Levels of Measurement in Statistics

Key Concepts

• Statistics: Represents the world with numbers.
• Variables: Can be categorized as either representing categories or measuring something.

Types of Variables

1. Categorical Variables

• Purpose: Create categories.
• Types:
  • Ordered Categories (Ordinal):
    • Examples: Class standing (freshman, sophomore, etc.), Income status (labor, supervisor, etc.), Education level (Bachelor, Master, Doctorate).
    • Characteristics: Have an underlying hierarchy or order.
  • Unordered Categories (Nominal):
    • Examples: Team colors (Blue Team, Red Team, etc.), Gender (male, female), Experimental vs. Control groups.
    • Characteristics: No underlying order, categories are just groups.
• Also Known As: Qualitative variables (describe a quality, not an amount/quantity).
• Special Case: Dichotomous Variables (only two levels, e.g., ALIVE or DEAD).

2. Measurement Variables

• Purpose: Measure something with scales having equal intervals.
• Types:
  • Ratio Data:
    • Examples: Height (inches), Weight (pounds), Test scores.
    • Characteristics: Have an absolute zero point, cannot have less than zero.
  • Interval Data:
    • Examples: IQ scores, Personality tests, Temperature (Fahrenheit/Celsius).
    • Characteristics: Have equal intervals but no absolute zero (can have negative values or no zero score).
• Also Known As: Quantitative variables (describe an amount or quantity).

Review Summary

• Numbers/data can either define categories or measure something.
• Categorical Variables:
  • Unordered categories = Nominal
  • Ordered categories = Ordinal
  • Qualitative and discrete (whole numbers, no decimals/fractions).
• Measurement Scales:
  • Equal intervals, some with meaningful zero (Ratio), some without (Interval).
  • Quantitative and continuous (can have decimals/fractions).

Application

• Apply understanding of these concepts to categorize and measure variables appropriately.