🏜Experimental Design — Basic Concepts

An agronomist wants to compare five fertiliser doses on rice yield. She cannot simply apply dose A to a fertile corner and dose E to a barren patch — that would confound treatment effects with soil differences. How should she arrange the experiment to draw fair, reliable conclusions? The answer lies in the principles of experimental design, pioneered by R.A. Fisher for exactly this kind of agricultural problem.

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Data Collection: Survey vs Experiment

The ability to establish cause-and-effect relationships is what makes experimentation so powerful compared to observational studies.

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Pioneer of Experimental Design

• Modern experimental design concepts are due primarily to R.A. Fisher, developed during the 1920s-1930s at Rothamsted Experimental Station, England, for planning agricultural field experiments.

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Basic Concepts

Blocks

• In agricultural experiments, the entire field is divided into relatively homogeneous sub-groups called blocks.
• Plots within the same block are similar in soil fertility, moisture, and other characteristics, so observed differences between treatments can be more confidently attributed to the treatments themselves.

Treatments

• The objects of comparison in an experiment. Each specific condition or factor level being evaluated is a treatment.
• Examples:
  • Different spacings tested for yield effect → each spacing is a treatment
  • Different fertiliser doses → each dose is a treatment
  • Different teaching methods → each method is a treatment
  • Different skin creams → each cream is a treatment

Experimental Unit

• The object to which a treatment is applied to record observations — the smallest unit receiving a treatment independently.
• Examples:
  • Groups of insects receiving different insecticides → each group is an experimental unit
  • Plots receiving different varieties → each plot is an experimental unit

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Three Basic Principles of Experimental Design

1. Replication

• Repetition of a treatment across different experimental units.
• Without replication, we cannot distinguish treatment effects from random variation.

Why replicate?

• To secure a more accurate estimate of experimental error
• To reduce experimental error and increase precision
• Standard error of treatment mean = σ/√r (as r increases, S.E. decreases)

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2. Randomisation

• Random allocation of treatments to experimental units — every treatment has an equal chance of being allotted to any unit.
• Done using random number tables or computer-generated random numbers.

Purpose:

• Removes bias and uncontrollable extraneous variation
• Forms the basis of any valid statistical test (along with replication)
• Controls variance in field experiments

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3. Local Control

• Grouping of homogeneous experimental units into blocks to isolate and remove known sources of variation from the error term.
• Reduces experimental error by ensuring that variation between blocks is accounted for separately.

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Experimental Error

• Variation due to uncontrolled factors — everything not accounted for by treatments or blocks.
• Smaller error = more precise comparisons. The goal of good design is to minimise this error.

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Shape and Arrangement of Plots and Blocks

• Plot shape and block arrangement directly affect precision.
• For maximum precision: plots should be rectangular with their long sides parallel to the fertility gradient.
• Blocks should be arranged one after another along the fertility gradient.

The reasoning: rectangular plots running along the gradient capture more soil variability within each block, reducing within-block variation.

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What Is an Experimental Design?

A plan specifying:

1. Arrangement of treatments
2. Grouping of experimental units
3. Method of randomisation

All aimed at obtaining valid and efficient results.

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Comparison of Experimental Designs

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Summary Table

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Which Experimental Design to Use? — Decision Guide

The most tested decision in agricultural statistics:

Decision flowchart for exams:

1. Is the experimental area uniform? → CRD
2. Is there one-directional variation? → RBD (most commonly used in agriculture)
3. Is there two-directional variation AND treatments ≤ 12? → LSD (constraint: treatments = replications)
4. Testing two or more factors? → Factorial experiment (laid out in RBD or LSD)

Key constraints to remember:

• CRD: Unequal replication allowed (only design where this is OK)
• RBD: Each treatment appears exactly once per block
• LSD: Number of treatments = number of rows = number of columns (so max ~12 treatments practical)
• LSD has maximum error df when treatments = 5 (error df = 12)

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Summary Cheat Sheet