Measurement Scales – Nominal, Ordinal, Interval & Ratio 📏

🎯 Learning Objectives

By the end of this lesson, you will be able to:
✔ Identify the four levels of measurement
✔ Differentiate between Nominal, Ordinal, Interval, and Ratio scales
✔ Recognize examples in a medical context
✔ Understand why these scales matter for statistical tests

1️⃣ Introduction

Not all data is created equal! How you measure data determines the statistical methods you can use. In medical statistics, we use four measurement scales:
✅ Nominal
✅ Ordinal
✅ Interval
✅ Ratio

2️⃣ Nominal Scale

Definition:

• Data classified into categories without any order.
• Labels only, no ranking, no arithmetic.

✔ Examples:

• Blood group: A, B, AB, O
• Gender: Male, Female
• Type of disease: Diabetes, Hypertension

✔ Key Features:

• Categories only (no order)
• Mathematical operations: ❌ Cannot compute mean

3️⃣ Ordinal Scale

Definition:

• Data classified into categories with a meaningful order, but differences between ranks are not equal.

✔ Examples:

• Pain severity: Mild, Moderate, Severe
• Stage of cancer: Stage I, II, III, IV
• Likert scale responses: Agree, Neutral, Disagree

✔ Key Features:

• Order matters, but distance between ranks is unknown
• Median can be calculated, but not true mean

4️⃣ Interval Scale

Definition:

• Numerical scale with equal intervals between values, but no true zero.

✔ Examples:

• Temperature in Celsius or Fahrenheit
• IQ score

✔ Key Features:

• Equal differences = equal meaning
• No true zero (0°C ≠ absence of temperature)
• Can calculate mean & SD, but ratios are meaningless

5️⃣ Ratio Scale

Definition:

• Numerical scale with equal intervals and a true zero, allowing full mathematical operations.

✔ Examples:

• Height (cm)
• Weight (kg)
• Blood pressure (mmHg)
• Heart rate (bpm)

✔ Key Features:

• Equal differences
• True zero (0 means absence of quantity)
• Can compute mean, SD, and meaningful ratios

6️⃣ Comparison Table

7️⃣ Quick Check: Test Your Understanding ✅

Q1: Which scale is used for measuring body weight?
a) Nominal
b) Ordinal
c) Interval
d) Ratio

👉 Answer: d) Ratio

Q2: Pain score (mild, moderate, severe) belongs to:
a) Nominal
b) Ordinal
c) Interval
d) Ratio

👉 Answer: b) Ordinal

Q3: Which scale has equal intervals but no true zero?
👉 Answer: Interval

✨ Key Takeaways

• Nominal: Categories only
• Ordinal: Categories + Order
• Interval: Order + Equal intervals (no true zero)
• Ratio: Order + Equal intervals + True zero
• Statistical tests depend on the scale of measurement!