Experimental Design: Steps and Components

• Experimental design is a set of rules and course of action in the conduct of an experiment.
• Experimental designs provide cost effective collection of appropriate data
• Experimental designs guide valid data analysis and provide reliable inferences

Steps in Conducting an Experiment

• Define the problem of the study, including the population, variables, influencing factors, and objectives.
• Formulate hypotheses.
• Define the data to be collected and the statistical analyses to be performed.
• Devise the experimental technique and design, defining treatments, experimental units, experiment size, randomization, error control, and layout.
• Conduct the experiment.
• Analyze the data.
• Prepare the report of the results.
• Present the results.

Components of Experimental Design

• Treatments: Independent variables
• Experimental units: Objects or units of material
• Response variable(s): Dependent variables
• Replication
• Randomization
• Error control
• Replication, Randomization and Error control define the three basic principles of experimental design

Definitions

• Treatment or Factor: A set of experimental procedures or conditions whose effects are to be measured and compared.
• Experimental Unit (eu): A unit or group of units (experimental material or individual) to which a single treatment is applied in one replication of the basic experiment.
• Response Variable: Characteristics used to measure the effect of a treatment.
• Experimental Error: Measure of variation among experimental units treated alike.

Sources of experimental error:

• Inherent variability of the experimental units
• Errors in experimentation, such as lack of uniformity or failure to standardize techniques
• Errors in observations and measurements.
• Combined effects of all extraneous and uncontrollable factors.
• Sampling Unit (su): Portion of the experimental unit on which the response variable is observed or measured, such as a leaf in a plant or a plant in a plot.
• Sampling Error: Measure of variation among sampling units within experimental units.
• Layout refers to the final arrangement of treatments over the whole set of experimental units.

Principles of Experimental Design

• Replication: Repetition of the application of treatments on a number of experimental units.
  • Replication provides an estimate of the experimental error and enables tests of significance and interval estimation.
  • Replication increases the precision of the estimates.
• Factors affecting the number of replications include the degree of precision required, uniformity of experimental units, number of treatments, experimental design, and available resources like time and cost.

Randomization

• Randomization allocates treatments to the experimental units.
• Every treatment has an equal chance of being assigned to any experimental unit.
  • Randomization provides a random sample of observations.
  • Randomization satisfies the assumption of independence of observations.
  • Randomization eliminates systematic bias in assigning the treatments.
• Error or Local Control is any process or technique used to minimize the experimental error.

Common techniques for local control include

• Proper choice of experimental design.
• Proper choice of size and shape of experimental units.
• Use of concomitant variables.
• Refinement of experimental techniques, including uniform application of treatments, more control over external influences, unbiased measurement techniques, and preventing gross errors.
• Grouping: Placing the set of homogeneous experimental units into groups so different groups may be subjected to different treatments.
• Blocking: Grouping the experimental units into blocks such that the units within a block are relatively homogeneous.
• Balancing: Obtaining the experimental unit, the grouping, the blocking, and assignment of the treatments to the experimental unit to achieve a balanced configuration

Balanced Design Benefits

• Test statistic is insensitive to small departures from with assumption of equality of variances
• Power is maximised with equal sample sizes

Structures of Experimental Design

• Treatment structure: Treatment combinations chosen to be studied.
• Design structure: Grouping of experimental units into homogeneous blocks.

Types of Treatment Structures

• One-way treatment structure: Treatments consist of levels of a single factor.
• Two-way treatment structure: Treatments consist of the treatment combinations resulting from combining levels of two different factors tested.
• Factorial arrangement treatment structure: Consists of all possible combinations of the levels of two or more factors being tested.
• Fractional factorial: Consists of only a part or fraction of the possible treatment combinations in a factorial treatment structure.

Types of Design Structures

• Completely Randomized Design: All experimental units are homogenous, can be classified as one block, and treatments can be assigned completely at random.
• Randomized Complete Block Design: Takes care of a single gradient existing among the experimental units; number of experimental units within a block is a multiple of the number of treatments, so the complete set of treatments can be assigned completely among units within each block.
• Latin Square Design: Accounts for two sources of variation among experimental units (row and column), with treatments occurring once in each column and row.
• Incomplete Block Design: Number of experimental units in a block is less than the number of treatments.

Fixed vs Random Models

• Random Factor: Factor with levels consisting of a random sample from a population.
• Fixed Factor: Factor with levels selected by a non-random process or consisting of a random set of levels from a population.
• Fixed Model: Levels of the factors are selected on purpose.
• Random Model: Levels of the factor are a random sample from a large population.
• Mixed Effects Model: Combination of fixed and random effects.

Analysis of Variance & the F-Distribution

• F-distribution requires the sample variances (S1^2 and S2^2) of independent random samples of sizes n1 and n2 from normal populations with variances σ1^2 and σ2^2
• F = (S1^2/σ1^2) / (S2^2/σ2^2)
• Results in F distribution.
• F-Test tests Ho: σ1^2 = σ2^2 versus Ha: σ1^2 ≠ σ2^2.
• Test Statistic: Fc = (S1^2/σ1^2) / (S2^2/σ2^2) = S1^2 / S2^2
• Decision Rule: Reject Ho if Fc > Fα(n1-1, n2-1).

Key Elements to Include

• Description
• Layout and Randomization
• Linear Model
• Data Presentation
• ANOVA Table
• Example