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.
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.
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.
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.
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.