Interval and Ratio Scale

Interval Scale

🔹 Definition:

A numeric scale where the intervals (differences) between values are equal and meaningful, but there is no true zero point (zero does not mean “none” of the quantity).

🔹 Key Characteristics:

• Values are ordered and measurable.

• Equal intervals between units (e.g., the difference between 10°C and 20°C is the same as between 20°C and 30°C).

• No true zero point — zero is arbitrary, not the absence of the variable (e.g., 0°C does not mean “no temperature”).

• Can perform addition and subtraction, but ratios (like “twice as much”) are not meaningful.

• Statistical measures like mean, median, mode, and standard deviation can be calculated.

🔹 Examples:

• Temperature (Celsius or Fahrenheit)

• IQ scores

• Calendar years (e.g., 2000, 2020 — the difference is meaningful, but “0 year” doesn’t mean “no time”)

Ratio Scale

🔹 Definition:

A numeric scale with equal intervals and a true zero point, where zero represents the absence of the measured quantity.

🔹 Key Characteristics:

• Has all properties of interval scale (order + equal spacing).

• True zero allows for meaningful ratios (e.g., 20 kg is twice as heavy as 10 kg).

• You can perform all arithmetic operations — addition, subtraction, multiplication, and division.

• Supports all statistical analyses (mean, median, mode, range, standard deviation, etc.).

🔹 Examples:

• Height

• Weight

• Age

• Length

• Income

• Blood pressure (if measured from zero baseline)

🧩 Summary Table

✳ In short:

• Interval scale → measures difference but no true zero (e.g., temperature).

• Ratio scale → measures difference and ratio with a true zero (e.g., weight, height).