Overview
This lecture covers the four levels of measurement in statistics: nominal, ordinal, interval, and ratio, explaining their characteristics and providing examples for each.
Levels of Measurement
Nominal Level
- Nominal data consists of names, labels, or categories with no logical order (e.g., ice cream flavors, student ID numbers, phone numbers).
- Numbers may appear, but they act as identifiers or labels rather than quantities.
- Averaging nominal data or performing mathematical operations on them is meaningless.
Ordinal Level
- Ordinal data can be arranged in a meaningful order, but differences between data points are not quantifiable (e.g., ranking drinks, star ratings for movies).
- You know which category ranks higher or lower, but not by how much.
- Differences between ranks or positions are not consistent or meaningful.
Interval Level
- Interval data can be ordered, and differences between values are meaningful (e.g., temperature in Fahrenheit, years, clothing sizes).
- There is no natural zero point—zero does not mean a total absence of the measured attribute (e.g., 0°F does not mean "no temperature").
- Ratios (e.g., "twice as hot") do not make sense due to the arbitrary zero point.
Ratio Level
- Ratio data has all the properties of interval data plus a true zero point, meaning zero indicates an absence of the quantity (e.g., money, height).
- Differences and ratios are meaningful (e.g., $20 is twice as much as $10).
- Zero represents none of the property being measured.
Key Terms & Definitions
- Nominal — Data that use names, labels, or categories without any order.
- Ordinal — Data that can be ordered but with undefined or inconsistent differences between values.
- Interval — Data with meaningful order and differences, but no true zero; ratios are not meaningful.
- Ratio — Data with meaningful order, differences, and a true zero; ratios between values are meaningful.
Action Items / Next Steps
- Review homework questions about determining the level of measurement for various data sets.
- Prepare examples of each level for class discussion.