Section 1.2 - Observation, Measurement, and Variables

Observations, Measurements, and Variables

• This section focuses on the foundational elements of statistics: making measurements and identifying variables.

• Researchers identify variables to measure and conduct surveys to gather data.

• Example: Average age of students in a school is measured through surveys asking students about their ages.

Key Concepts

• Constructs and Operational Definitions

  • Important concepts but not often emphasized throughout the text.

• Types of Variables

  • Discrete Variables

    • Consist of separate and distinct categories.

    • No values fall between these categories.

    • Example: The number of daily hospital admissions (e.g., 11 admissions vs. 12 admissions, no in-between numbers).

  • Continuous Variables

    • Have an infinite number of possible values between any two values.

    • Example: Average age can vary even by small increments (e.g., 21 years and a few seconds).

    • Height and weight are also continuous variables as they can be measured with precision.

Real Limits

• Define the boundaries for continuous variables represented on a number line.

• They help determine rounding behavior.

• Example: If weighing someone gives a result of 150.3 pounds, real limits help decide if rounding goes to 150 or 151 pounds.

  • Halfway points:

    • 150.5 is the cutoff between rounding up or down.

• Awareness of rounding is crucial, particularly when measuring less than whole units.

Scales of Measurement

• Types of Scales

  • Numerical Scales

    • Include values that can be measured mathematically.

  • Non-numerical Scales

    • Examples include categorical responses (e.g., 'What city were you born in?').

  • Non-numeric Scale Types

    • Nominal Scale

      • Classifies data into distinct categories without order (e.g., types of fruits).

    • Ordinal Scale

      • Describes order or rank (1st place, 2nd place).

      • Categories can be ranked but not quantified.

  • Numeric Scale Types

    • Interval Scale

      • No true zero point (e.g., temperature).

      • Example: 0 degrees Fahrenheit does not mean no heat; it can go lower.

    • Ratio Scale

      • Has an absolute zero point (e.g., age).

      • Example: Being 0 years old means no age exists.

Differences in Scales of Measurement

• Ordinal vs. Interval Scale

  • Measuring individuals on an interval scale versus an ordinal scale provides additional information:

    • Ordinal Scale: Determines the direction of differences (higher or lower).

    • Interval Scale: Indicates both the direction and the size of differences (exact numerical values).

• Example: Finishing a race in specific times (interval scale) gives more precise information than just ranking (ordinal scale).

• Nominal Scale: Assesses whether measurements are the same or different.