Interval Level Measurement in Statistics

Measurement Scales

• Ordered categories: {none = 0, low=1, medium=2, high=3}
• Interval level measurement:
  • Distances (absolute differences) are meaningful
  • A fixed difference anywhere on the measurement scale always corresponds to the same difference on the trait being measured
  • The zero state of an interval scale is not a true zero value
• Examples of interval level measurement: Temperature (°F), where a one-degree temperature difference always means the same thing

Ratio Level Measurement

• Both differences and ratios are meaningful
• There is a true zero, meaning a total absence of the variable being measured
• Examples: Length, area, and population, where the relative difference between two values is the same regardless of the starting point
• Kelvin scale is a ratio scale, with a true zero (0 K) where nothing can be colder

Perceptual Channels

• Position: the most used perceptual channel, suitable for most data types
• Size (length, area, volume): good for 1D, 2D, easy to compare
• Color: value (lightness) is perceived as ordered, encode ordinal variables (O), hue is perceived as unordered, encode nominal variables (N)

Bertin's Levels of Organization

• Position: N, O, Q (nominal, ordinal, quantitative)
• Size: N, O, Q
• Value: N, O, Q
• Texture: N
• Color: N
• Orientation: N
• Shape: N

Mackinlay's Ranking

• Expanded Bertin's variables and conjectured effectiveness of encodings by data type

Data Visualization

• Goal: learn how data is mapped to images
• The Big Picture: domain, goals, questions, assumptions, data, processing algorithms, data transformation, image, conceptual model, visual encoding, analysis task

Properties of Data

• Taxonomy of datasets: 1D (sets and sequences), temporal, 2D (maps), 3D (shapes), nD (relational), trees (hierarchies), networks (graphs), and combinations
• Levels of measurement: nominal, ordinal, quantitative (interval, ratio)

Nominal Level Measurement

• Classifies units into non-ordered categories
• Examples: male/female, eye colors, car models

Ordinal Level Measurement

• Classifies units into ranks or ordered categories
• Examples: ranks (1st, 2nd, 3rd...), education levels