complete te Block Block Design Design • Lati Latin n Squa Square re Desi Design gn
An experiment experiment involving involving 5 N-rates N-rates and 4 Varieties is to be conducted conducted in a RCB design in 3 replications. How do you make the layout? layout?
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• Spli Splitt Plot Plot Famil Family y of Desi Design gns s • Stri Strip p Plot Plot Famil Family y of Desi Design gns s
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An experiment involving 5 N-rates and 4 Varieties Varieties is to be conducted conducted in a Split-plot design in 3 replications. replications. How do you make the layout? layout?
Split-Plot Design 30 larger one is called called mainplot mainplot and the • Has two plot sizes: the larger • •
smaller one subplot. Precisio Precision n for the comp comparis arison on of of the subplot subplot treat treatmen ments ts is expected to be higher higher than that for the mainplot mainplot treatments. treatments.
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Smaller Smaller differenc difference e can be detected detected among among subplot subplot treatmen treatments ts than among among mainplot treatments. treatments.
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An experiment involving 5 N-rates and 4 Varieties Varieties is to be conducted conducted in a Split-plot design in 3 replications. replications. How do you make the layout? layout?
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Possible Reasons for Using Split-Plot
Stri St ripp-Pl Plot ot De Desi sign gn
• Manageme Management nt requireme requirement: nt: some treatments treatments such as water management is easier to manage in bigger plot.
• Higher Higher degree degree of prec precisi ision on is is given given to the the measurement of the interaction effect than main m ain effects.
• Insertion Insertion of an addition additional al factor factor into an estab establishe lished d experiment.
• Horizonta Horizontall and and vertical vertical plots plots are are perpendic perpendicular ular to each other. other. There is no no relationship between their their sizes.
• Need to increa increase se precisi precision on on on the the effect effect of one one factor factor at the expense of another.
• Can accomm accommoda odate te two two mecha mechanic nical al facto factors. rs.
:: color, composition, and layout
Suppose an experiment experiment involving involving 5 N-rates and 4 Water Water Levels is to be conducted in a Strip-plot design design in 3 replications. How do you make the layout?
:: color, composition, and layout
Suppose an experiment experiment involving 5 N-rates and 4 Water levels to be conducted in a Strip-plot design design in 3 replications. How do you make the layout?
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