Lecture Notes: Scales of Measurement

Key Concepts

• Ratio Scale

  • Ratios are meaningful.
  • Has a true zero point (zero represents the absence of the property).
  • Example: Weight (e.g., 10 pounds is twice as heavy as 5 pounds).

• Interval Scale vs. Ordinal Scale

  • Interval Scale
    • Example: Temperature.
    • Differences are consistent across the scale (e.g., one degree difference is the same throughout).
  • Ordinal Scale
    • Example: Race positions (first, second, third).
    • Order matters, but differences between ranks are not consistent (e.g., time differences between positions can vary).

Comparison of Scales

• Interval vs Ordinal

  • Interval: Same difference across the scale (e.g., temperature).
  • Ordinal: Only ranking is known, and differences are not consistent (e.g., race positions).

• Interval vs Ratio

  • Ratio: Meaningful ratios, true zero point (e.g., weight).
  • Interval: No true zero, ratios not meaningful (e.g., temperature).

Examples

• Nominal Scale (e.g., Baseball Uniform Numbers)
  • Numbers are for identification only; no order or meaningful differences.
  • Example: Player numbers (25, 23, 30, 35).
  • No true zero point (e.g., uniform number zero doesn’t mean absence of a player).

Conclusion

• Importance of understanding different scales for proper data interpretation.
• Each scale has unique characteristics that define the type of data it represents.