Comprehensive Guide to Experimental Designs and Survey Sampling in R

Introduction

The session covered practical steps for setting up experiments, generating randomizations with R, and designing surveys. It combined technical demonstrations (R code, the agricolae package) with conceptual explanations of why certain designs are chosen.

Preparing Materials and Registration

• Participants were asked to use a shared Google link to download registration forms for Day 4.
• Updated PowerPoint files for Days 1‑4 were made available in the shared folder.
• Dr. Thomas would join later to review and repeat key points from the previous day.

Randomized Complete Block Design (RCBD) in R

• Seed setting ensures reproducibility of randomizations.
• A factor vector f was created to represent treatments (e.g., A, B, C) with equal replication (4 × each → 12 experimental units).
• Random assignment was performed by sampling without replacement, then a data frame was built with columns for experimental unit and treatment.
• The resulting plan can be inspected, and changing the seed produces a different layout.

Importance of Blocking and Experimental Error

• When experimental units are homogeneous, variation not explained by treatment is pooled into experimental error.
• Heterogeneous units introduce additional variation, inflating error and reducing the ability to detect treatment effects.
• Blocking groups similar units together, thereby reducing noise and improving precision.

Latin Square Design

• Controls variation in two directions (rows and columns) by arranging treatments so each appears once per row and column.
• Suitable when two sources of systematic variation exist (e.g., soil fertility gradient and slope).
• Limitations: requires a square number of treatments; large squares become impractical in field work.

Split‑Plot Design

• Used when one factor (e.g., irrigation) requires larger plots than another factor (e.g., seed variety).
• Whole plots receive the coarse‑scale factor; sub‑plots receive the fine‑scale factor.
• Can be combined with CRD, RCBD, or Latin square structures.
• Analysis involves separate error terms for whole‑plot and subplot factors.

Incomplete Block Designs

• Balanced Incomplete Block Design (BIBD): each pair of treatments occurs together the same number of times across blocks.
• Partially Balanced: some pairs occur more frequently than others.
• Resolvable Designs: blocks are grouped so each group forms a complete replicate of all treatments, useful when the number of treatments exceeds block size.
• The agricolae functions design.bib and design.rcbd automate generation of these designs.

Row‑Column and Alpha Lattice Designs

• Row‑column designs are incomplete Latin squares where either rows, columns, or both are reduced to fit practical field sizes.
• Alpha lattice designs (e.g., 10 × 10) allow flexible block sizes and are popular in plant breeding; they require the relationship t = s × k to hold.

Using the agricolae Package

• Install with install.packages("agricolae") and load via library(agricolae).
• Functions:
• design.rcbd(trt, r, seed) – randomized complete block.
• design.lsd(trt, seed) – Latin square.
• design.bib(trt, k, seed) – balanced incomplete block.
• design.alpha(trt, k, r, seed) – alpha lattice.
• Each function returns a list containing parameters, a sketch, and a data frame (book) ready for field use.

Survey Sampling Overview

• Surveys aim to infer population characteristics from a sample.
• Margin of error (or sampling error) quantifies the uncertainty; a common target is ±5 % at 95 % confidence.
• Example: a health‑concern survey in Uganda reported 29 % prevalence with a ±3 % margin of error (n = 872).

Sampling Methods

• Cross‑sectional – single point in time.
• Longitudinal – repeated measurements (cohort, panel).
• Simple Random Sampling (SRS) – every unit has equal selection probability.
• Systematic Sampling – select a random start, then every k‑th unit; interval k = N/n.
• Stratified Sampling – divide population into homogeneous strata, sample within each; improves precision for heterogeneous populations.
• Cluster Sampling – select whole groups (clusters) first, then sample within clusters; can be one‑stage or two‑stage.
• Multi‑stage Sampling – combines stratification, clustering, and simple/random/systematic sampling; common in national surveys.

Practical Tips and Common Pitfalls

• Always inspect the experimental material before randomization; field scouting helps define blocks.
• Keep the seed constant when you need to reproduce a layout.
• For large numbers of treatments, consider incomplete or resolvable designs to keep field size manageable.
• In surveys, ensure the sampling frame is representative; avoid convenience sampling unless bias is acceptable.
• Document the chosen design, replication, and block size; this information is essential for reproducibility and for reviewers.

Conclusion

• Proper experimental design—whether RCBD, Latin square, split‑plot, or an incomplete block—reduces experimental error and increases the power to detect true treatment effects.
• The agricolae package streamlines generation of these designs in R, allowing researchers to focus on scientific questions rather than manual randomization.
• In survey work, selecting an appropriate sampling method and controlling the margin of error are crucial for producing reliable, unbiased population estimates.

Choosing the right design and randomization method—matched to the homogeneity of experimental units or the structure of the target population—minimizes noise, maximizes precision, and ensures that results are both reproducible and statistically robust.