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.

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