DESIGN AND ANALYSIS OF EXPERIMENTS: Basics Hairul Hafiz Mahsol Institute for Tropical Biology & Conservation School of Science & Technology POSTGRADUATE METHODOLOGY COURSE

Introduction to Design n What is Research Design? –Research design can be thought of as the structure of research -- it is the "glue" that holds all of the elements in a research project together. –We often describe a design using a concise notation that enables us to summarize a complex design structure efficiently.

n The `blueprint’ for collecting, measure and data analysis. –It also help to allocate the limited source such as: n Choosing between the type of design –Experiment –Observation –Interview –Simulation n Collecting data whether in the form of structural or not. n Small or large sample n Quantitative or qualitative research

n The research plan and structure regarding to answer the research question n Overall scheme or program starting from hypothesis writing, the operational implication to data analysis. n The design will showed the relation between variable and research plan to collect empirical data that related to the facing problems

n Three questions: n What type of technique to be used for collecting data? n What type of sampling that will be used for the experiment? n How to save money and time consuming?

Terminology

Elements of Experimental Design

Structures of an Experimental Design

Types of Treatment Structures

Types of Design Structures

Considerations when Designing an Experiment

“figures never lie, only statisticians do” IS NOT TO BE REVIVED

TYPES OF DESIGN STRUCTURES Completely Randomized Designs (CRD) POSTGRADUATE METHODOLOGY COURSE

INTRODUCTION n If all the experiment material are homogenous or equivalent, the design structure that suitable to this situation is CRD. n The CRD is the simplest of all designs. n It is equivalent to a t-test when only two treatments are examined.

Field marks: n Replications of treatments are assigned completely at random to independent experimental subjects. n Adjacent subjects could potentially have the same treatment.

Sample layout: n Different colors represent different treatments. n There are 4 (A-D) treatments with 4 replications (1-4) each. –A: A1 A2 A3 A4 –B: B1 B2 B3 B4 –C: C1 C2 C3 C4 –D: D1 D2 D3 D4

A1 B1 C1 A2 D1 A3 D2 C2 B2 D3 C3 B3 C4 A4 B4 D4

ANOVA table format: Source of variation Degrees of freedom a Sums of squares (SSQ) Mean square (MS) F Treatments (Tr) t-1SSQ Tr SSQ Tr /(t-1)MS Tr /MS E Error (E)t*(r-1)SSQ E SSQ E /(t*(r-1)) Total (Tot)t*r-1SSQ Tot a where t=number of treatments and r=number of replications per treatment.

Sample ANOVA table: Source of variation Degrees of freedom Sums of squares (SSQ) Mean square (MS) F Treatments a Error Total a F test with 3,12 degrees of freedom at P=0.05 is 3.49

The advantage n Easy to use n The experiment material can be used as many as possible n The treatment also can be used as many as possible

TYPES OF DESIGN STRUCTURES The Randomized Complete Block design (RCBD) POSTGRADUATE METHODOLOGY COURSE

INTRODUCTION n The RCB is the standard design for agricultural experiments. n The field or orchard is divided into units to account for any variation in the field. n Treatments are then assigned at random to the subjects in the blocks - once in each block.

Field marks: n Treatments are assigned at random within blocks of adjacent subjects, each treatment once per block. n The number of blocks is the number of replications. n Any treatment can be adjacent to any other treatment, but not to the same treatment within the block. n Used to control variation in an experiment by accounting for spatial effects.

Sample layout: n Different colors represent different treatments; each horizontal row represents a block. n There are 4 blocks (I-IV) and 4 treatments (A-D) in this example. –I: A B C D –II: A B C D –III: A B C D –IV: A B C D

Block I A B C D Block II D A B C Block III B D C A Block IV C A B D

ANOVA table format: Source of variation Degrees of freedom a Sums of squares (SSQ) Mean square (MS) F Blocks (B) b-1 SSQ B SSQ B /(b-1) MS B /MS E Treatments (Tr) t-1 SSQ Tr SSQ Tr /(t-1) MS Tr /MS E Error (E) (t-1)*(b-1) SSQ E SSQ E /((t-1)*(b-1)) Total (Tot) t*b-1 SSQ Tot a where t=number of treatments and b=number of blocks or replications.

Sample ANOVA table: Source of variation Degrees of freedom Sums of squares (SSQ) Mean square (MS) F Blocks a Treatments a Error Total a F test with 3,9 degrees of freedom at P=0.05 is 3.86

The advantage n Block is used to be one of the error variation n Effect for the treatment will be higher.

TYPES OF DESIGN STRUCTURES Latin Square Designs POSTGRADUATE METHODOLOGY COURSE

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

Field marks: n Treatments are assigned at random within rows and columns, with each treatment once per row and once per column. n There are equal numbers of rows, columns, and treatments. n Useful where the experimenter desires to control variation in two different directions

Sample layout: n Different colors represent different treatments. n There are 4 treatments (A-D) assigned to 4 rows (I-IV) and 4 columns (1-4).

Row I A B C D Row II C D A B Row III D C B A Row IV B A D C Column

ANOVA table format: Source of variation Degrees of freedom a Sums of squares (SSQ) Mean square (MS) F Rows (R)r-1SSQ R SSQ R /(r-1)MS R /MS E Columns (C)r-1SSQ C SSQ C /(r-1)MS C /MS E Treatments (Tr)r-1SSQ Tr SSQ Tr /(r-1)MS Tr /MS E Error (E)(r-1)(r-2)SSQ E SSQ E /((r-1)(r-2)) Total (Tot)r 2 -1SSQ Tot a where r=number of treatments, rows, and columns.

Sample ANOVA table: Source of variation Degrees of freedom Sums of squares (SSQ) Mean square (MS) F Rows a Columns a Treatments a Error Total a F test with 3,6 degrees of freedom at P=0.05 is 4.76

The advantage n Two block (row & column) is used to be one of the error variation n Effect for the treatment will be higher.

TYPES OF DESIGN STRUCTURES Factorial Designs POSTGRADUATE METHODOLOGY COURSE

Factorial Design n There are more than one treatments n `treatments on treatments’ n A A1 A2 B1 B2 B1 B2