You have 50,000 measurements from 200 patients. What is your sample size?

hard

Answer

$Closer to 200 than to 50,000, because observations within a patient are correlated and each additional measurement from the same patient carries much less new information than a measurement from a new patient.$
$Treating all 50,000 as independent shrinks the standard errors dramatically and produces confidence intervals far too narrow, which is how clustered data generates confident nonsense.$
$The effective sample size depends on the intraclass correlation, and even a modest value collapses the benefit of many repeats per subject.$
$The correct treatments are a mixed effects model with a random intercept per patient, cluster-robust standard errors, or aggregating to one summary per patient and analyzing those.$
$Randomization must also happen at the patient level, otherwise the treatment is entangled with the cluster.$

Check yourself — multiple choice

50,000 independent observations
Nearer 200: within-patient correlation means repeats add little information, so use mixed effects, cluster-robust errors or per-patient aggregation and randomize by patient
The average of the two
Sample size is irrelevant here

Intraclass correlation reduces effective sample size, so clustered data needs mixed effects or robust errors.

#mixed-effects#regression

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