= Sampling limits in anatomical variant frequencies
\b[Sampling limits in anatomical variant frequencies] distinguish how often a structure was observed in a specimen set from how common it is in a defined population. The denominator must identify the independent anatomical unit: people, hearts, limbs or images are different units. Preserved material and the detection procedure also determine what can be observed.
A primary example dissected 37 formalin-fixed adult human hearts, finding the <small cardiac vein> in 54% of specimens and an approximately 1 mm venous connection in 19%.<The anatomy of the coronary sinus and its tributaries by J. R. Ortale and others>[Abstract, specimen preparation and variant frequencies]{ref} Those percentages describe that study's material; they do not establish a universal frequency across populations or measurement methods.
Under an original independent, representative-sampling model with perfect detection, a <binomial distribution> gives $X\sim\operatorname{Bin}(n,p)$. If no examples of a specified variant are seen, $\Pr(X=0)=(1-p)^n$. Inverting the one-sided test at level $\alpha$ gives
$$
p_{\rm upper}=1-\alpha^{1/n}.
$$
For a hypothetical zero observations among 37 specimens and $\alpha=0.05$, the upper limit is approximately 0.0778, not zero. The familiar approximation $-\log(\alpha)/n$ is about 0.0810 here. These are illustrations, not unreported results from the anatomical paper.
<Detection-limited anatomical prevalence bounds> add another assumption explicitly. If a real variant is detected with probability $q$ and false detections are absent, the observed-event probability is $qp$. Zero observed cases therefore gives $p_{\rm upper}=\min\{1,(1-\alpha^{1/n})/q\}$ when $q$ is known. At stipulated $q=0.5$, the example limit becomes approximately 0.156. Unknown detection probability cannot be repaired by reporting a more precise count.
Repeated photographs of the same heart do not create independent new hearts. Counting every image as an independent specimen would artificially narrow a <confidence interval>. Selection of unusually accessible, preserved or clinically referred specimens can also produce bias that a <binomial distribution> does not quantify. A useful anatomical report states selection, preservation, observation criteria and the denominator alongside its frequency; uncertainty calculations then make their sampling and detection assumptions visible.
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