Even with a perfect 2² combination table, executing from low-low through high-high in standard order can mix condition effects with time drift as equipment warms. Design geometry alone does not complete a good experiment.
This unit asks one question.
When executing the same treatment combinations, which bias and uncertainty do order, replication, and blocks prevent?
Separate standard order from run order
Standard order is a mathematical ordering that makes a design easy to read. Actual run order should be randomized where possible. Randomization prevents unknown noise—time drift, operator learning, equipment temperature, or material changes—from attaching systematically to particular treatments.
Randomization does not remove drift. It distributes drift across conditions, supporting treatment as random error; inspect trends in residuals by run order if time is recorded. If full randomization is impossible because of safety, cleaning, or material constraints, record the constraint and use a suitable design and model such as split-plot. Do not arrange runs arbitrarily and call them randomized.
Replication reapplies the treatment to a new experimental unit
Independent replication reruns the same treatment combination on a new independent unit. It observes natural variation directly, estimates pure error, and permits effect SE and lack-of-fit assessment.
Technical repeats read the same sample multiple times on an instrument. They can improve measurement precision and support QC, but do not increase independent n for biological or process variation.
- measuring each condition in 6 donors: donor n=6
- dispensing one donor sample into 6 wells: donor n=1, technical wells=6
- reading each of 3 independent batches twice: batch n=3
‘n=12’ does not say whether there are 12 donors or 12 wells from one donor. Separate biological/process replicates and technical replicates in tables and analysis. Counting technical repeats as independent n is pseudoreplication.
A block makes a fair comparison within a known large noise source
When an experiment spans days and Day 1 versus Day 2 differences are expected, use date as a block. Put treatment conditions to be compared in balanced fashion within each block, randomize within blocks, and include block effects in the model to separate date differences from effects of interest.
Blocking is not free. Some factorial interactions can be confounded with block effects; if one block contains only a specific treatment, treatment and block cannot be separated. Check before design that important treatments can appear in every block.
In-Silico Lab: attach drift to standard and random order
- At drift=1 per run, inspect whether later standard-order conditions are systematically higher.
- With the same drift, set randomized=yes and inspect how the connection between condition and time changes.
- Change the seed to confirm randomization is not one uniquely correct order.
- Explain why the two rows of each treatment combination must be independent replications.
Break the coupling of time drift and execution order
Run the same 2² combination twice, but compare which condition drift is attached to in the standard order and the random order.
If this is your first time: What should I press?
- 1. Read the question firstIn the Lab title, check the one thing you will compare this time.
- 2. Change just one conditionInitially, change only one of the inputs: n, effect, or spread.
- 3. new composite specimen pressureNew synthetic data is created. The same conditions may vary depending on the sample.
- 4. Pictures and calculation results CompareWrite in one sentence what moves and what stays the same before and after the change.
If it gets stuckresetGo back to see the default results and change just one condition. This Lab is not a correct answer tester but a pattern observation tool.
Synthetic observations of the same settings
| order | A | B | rep | Y observed |
|---|---|---|---|---|
| 1 | 1 | 1 | 4 | 87.0 |
| 2 | -1 | 1 | 3 | 64.0 |
| 3 | 1 | -1 | 3 | 71.0 |
| 4 | 1 | -1 | 4 | 72.0 |
| 5 | -1 | -1 | 1 | 65.0 |
| 6 | 1 | 1 | 5 | 92.0 |
| 7 | -1 | 1 | 2 | 69.0 |
| 8 | -1 | -1 | 2 | 68.0 |
calculation result
Randomization does not eliminate drift. Avoid systematically attaching to a specific process, and separate known large sources into blocks.
educational synthetic modelbjs-factorial-sequence-v1. Actual research judgments must separately reflect experimental units, missingness, distribution, multiplicity, pre-planning, and domain criteria.
Blinding and allocation concealment are also execution quality
If assessors know treatment, threshold calls or exclusions can be biased. Where possible, blind sample IDs, prespecify exclusion rules, and record every run failure and rerun. Retaining only the randomization seed while hiding execution deviations is not a reproducible design.
A JMP design table needs three distinct columns
Distinguish between standard order and actual execution order.
Only independent reruns contribute to the net error information.
Isolate known sources of noise, such as dates and raw material batches, into the model.
Read Pattern or Standard Order, Run Order, and Block separately, linked to raw-data row IDs. Declaring replicate count in software does not guarantee real independence; software cannot know whether a row is a new batch or a reread of the same sample.
Items for an execution receipt
- design version and candidate model
- actual factor units and permitted ranges
- standard order, randomized run order, and seed
- block definition and within-block randomization
- independent experimental-unit IDs and technical-replicate IDs
- run time, equipment, operator, and material lot
- missing runs, reruns, protocol deviations, and reasons
- time of blind release
Takeaways
- Randomization breaks systematic attachment of treatments to time and order noise.
- Independent replication estimates pure error and effect SE.
- Technical repeats do not increase independent experimental units.
- Blocks compare conditions within known large noise sources.
- Arrange blocks so they do not confound treatment effects.
- Preserve both the design table and actual execution deviations.
The next unit connects executed responses to effects, ANOVA, regression equations, and Profiler while retaining residual and model-hierarchy checks.
Official supplementary resources
The run table and Lab in this article are educational synthetic material.