Statistical Parameters: Sensitivity, Specificity & Predictive Value

Why Statistics Belong on a Physics Exam

Domain 5 of the SPI blueprint (task 5.F) requires sonographers to understand the statistical parameters used to judge how well a diagnostic test — including ultrasound itself — performs against a reference, or gold, standard. These parameters describe test performance across a population, not the certainty of any single scan, and they underpin how QA results, screening-program design, and imaging findings should be interpreted in context.

The 2×2 Framework: True/False Positives and Negatives

Every diagnostic-accuracy statistic on SPI is built from four outcome categories, defined by comparing the test result against the reference standard:

• True Positive (TP): the test correctly identifies disease.
• False Positive (FP): the test indicates disease, but none is present.
• False Negative (FN): the test indicates no disease, but disease is present.
• True Negative (TN): the test correctly identifies the absence of disease.

The Five Core Formulas

Memorize these by matching the denominator to what is being asked: sensitivity and specificity are denominated by the true disease status (all truly diseased, or all truly disease-free), while PPV and NPV are denominated by the test result (all who tested positive, or all who tested negative). Accuracy is the only parameter that uses the entire tested population as its denominator.

A Worked Example

Suppose 100 patients undergo an ultrasound-based screening exam, and every result is later confirmed against a surgical/pathologic reference standard: 40 have the disease, 60 do not. Of the 40 truly diseased, the test correctly flags 36 (TP = 36, FN = 4). Of the 60 truly disease-free, the test correctly clears 54 (TN = 54, FP = 6). Sensitivity = 36/(36+4) = 90%; specificity = 54/(54+6) = 90%; PPV = 36/(36+6) = 86%; NPV = 54/(54+4) = 93%; accuracy = (36+54)/100 = 90%. Notice PPV and NPV differ from sensitivity and specificity even though the test's intrinsic performance (90%/90%) is unchanged — that gap is driven entirely by how common the disease is in this particular sample.

Why the Distinction Matters

Sensitivity and specificity describe how good the test itself is, independent of how common the disease is in the population being tested — these are intrinsic properties of the test. PPV and NPV, by contrast, are influenced by disease prevalence: the same test, applied to a population with a much lower rate of disease, will show a lower PPV — more of the positives will turn out to be false alarms — even though sensitivity and specificity have not changed. This is a classic SPI distractor: a question may describe a highly sensitive and specific test used to screen a low-prevalence population and ask why so many positives turn out to be false. The answer is prevalence's effect on PPV, not a flaw in the test's underlying sensitivity or specificity.

Applying This to Ultrasound Practice

A test with high sensitivity is preferred when missing a disease (a false negative) carries a serious cost — it is used to rule out disease, because a negative result on a highly sensitive test is reassuring. A test with high specificity is preferred when a false alarm (false positive) carries a serious cost — it is used to rule in disease, because a positive result on a highly specific test is convincing. Correctly assembling TP, FP, TN, and FN from a word problem, and recognizing which parameter a clinical scenario is really asking about, is exactly the skill SPI's task 5.F tests.

These parameters apply whenever ultrasound findings, or any diagnostic test, are validated against a reference standard — for example, comparing a sonographic diagnosis against surgical or pathologic confirmation, or evaluating how well a new imaging protocol identifies a target condition compared with an established reference test. On the exam, expect scenario-style items that give raw counts (or a completed 2×2 table) and ask you to compute one specific parameter, or that describe a change in the tested population and ask which parameter shifts as a result.

Quick Reference Recap

• Sensitivity = TP/(TP+FN) — catches true disease; a negative result rules disease out.
• Specificity = TN/(TN+FP) — clears true health; a positive result rules disease in.
• PPV = TP/(TP+FP) — trustworthiness of a positive result; prevalence-dependent.
• NPV = TN/(TN+FN) — trustworthiness of a negative result; prevalence-dependent.
• Accuracy = (TP+TN)/(TP+TN+FP+FN) — overall fraction correctly classified.