The Relationship between variables and levels of measurement

Full Answer Section

1. • Developed by psychologist Stanley Smith Stevens, there are four main levels, ordered from least to most informative:
     • Nominal Scale: Data are categorized without any inherent order or ranking. You can only say whether values are the same or different.
       • Example: Gender (Male, Female, Non-binary), Blood Type (A, B, AB, O), Marital Status (Single, Married, Divorced).
     • Ordinal Scale: Data are categorized and can be ranked or ordered meaningfully, but the intervals between categories are not necessarily equal or measurable. You can say one value is "greater than" or "less than" another, but not "how much greater."
       • Example: Education Level (High School, Bachelor's, Master's, PhD), Satisfaction Rating (Very Dissatisfied, Dissatisfied, Neutral, Satisfied, Very Satisfied), Military Ranks.
     • Interval Scale: Data can be ordered, and the intervals between values are equal and meaningful. However, there is no true zero point, meaning zero does not represent the complete absence of the characteristic being measured. Ratios are not meaningful.
       • Example: Temperature in Celsius or Fahrenheit (0°C doesn't mean no temperature), IQ Scores (an IQ of 0 doesn't mean no intelligence, and an IQ of 100 is not twice as intelligent as 50).
     • Ratio Scale: This is the highest level of measurement. It has all the properties of interval scales (order, equal intervals) plus a true, meaningful zero point. This means zero signifies the complete absence of the characteristic. Ratios are meaningful.
       • Example: Height, Weight, Age, Income, Number of Patients (0 patients means no patients, and 10 patients are twice as many as 5).

The Relationship:

The relationship is that every variable you work with in research or statistics will inherently belong to one of these four levels of measurement.

• How a variable is defined and measured determines its level of measurement. For instance, if you define "income" simply as "high, medium, or low," it's ordinal. If you collect the exact amount of income, it's ratio. The variable itself is income, but how you measure it dictates its level.
• The level of measurement dictates what statistical analyses are appropriate for that variable. You cannot perform the same mathematical operations on a nominal variable (like calculating a mean) that you can on a ratio variable. Using the wrong statistical test for a given level of measurement can lead to incorrect conclusions.
• The level of measurement informs the richness of the data and the interpretations you can make. A ratio variable (like age in years) provides much more information than a nominal variable (like "age group: child/adult"), allowing for more sophisticated analysis and precise conclusions.

In essence, variables are the data points you are interested in, and levels of measurement are the framework that classifies those variables based on the properties of their values, guiding how they can be analyzed and interpreted.

Sample Answer

The relationship between variables and levels of measurement is fundamental to understanding and working with data in statistics and research.

Here's a breakdown:

1. Variables:

   • A variable is any characteristic, attribute, or quantity that can be measured or counted and that can take on different values.
   • Think of it as a "placeholder" for information that can vary from one observation (e.g., person, event, item) to another.
   • Examples: Age, gender, income, educational attainment, patient satisfaction score, blood pressure, type of medication, number of children. Each of these can have different values when you collect data.

2. Levels of Measurement (or Scales of Measurement):

   • Levels of measurement describe the nature of the information contained within the values of a variable. They tell you how precisely a variable is recorded and what kind of comparisons or mathematical operations are meaningful for that data.