Overview
This lecture explains the four levels of measurement in quantitative research—nominal, ordinal, interval, and ratio—detailing their characteristics, examples, and implications for statistical testing.
Levels of Measurement Overview
- The level of measurement used impacts the types of statistical tests possible and the conclusions that can be drawn.
- The four levels, from lowest to highest, are: nominal, ordinal, interval, and ratio (acronym: NOIR).
Nominal Level
- Nominal data categorizes variables into mutually exclusive groups without any order.
- Numbers may be assigned as labels but have no quantitative meaning.
- Examples include gender, hair color, marital status; can be dichotomous (two categories) or categorical (more than two).
- Only the mode can be calculated; statistical options are limited to counts and percentages.
- Data is best displayed using bar or pie charts.
Ordinal Level
- Ordinal data categorizes variables in a meaningful order, but interval distances are unequal or unknown.
- Numbers indicate rank/order, not magnitude of difference.
- Examples: satisfaction ratings, pain scales.
- Median and mode can be calculated; mean should not be used.
- Permits comparison of order but not precise differences between rankings.
Interval Level
- Interval data has ordered categories with known, equal intervals between values, but zero is arbitrary (not a true absence).
- Examples: temperature in Celsius/Fahrenheit, test scores.
- Mean, median, mode, and standard deviation can be calculated.
- Cannot compute ratios or claim “twice as much” due to lack of true zero.
Ratio Level
- Ratio data has all the properties of interval data but includes a true, absolute zero.
- Examples: height, weight, length, bank balance (with debate).
- All statistical tests are possible, including calculations involving ratios.
- Zero means the absence of the measured attribute.
Applying Levels of Measurement
- Determining level: Is the variable ordered? Are intervals equal? Is zero meaningful?
- The higher the level of measurement, the broader the range of statistical tests.
- Properly identifying the level avoids inappropriate or misleading statistical analysis.
Key Terms & Definitions
- Nominal — Names discrete categories with no order (e.g., gender).
- Ordinal — Ranks categories in order, intervals unequal (e.g., satisfaction scale).
- Interval — Ordered categories with equal intervals, arbitrary zero (e.g., Celsius temperature).
- Ratio — Ordered, equal intervals, true zero (e.g., weight).
- Dichotomous — Only two categories (e.g., yes/no).
- Categorical — Non-numeric data with multiple categories.
Action Items / Next Steps
- Create a study table summarizing each level, its properties, and an example.
- Review how data is collected in articles to determine correct statistical tests.
- Practice identifying levels of measurement with sample variables.