Sensitivity & Specificity

1️⃣ First, Understand the Problem: Why Do We Need These Terms?

Imagine you created a blood test to detect a disease.
But how do you know if your test is good?

A good test should:

• Detect disease when it is truly present

• Not give positive results when disease is absent

This is where Sensitivity and Specificity help.

They tell us how accurate a diagnostic test is.

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2️⃣ The Foundation: The 2×2 Table

Everything starts with this simple table:

This table is the backbone of all diagnostic test evaluation.

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3️⃣ Sensitivity (Think: “How many sick people does the test catch?”)

Definition (Student-friendly):

Sensitivity measures how well the test detects people who actually have the disease.
It answers:
👉 “If 100 people truly have the disease, how many will my test correctly pick?”

Formula:

Sensitivity=TP / TP+FN

Sensitivity=TP+FN / TP​

Key Idea:

• High sensitivity = rarely misses patients

• Good for screening tests

Mnemonic:

“SnNout”:
High Sensitivity → when Negative, rules out disease.

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4️⃣ Specificity (Think: “How many healthy people does the test correctly identify?”)

Definition (Student-friendly):

Specificity measures how well the test identifies people who DO NOT have the disease.
It answers:
👉 “If 100 people are healthy, how many will my test correctly say are negative?”

Formula:

Specificity=TN / TN+FP

Specificity=TN+FP / TN​

Key Idea:

• High specificity = rarely labels healthy people as sick

• Good for confirmatory tests

Mnemonic:

“SpPin”:
High Specificity → when Positive, rules in disease.

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5️⃣ Simple Example for Clear Understanding

Suppose:

• 100 people HAVE the disease.

• Your test detects 90 correctly → TP = 90

• Misses 10 → FN = 10

So,

$$\text{Sensitivity}=90/100=90\%$$

Now for healthy people:

• 100 people DO NOT have the disease

• Your test correctly says 85 are negative → TN = 85

• Wrongly says 15 are positive → FP = 15

So,

Specificity=85/100=85%

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6️⃣ Why Are Sensitivity & Specificity Important?

They help decide:

• Which test to use for screening? → high sensitivity

• Which test to use for final confirmation? → high specificity

• How reliable a positive or negative result is

• How strong your research is

These are the building blocks before learning PPV, NPV, ROC curves, AUC, etc.

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7️⃣ Key Real-Life Examples