The short answer
Count the units that could independently receive the treatment.
Biological replicate
An independent unit for the intended inference
A separately prepared culture, animal, participant or experimental run can represent population variation when it was independently sampled or assigned at that level. Here there are three cultures per treatment.
Technical replicate
A repeated read of the same independent unit
Repeated wells, aliquots or instrument reads can improve measurement of one culture. They do not create new independent treatment assignments. Here each culture has four technical reads.
One hierarchy, shown without collapsing the readings
This simulated assay was designed to isolate the consequence of pseudoreplication. Technical variation within each culture is deliberately small; culture-to-culture variation is much larger. The values are a teaching example, not biological evidence or a model for every assay.
| Technical read | Control culture 1 | Control culture 2 | Control culture 3 | Treated culture 4 | Treated culture 5 | Treated culture 6 |
|---|---|---|---|---|---|---|
| 1 | 19 | 14 | 24 | 26 | 31 | 21 |
| 2 | 20 | 15 | 25 | 27 | 32 | 22 |
| 3 | 20 | 15 | 25 | 27 | 32 | 22 |
| 4 | 21 | 16 | 26 | 28 | 33 | 23 |
What the flattened t test claims
Flattening the subcolumns produces 12 “control” and 12 “treated” observations. A pooled unpaired t test then reports a mean difference of 7.0, t(22) = 3.962, P = 0.000661, with a 95% confidence interval from 3.34 to 10.66.
The arithmetic is correct for 24 independent observations. The design does not supply 24 independent observations. Four readings from culture 1 share preparation, treatment and culture-level variation, so assigning them four independent degrees of evidence understates uncertainty.
What the nested t test changes
The nested table keeps three culture subcolumns under each treatment and four reads within each culture. The group effect is tested against culture-to-culture variation, not against the much smaller read-to-read residual variation. Plotwright reports F(1, 4) = 2.940, equivalently t(4) = 1.715, P = 0.162.
The treatment mean difference remains exactly 7.0. Its 95% confidence interval is now −4.33 to 18.33 because the relevant sample is three culture means per treatment. The estimated intraclass correlation is 0.974: nearly all modeled variation in this constructed example lies between cultures rather than among repeated reads within a culture.
When averaging first gives the same answer
In this balanced example, averaging the four technical reads within each culture and running a pooled unpaired t test on the two sets of three culture means gives the same t(4) and P value as the nested test. That identity is checked directly in the executable test.
Averaging is simple and often defensible when every independent unit has the same number of technical reads and only the treatment contrast matters. A nested model keeps both variation levels explicit and can retain unequal read counts. Neither approach repairs a design with only one genuinely independent unit per treatment.
What the nested model still assumes
- Cultures are independent within and between treatment groups.
- Treatment was assigned at the culture level represented by the model.
- Culture effects and within-culture residuals are adequately modeled as Gaussian.
- The one-factor nested structure is sufficient; batches, plates or repeated time points may require another level or model.
- The six-culture teaching example is too small for a precise biological conclusion.
Plotwright's nested one-way analysis estimates subgroup and residual variance components. It does not expose arbitrary multilevel formulas, random slopes or crossed effects. Use a fuller hierarchical-model environment when the experimental structure requires them.
A transparent reporting template
“Three independently prepared cultures per treatment were measured four times each. Technical reads were nested within culture. The treatment contrast was tested against among-culture variation by a nested t test, t(4) = 1.715, two-sided P = 0.162, mean difference 7.0 (95% CI −4.33 to 18.33). Points show technical reads and open symbols show culture means.”
Replace “culture” and “technical read” with the actual experimental units and report how treatment assignment, batches and exclusions were handled.
What the executable checks establish
Regression tests run all 24 visible values through Plotwright's nested-analysis engine. They lock the sums of squares (group 294, cultures within groups 400, residual 12), the nested statistic and the variance split. Direct SciPy calls reproduce both the invalid flat t test and the valid culture-mean t-test identity.
Those checks establish numerical consistency for this constructed example. They do not determine the experimental unit for a real study, establish that the assumptions hold or convert technical replication into biological replication.
Sources and further reading
- Lazic SE, Clarke-Williams CJ, Munafò MR. What exactly is ‘N’ in cell culture and animal experiments? PLoS Biology. 2018;16:e2005282.
- Lazic SE. Genuine replication and pseudoreplication. Nature Reviews Methods Primers. 2022;2:23.
- Vaux DL et al. Empowering statistical methods for cellular and molecular biologists—biological and technical replication guidance.
- Aarts E et al. The problem of pseudoreplication in neuroscientific studies—experimental-unit definitions and analysis consequences.