Count evidence honestly by distinguishing new independent trials from multiple looks at one setup.
Field diagramA repeatable study cycle
Estimated reading
10 min
Estimated practice
20 min
Equipment
Paper or spreadsheet; supplied repeated-reading dataset.
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Objective
By the end, you can:
Define independent experimental units and repeated readings.
Recognize pseudoreplication and its effect on uncertainty.
Choose a summary that reflects the design.
What is being repeated?
An independent replicate is a new experimental unit that receives its condition independently. A repeated reading is another observation of the same unit or setup. Five balance readings of one object can describe display noise, but they are not five independent objects. Five separately prepared water fills may be independent trials if preparation, assignment, and handling are independent under the design.
Pseudoreplication occurs when repeated observations are counted as though they were independent units. It can make a standard error look smaller and a comparison look more certain than the design supports. Repeated readings are still useful: they can reveal instrument resolution, drift, observer variability, or within-unit change. Keep the levels separate in the record and analysis.
Unit-level variation asks how independently prepared units differ.
Within-unit variation asks how readings of one unit change under the reading process.
Nested data need a plan: summarize readings within unit or use a model that represents the nesting.
The number of readings is not a universal substitute for the number of independent units.
Plan the hierarchy
Draw the nesting before data collection: batch contains units; unit contains readings. Decide which level answers the question. If the question is vessel-to-vessel repeatability, each independent fill is a unit. If the question is display stability, repeated readings of one stable object may be appropriate. Report both counts so a reader can see what the evidence represents.
Use unique identifiers for unit and reading, such as A03-R2.
Avoid averaging away a trend before checking for drift or order effects.
When resources limit independent units, narrow the claim rather than relabeling readings as replicates.
Worked example
A transparent summary
Two vessels each receive four independent water fills. Each fill is read twice because the operator checks display stability.
01Independent units: 4 fills per vessel; n = 4 for the vessel comparison.
02Repeated readings: 2 per fill; used to identify display instability and summarize within-fill variation.
03Analysis: average or otherwise summarize the two readings within each fill only after checking for drift; compare the four fill-level summaries.
04Report: “4 independent fills per vessel, 2 readings per fill,” not n = 8.
Materials
Set out what you need.
Hierarchy worksheet
Supplied dataset with unit and reading identifiers
Safety & stop conditions
Pause if the work no longer fits the plan.
No physical procedure is required. If later practice involves repeated measurements, use only reviewed water-only activities and preserve all readings.
Method
Work through the steps.
01
Name the unit
Write what was independently prepared, assigned, or exposed to the condition. Give it a persistent ID.
02
Label repeated readings
Record each observation under its unit ID and note time, instrument, and order.
03
Choose the analysis level
Summarize within unit when the question concerns units, or use a method that explicitly represents nested readings.
Checkpoints
Observe, record, investigate.
The denominator for n is stated.
Repeated readings remain available for diagnosing drift or noise.
The conclusion matches the level that received independent conditions.
Common mistakes
Correct the process, preserve the record.
Calling triplicate readings of one sample three replicates.
Call them repeated readings unless three independently prepared samples were used.
Averaging readings before checking order.
Inspect the sequence first; averaging can hide drift or a changing setup.
Assuming independence because values are in separate spreadsheet rows.
Independence comes from the design and preparation, not the layout.
Practice
Count the evidence
A dataset has 3 water fills per vessel and 4 display readings per fill. Determine the independent n for a vessel comparison and the role of the 4 readings.
What is the experimental unit?
What could the repeated readings diagnose?
How would the answer change if all readings came from one fill?
01Why can pseudoreplication make a result look stronger?
Answer: It treats correlated observations as independent, which can understate variation and uncertainty. The apparent sample size grows without adding independent information.
02Are repeated readings useless?
Answer: No. They reveal reading noise, drift, and stability. They simply answer a different question from variation among independently prepared units.
03If one unit is measured five times and another once, what should you do?
Answer: Preserve the imbalance, inspect why it occurred, and choose an analysis or summary that represents units without pretending equal independent replication. Record the deviation and limit the conclusion if needed.
