Principles of Experimental Design Study Notes

Principles of Experimental Design

Learning Objectives

• Methods of Agricultural Research
  1. Define important terms used in experimental design.
  2. Discuss the principles of experimental design.
  3. Discuss the three basic experimental designs.
  4. Compare the three basic experimental designs.

Definition of Terms

• Experiment: A planned inquiry to discover new facts, or to confirm or deny the results of previous investigations.
• Treatment: A procedure whose effect on the experimental material is to be measured. A class of related treatments is often called a factor.
• Levels of Factor: The states of a factor.
• Experimental Unit: The pieces of experimental material to which one trial of a single treatment is applied.
• Sampling Unit: The fraction of the experimental unit on which the effect of the treatment is measured. A group of homogeneous experimental units is called a block.
• Experimental Design: A set of rules by which the treatments are assigned to the experimental units.
• Experimental Error: The variation among experimental units that have been treated alike.
• Response Variable: A variable used as the measure of the treatment effect.

Well-Planned Experiment

• An experiment must be performed most effectively and efficiently.
• A scientific approach to planning the experiment must be employed.
• There are two aspects to any experimental problem:
  • The design of the experiment
  • The statistical analysis of the data (Montgomery, 1984).

Elements of Experimental Design

• Three Basic Important Elements of Experimental Design:
  1. Replication
  • Refers to the repetition of the basic experiment.
  • Provides an estimate of experimental error, allowing measurement of variation among plots treated alike.
  • Increases precision by reducing standard errors.
    • The standard error of the mean is given by:
      $s_y = \frac{ ext{s}}{ ext{var}} / n$
      where $s^2$ is the sample variance and $n$ is the number of observations (replications).
  • Broadens the base for making inferences by involving a wider variety of plots in the experiment.
  1. Randomization
  • A procedure where each treatment is equally likely to be assigned to any given experimental unit.
  • In randomized controlled experiments, treatments are assigned by chance, minimizing bias.
  • Purpose of Randomization:
    1. Eliminates bias — ensuring no treatment is favored or discriminated against.
    2. Ensures independence among observations — required for valid significance tests and interval estimates.
  1. Local Control
  • A technique to control variability is blocking, which groups plots into blocks of homogeneous units.
  • Reasons for Blocking:
    1. Increases precision by removing differences among blocks from experimental error.
    2. Makes treatment comparisons more uniform.
    3. Increases information from an experiment by enabling sampling of a wider range of conditions.

Ways to Reduce Experimental Error

1. Increase the size of the experiment:
   • By increasing replications.
   • By increasing the number of treatments.
2. Proper selection of treatments:
   • Factorial combinations of treatments have built-in hidden replication for some comparisons.
3. Refine experimental techniques:
   • Using good techniques attempts to reduce variance ($s^2$).
4. Use blocking:
   • Differences between blocks are accounted in experimental error, thus reducing $s^2$.
5. Measure a concomitant variable:
   • Utilizing covariance analysis with the concomitant variable can also reduce $s^2$.

Basic Experimental Designs

• Three Basic Experimental Designs Commonly Used in Agriculture:
  1. Completely Randomized Design (CRD)
  2. Randomized Completely Block Design (RCBD)
  3. Latin Square Design (LS)

A. Completely Randomized Design (CRD)

• Basic Features:

  1. The simplest and least restrictive experimental design.
  2. Treatments are assigned to experimental units (plots) without restrictions.
  3. Every experimental unit is equally assigned to any treatment.

• Advantages:

  1. Flexible: Any number of treatments and replications can be used; replications need not be identical across treatments.
  2. Simple statistical analysis: Easy even with unequal replication.
  3. No issue with missing plots: Missing data do not complicate analysis.
  4. Maximizes error degrees of freedom: More error degrees of freedom provided given the same number of plots and treatments.

• Disadvantage:

  1. Low precision if plots are not uniform.

• Uses:

  1. When the experimental site is relatively uniform or no grouping basis exists.
  2. When a large fraction of plots may not respond or might be lost.
  3. When the number of plots is limited.
  4. When maximizing degrees of freedom is desired.

B. Randomized Completely Block Design (RCBD)

• Basic Features:

  1. Employs one-directional blocking of experimental units where units within a block are homogeneous.
  2. Each block is a complete replication of the entire set of treatments.
  3. Number of experimental units in a block should equal the number of treatments or a multiple of it.

• Advantages:

  1. Removes one source of variation from experimental error, increasing precision.
  2. Broader scope of trials by placing blocks under different conditions.
  3. Any number of treatments and blocks can be used, given treatments are replicated equally in each block.
  4. Simple statistical analysis of results.

• Disadvantage:

  1. Missing data can complicate the analysis; few missing plots can be handled, but multiple missing data can cause major issues.
  2. Misassignment of treatments to wrong plots can lead to analytical problems.
  3. Less efficient in the presence of multiple sources of unwanted variation.
  4. If plots are uniform, less efficient than CRD.

• Uses:

  1. Used to eliminate one source of unwanted variation, providing satisfactory precision without needing a more complex design.
  2. Provides unbiased estimates of the means of the blocking factor.

C. Latin Square Design (LS)

• Basic Features:

  1. Number of experimental units is the square of the number of treatments.
  2. Utilizes row and column blocking.
  3. Each treatment appears once in each row and column.

• Advantages:

  1. Allows control over two sources of variation.

• Disadvantage:

  1. Small error degrees of freedom when few treatments are involved.
  2. Large experiment size as the number of treatments increases.
  3. Complicated statistical analysis due to missing plots or misassigned treatments.

• Uses:

  1. Useful when controlling two sources of variation is necessary.
  2. Practical purposes restrict use to trials with more than four but fewer than ten treatments.

Table 1: Comparison of Basic Designs According to Some Criteria

Learning Activity

Scenario: A researcher plans to experiment on levels of temperature (30, 35, 40, 45, and 50 °C) on corn growth, using three petri dishes for each level and a growth chamber with a temperature control system.

1. Appropriate Design: Determine the most suitable experimental design for the situation.
2. Treatment Definition: Identify the treatment involved.
3. Experimental Units: Define the experimental units in this scenario.
4. Response Variable: Specify the response variable being measured.