Tensions in Practice: Assignment control in tension with analytic flexibility¶
A toy comparison across two workshop shifts
A workshop compares treatment T with control C using two units in the morning and two in the evening. If shift can affect the outcome, it can assign one T and one C within each shift. Or it can randomize across the whole pool and use shift information in the later analysis model. The first changes the allowed assignments; the second changes how outcomes are interpreted.
Build balance into assignment
Ensure treatment counts are balanced within the declared shifts.
Keep assignment less constrained
Account for a known covariate through an explicit analysis model.
Why these aims pull against each other
Blocking constrains allocation before results exist. Later adjustment saves that allocation constraint but requires adequate data and defensible modeling.
Choose an arrangement to see what changes and what remains difficult.
Arrows express the declared relations, not measured effect sizes. Examples and quantities are illustrative.
What this choice protects
What it costs
When it fits
Compare the arrangements
Randomize within each shift
Form the known shift pairs and randomly choose one treated and one control unit inside each.
- What it protects
- Both treatments occur within each shift in this toy.
- What it costs
- The assignment must respect shift membership and availability; maintaining blocks adds work.
- When it fits
- The anticipated shift difference matters and the pairwise allocation is feasible.
Illustration note: No variance reduction, power or confounder balance beyond the declared counts is quantified.
Adjust for shift in analysis
Randomize across the full pool, then include the recorded shift in the outcome model.
- What it protects
- Assignment need not enforce a quota inside each shift.
- What it costs
- Some realized assignments can confound treatment and shift completely in this tiny sample, leaving the desired model comparison unidentified.
- When it fits
- The realized data provide the needed overlap and the model is appropriate; otherwise more information or redesign is required.
Illustration note: This is an alternative location for control, not a claim that regression repairs any allocation.
What this illustration does—and does not—establish
The source supplies the stated tension; the selected arrangements are bounded editorial illustrations. Costs and conditions remain part of the comparison.
- The four units illustrate assignment structure, not an adequate real study size.
- Blocking and model adjustment can be combined; the contrast isolates where each acts.
- Known blocks do not control unmeasured differences, attrition, spillovers or bad measurements.
- This is experimental treatment assignment, not stratified population sampling.
Source entries
Blocking (In Experimental Design)
This source passage supplies the contextual tension. The concrete arrangements and schematic examples are editorial illustrations, not measured findings.
Design-based control versus model-based control
T3 — Design-based control versus model-based control. Blocking achieves variance reduction through how units are assigned; covariate adjustment in regression achieves it through how the model is fit. The two can produce similar efficiency gains when the covariate relationship is linear and well-specified.
The source operation
(1) Blocking partitions experimental units into groups (blocks) that share similar levels of known nuisance variables — soil fertility, patient age, machine shift, calendar week — so that each treatment is tested *within* each block rather than across the whole population at once.