Understanding Scales of Measurement in Statistics

Sep 5, 2024

Scales of Measurement in Statistics

Introduction

  • Professor Matthias Bertel, University of Applied Sciences, Offenburg.
  • Topic: Scales of measurement in statistics.

Overview of Scales of Measurement

  • Statistics applies across various fields (medicine, criminology, economics).
  • Example used: measuring attributes of apples.

Attributes of Apples

  • Measurable Attributes:
    • Color (Red, Green, Yellow)
    • Weight (5 oz, 7 oz, 6 oz)
    • Harvest Date (September 14, September 4, October 4)
    • Sweetness (Medium, Very Sour, Quite Sweet)

Data Presentation

  • Data collected presented in a table for comparison.
  • Operations possible with numerical data:
    • Calculate differences (e.g., weight difference of apples).
    • Calculate averages (e.g., average weight).

Levels of Measurement

  1. Nominal Scale:

    • Characterized by equality comparisons.
    • Example: Color of apples (can only say if they are the same or not).
    • Other examples: State of residence, equal brands.

  2. Ordinal Scale:

    • Allows equality comparisons and ordering.
    • Example: Sweetness of apples (order them by sweetness).
    • Common in surveys (e.g., opinion ratings).

  3. Interval Scale:

    • Allows equality comparisons, ordering, and measurement of distance.
    • Example: Harvest dates of apples (can calculate days between dates).
    • Allows operations like addition and subtraction of distances.

  4. Ratio Scale:

    • Permits equality comparisons, ordering, measurement of distance, and calculation of ratios.
    • Example: Weight of apples (can state one apple is heavier than another in ratios).
    • Common in measurements like monetary values (revenue, cost).

Recap of Scales

  • Nominal Scale: Only equality comparison (e.g., color).
  • Ordinal Scale: Equality and order (e.g., sweetness).
  • Interval Scale: Equality, order, and distance (e.g., dates).
  • Ratio Scale: All comparisons including ratios (e.g., weight).

Importance of Understanding Scales of Measurement

  • Fundamental for choosing appropriate statistical methods.
  • Different methods require different types of measurement operations.
  • Analogy: Using the right tool for the job (screwdriver vs. hammer).

Conclusion

  • Understanding scales of measurement is crucial for applying statistics correctly.
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