DESIGN AND DESIGN AND ANALYSIS OF ANALYSIS OF EXPERIMENTS: EXPERIMENTS: BasicsBasics

Hairul Hafiz MahsolHairul Hafiz MahsolInstitute for Tropical Biology & Institute for Tropical Biology & ConservationConservationSchool of Science & School of Science & TechnologyTechnology

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Introduction to DesignIntroduction to Design

What is Research Design?What is Research Design?– Research design can be thought of as Research design can be thought of as

the the structurestructure of research -- it is the of research -- it is the "glue" that holds all of the elements "glue" that holds all of the elements in a research project together. in a research project together.

– We often describe a design using a We often describe a design using a concise notation that enables us to concise notation that enables us to summarize a complex design summarize a complex design structure efficiently. structure efficiently.

The `blueprint’ for collecting, measure The `blueprint’ for collecting, measure and data analysis. and data analysis. – It also help to allocate the limited source such It also help to allocate the limited source such

as:as: Choosing between the type of designChoosing between the type of design

– ExperimentExperiment– ObservationObservation– InterviewInterview– SimulationSimulation

Collecting data whether in the form of Collecting data whether in the form of structural or not. structural or not.

Small or large sampleSmall or large sample Quantitative or qualitative researchQuantitative or qualitative research

The research plan and structure regarding The research plan and structure regarding to answer the research questionto answer the research question

Overall scheme or program starting from Overall scheme or program starting from hypothesis writing, the operational hypothesis writing, the operational implication to data analysis.implication to data analysis.

The design will showed the relation The design will showed the relation between variable and research plan to between variable and research plan to collect empirical data that related to the collect empirical data that related to the facing problemsfacing problems

Three questions:Three questions: What type of technique to be used for What type of technique to be used for

collecting data? collecting data? What type of sampling that will be used What type of sampling that will be used

for the experiment? for the experiment? How to save money and time consuming?How to save money and time consuming?

TerminologyTerminology

Elements of Experimental Elements of Experimental DesignDesign

Structures of an Experimental Structures of an Experimental DesignDesign

Types of Treatment Types of Treatment StructuresStructures

Types of Design StructuresTypes of Design Structures

Considerations when Considerations when Designing an ExperimentDesigning an Experiment

““figures never lie, only statisticians do”figures never lie, only statisticians do”

IS NOT TO BE REVIVEDIS NOT TO BE REVIVED

TYPES OF TYPES OF DESIGN DESIGN STRUCTURESSTRUCTURES

Completely Completely Randomized Designs Randomized Designs (CRD)(CRD)

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INTRODUCTIONINTRODUCTION

If all the experiment material are If all the experiment material are homogenous or equivalent, the homogenous or equivalent, the design structure that suitable to design structure that suitable to this situation is CRD.this situation is CRD.

The CRD is the simplest of all The CRD is the simplest of all designs.designs.

It is equivalent to a t-test when It is equivalent to a t-test when only two treatments are examined.only two treatments are examined.

Field marks: Field marks:

Replications of treatments are Replications of treatments are assigned completely at random to assigned completely at random to independent experimental independent experimental subjects. subjects.

Adjacent subjects could potentially Adjacent subjects could potentially have the same treatment. have the same treatment.

Sample layout: Sample layout:

Different colors represent different Different colors represent different treatments. treatments.

There are 4 (A-D) treatments with There are 4 (A-D) treatments with 4 replications (1-4) each.4 replications (1-4) each.– A: A1 A2 A3 A4A: A1 A2 A3 A4– B: B1 B2 B3 B4B: B1 B2 B3 B4– C: C1 C2 C3 C4C: C1 C2 C3 C4– D: D1 D2 D3 D4D: D1 D2 D3 D4

A1 B1 C1 A2 A1 B1 C1 A2

D1 A3 D2 C2 D1 A3 D2 C2

B2 D3 C3 B3 B2 D3 C3 B3

C4 A4 B4 D4 C4 A4 B4 D4

ANOVA table format: ANOVA table format:

Source ofvariation

Degrees offreedoma

Sums ofsquares (SSQ)

Meansquare (MS)

F

Treatments (Tr)

t-1 SSQTr SSQTr/(t-1) MSTr/MSE

Error (E) t*(r-1) SSQE SSQE/(t*(r-1))  

Total (Tot) t*r-1 SSQTot    

awhere t=number of treatments and r=number of replications per treatment.

Sample ANOVA table: Sample ANOVA table:

Source ofvariation

Degrees offreedom

Sums ofsquares (SSQ)

Meansquare (MS)

F

Treatments 3 80.92 26.97 9.68a

Error 12 33.43 2.79  

Total 15 114.35    

aF test with 3,12 degrees of freedom at P=0.05 is 3.49

The advantageThe advantage

Easy to useEasy to use The experiment material can be The experiment material can be

used as many as possibleused as many as possible The treatment also can be used as The treatment also can be used as

many as possiblemany as possible

TYPES OF TYPES OF DESIGN DESIGN STRUCTURESSTRUCTURES

The Randomized The Randomized Complete Block Complete Block design (RCBD)design (RCBD)

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INTRODUCTIONINTRODUCTION

The RCB is the standard design for The RCB is the standard design for agricultural experiments. agricultural experiments.

The field or orchard is divided into The field or orchard is divided into units to account for any variation units to account for any variation in the field.in the field.

Treatments are then assigned at Treatments are then assigned at random to the subjects in the random to the subjects in the blocks -once in each block. blocks -once in each block.

Field marks: Field marks:

Treatments are assigned at random Treatments are assigned at random within blocks of adjacent subjects, each within blocks of adjacent subjects, each treatment once per block. treatment once per block.

The number of blocks is the number of The number of blocks is the number of replications. replications.

Any treatment can be adjacent to any Any treatment can be adjacent to any other treatment, but not to the same other treatment, but not to the same treatment within the block. treatment within the block.

Used to control variation in an Used to control variation in an experiment by accounting for spatial experiment by accounting for spatial effects. effects.

Sample layout: Sample layout:

Different colors represent different Different colors represent different treatments; each horizontal row treatments; each horizontal row represents a block. represents a block.

There are 4 blocks (I-IV) and 4 There are 4 blocks (I-IV) and 4 treatments (A-D) in this example.treatments (A-D) in this example.

– I: A B C DI: A B C D– II: A B C DII: A B C D– III: A B C DIII: A B C D– IV: A B C DIV: A B C D

Block I A B C D Block I A B C D

Block II D A B C Block II D A B C

Block III B D C A Block III B D C A

Block IV C A B D Block IV C A B D

ANOVA table format: ANOVA table format:

Source ofSource ofvariationvariation

Degrees Degrees ofof

freedomfreedomaa

Sums ofSums ofsquares squares (SSQ)(SSQ)

MeanMeansquare (MS)square (MS) FF

Blocks (Blocks (BB)) b-1b-1 SSQSSQBB SSQSSQ

BB/(b-1)/(b-1) MSMSBB/MS/MS

EE

Treatments Treatments ((TrTr))

t-1t-1 SSQSSQTrTr SSQSSQ

TrTr/(t-1)/(t-1) MSMSTrTr/MS/MS

EE

Error (Error (EE)) (t-1)*(b-1)(t-1)*(b-1) SSQSSQEE SSQSSQ

EE/((t-1)*(b-1))/((t-1)*(b-1))   

Total (Total (TotTot)) t*b-1t*b-1 SSQSSQTotTot      

aawhere t=number of treatments and b=number of blocks or replications.where t=number of treatments and b=number of blocks or replications.

Sample ANOVA table: Sample ANOVA table:

Source ofSource ofvariationvariation

Degrees ofDegrees offreedomfreedom

Sums ofSums ofsquares (SSQ)squares (SSQ)

MeanMeansquare (MS)square (MS) FF

BlocksBlocks 33 26.3626.36 8.798.79 1.361.36aa

TreatmentsTreatments 33 216.23216.23 72.0872.08 11.1911.19aa

ErrorError 99 57.9557.95 6.446.44   

TotalTotal 1515 300.54300.54      

aaF test with 3,9 degrees of freedom at F test with 3,9 degrees of freedom at PP=0.05 is 3.86=0.05 is 3.86

The advantageThe advantage

Block is used to be one of the error Block is used to be one of the error variationvariation

Effect for the treatment will be Effect for the treatment will be higher. higher.

TYPES OF TYPES OF DESIGN DESIGN STRUCTURESSTRUCTURES

Latin Square DesignsLatin Square Designs

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The Latin Square designThe Latin Square design

The Latin square design is used The Latin square design is used where the researcher desires to where the researcher desires to control the variation in an control the variation in an experiment that is related to rows experiment that is related to rows and columns in the field.and columns in the field.

Field marks: Field marks:

Treatments are assigned at Treatments are assigned at random within rows and columns, random within rows and columns, with each treatment once per row with each treatment once per row and once per column. and once per column.

There are equal numbers of rows, There are equal numbers of rows, columns, and treatments. columns, and treatments.

Useful where the experimenter Useful where the experimenter desires to control variation in two desires to control variation in two different directions different directions

Sample layout: Sample layout:

Different colors represent different Different colors represent different treatments. treatments.

There are 4 treatments (A-D) There are 4 treatments (A-D) assigned to 4 rows (I-IV) and 4 assigned to 4 rows (I-IV) and 4 columns (1-4).columns (1-4).

Row I A B C D Row I A B C D

Row II C D A B Row II C D A B

Row III D C B A Row III D C B A

Row IV B A D C Row IV B A D C

Column 1 2 3 4 Column 1 2 3 4

ANOVA table format: ANOVA table format:

Source ofvariation

Degrees offreedoma

Sums ofsquares (SSQ)

Meansquare (MS)

F

Rows (R) r-1 SSQR SSQR/(r-1) MSR/MSE

Columns (C) r-1 SSQC SSQC/(r-1) MSC/MSE

Treatments (Tr) r-1 SSQTr SSQTr/(r-1) MSTr/MSE

Error (E) (r-1)(r-2) SSQE SSQE/((r-1)(r-2))  

Total (Tot) r2-1 SSQTot    

awhere r=number of treatments, rows, and columns.

Sample ANOVA table: Sample ANOVA table:

Source ofvariation

Degrees offreedom

Sums ofsquares (SSQ)

Meansquare (MS)

F

Rows 3 40.77 13.59 5.91a

Columns 3 125.39 41.80 18.16a

Treatments 3 160.57 53.52 23.26a

Error 6 13.81 2.30  

Total 15 340.54    aF test with 3,6 degrees of freedom at P=0.05 is 4.76

The advantageThe advantage

Two block (row & column) is used Two block (row & column) is used to be one of the error variationto be one of the error variation

Effect for the treatment will be Effect for the treatment will be higher. higher.

TYPES OF TYPES OF DESIGN DESIGN STRUCTURESSTRUCTURES

Factorial DesignsFactorial Designs

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Factorial DesignFactorial Design

There are more than one There are more than one treatmentstreatments

`treatments on treatments’`treatments on treatments’

AA

A1

A2

B1

B2

B1

B2