TL;DR
Your n is the number of independent experimental units, not the number of measurements. Measuring the same sample three times gives you precision on that sample (technical replicates), not three independent data points. Counting technical replicates as n (pseudoreplication) fakes statistical power and is one of the most common (and most serious) errors in biology papers.
Technical vs. biological replicates
- Technical replicates: repeated measurements of the same biological sample, such as three qPCR wells from one RNA extraction or three reads of the same plate. They quantify measurement noise. Average them; they collapse to a single value for your biological unit.
- Biological replicates: independent biological units, such as different animals, different mice, separately cultured and independently treated dishes, or independent experiments on different days. These are what your statistics generalize over.
Your n is the number of biological/independent units, because that's the level at which you want to draw conclusions about the population.
Pseudoreplication
Pseudoreplication is treating non-independent measurements as if they were independent, inflating n and artificially shrinking your error bars and p-values. Classic versions in biology:
- Counting wells from a single culture flask as independent samples.
- Counting multiple cells from one animal as n = (number of cells) instead of n = (number of animals).
- Pooling repeated measurements on the same subject as separate observations.
- Treating one experiment imaged many times as many experiments.
The giveaway: a huge "n" that came from subsampling one or a few true units. It makes results look far more precise and significant than the data support, and such findings frequently fail to replicate.
Toggle between counting wells and counting animals on the same experiment. The error bars tell two very different stories:
n = 12 "wells". Counting technical wells as independent shrinks the 95% CI to near-nothing: false confidence. The wells are not independent samples.
How to handle nesting correctly
When you have structure (cells within animals, wells within experiments), you have two valid options:
- Summarize to the independent unit. Average the technical replicates per animal/experiment, then run your test on those per-unit means with n = number of units. Simple and usually correct.
- Model the structure explicitly with a linear mixed-effects model, including a random effect for the grouping (e.g.,
(1 | animal)). This keeps all the data while accounting for non-independence, and is the better approach when the nested structure is itself of interest or unbalanced → see ANOVA/mixed models in ANOVA.
What you must not do is feed all the subsamples into a t-test as independent points: either average to the independent unit, or model the structure with a mixed-effects model.
A biology example
You treat cells and run the assay in 3 wells per condition, repeated across 3 independent experiments. The wells are technical replicates; the experiments are your biological replicates, so n = 3, not 9. Average the 3 wells within each experiment, then compare the 3 per-experiment means. Reporting n = 9 here would roughly triple your apparent precision on a false basis, exactly the kind of thing reviewers now look for.
Common mistakes
- Reporting n = number of cells/wells/images instead of number of independent units.
- Pooling technical replicates into the test as if independent.
- Not stating clearly in the methods what one "n" is. Reviewers increasingly require this for every figure.
- Designing for technical replication when you needed biological replication. Three measurements of one mouse can't tell you about mice in general; you need more mice.
- Confusing more measurements with more power. Power comes from independent units → power and sample size.
Related
Power and sample size · ANOVA and mixed models · Reporting statistics