6.1 RCB Design and its Observational Relatives

Definition of a block and Randomized Complete Block (RCB) Design.
Comparison of statistical methods (block designs vs. repeated measures) in psychology.
Historical significance of block design in both agriculture and psychology.
Abstract equivalence of experimental units (farmland, rats, humans) discussed.

Example: Financial incentives for weight loss.
Challenge: High unit-to-unit differences due to individual variability in weight loss commitment and responsiveness to incentives.
Revised proposal: Implement paired t-tests with matched pairs based on two variables.
Benefit of new design: Reduced residuals, increased power, larger effect size, and narrower confidence interval.

Design types for weight loss experiments:
- Two-sample t-test: Completely randomized design assigning subjects to either Control or Financial Incentive.
- Paired t-test: RCB Design where subjects are paired and randomly assigned to one treatment within each pair.
Principles of block design:
- Goal: Reduce residual error.
- Key idea: Compare "like with like."
- Strategy: Create blocks of similar experimental units.

Visualization of Fisher’s block design comparing wheat varieties.
Explanation of experimental plans through two panels illustrating the same assignment structure.
Historical context: Fisher initiated the application of block design in agriculture, which later spread to other fields.

Types of block creation:
- Subdividing large plots of land.
- Sorting and matching subjects into groups based on characteristics.
- Reusing subjects across different treatment conditions.
Block creation examples:
- Fisher’s wheat trial: Noted for subdividing large fields into smaller plots.
- Weight loss study: Blocks from matching subjects based on motivation and receptivity.

Study on impacts of caffeine, theobromine, and placebo on reaction time.
Focus on utilizing each subject as a block across multiple treatments.
Consideration of confounding effects:
- Wash-out period for carry-over effects.
- Randomizing order of treatments to mitigate time trends.

Investigation aimed to discern efficiency based on left vs. right brain activity during tasks.
Tasks categorized into decisions and reports:
- Decision tasks compared (visual vs. verbal).
- Reporting mechanisms (visual vs. verbal).
Results examination: Interaction effects are more significant than average responses for individual tasks.

Definition: A block contains sets of similar experimental units.
Structure of RCB design:
- Each block has equal units to treatments.
- Random treatment assignment within blocks.

Introduction of observational designs paralleling experimental designs.
Examples:
- Radioactive twins: Comparing city vs. rural lung health using twins as blocks.
- Sleeping shrews: Heart rate monitoring across sleep phases using individual shrews as blocks.
- River iron: Measurement of chemical components across different river locations using river sites as blocks.

Key terms introduced:
- Factors and levels: Categorical predictors.
- Crossed factors: Collecting data on all factor combinations.
- Nuisance vs. Interest Factors: Different roles impacting variation.
- Fixed vs. Random Factors: Differentiating how factors behave in the context of study.
- Main Effects: Differences highlighted for treatments and blocks.
- Additive Main Effects: Assumption that treatments provide consistent effects across subjects.