Levels of Measurement

Levels of measurement - amount of information contained in numbers assigned to represent characteristic being measured. Sometimes inherent to the variable (e.g., standard to consider “race” as categorical), sometimes dependent on measurement technique (e.g., number hhold purchases of brand X per month vs. “heavy” and “light” users), determines allowable data analytic techniques.

Measurement hierarchy:

1. Nominal: numbers are simply categorically different

e.g., 1=men, 2=women or 1=men, 0=women or 47=men, 22.3=women

2. Ordinal: larger numbers represent greater amounts of property measured

e.g., movie ratings **** vs. ***

Levels of Measurement

3. Interval: differences between numbers are meaningful

e.g., physical temperature 70 degrees - 50 degrees = 30 degrees - 10 degrees

.ne. Ψ comfort

point at which statistics (mean, Sx, etc.) kick in.

4. Ratio: meaningful zero

e.g., number visits to grocery in January, 0-100 purchase brand X

#1 and 2 also called "discrete" or "categorical" or even "qualitative." Log linear models are applied to categorical data (mostly 1, sometimes 2).

Levels of Measurement

• Choice models• Binary Choice

– Buy or Not Buy– Yes / No– Own or Don’t own– Dem / Repub

• Multinomial Choice– Tide, Cheer, Yes, or Wisk– Restaurant A, B, C– Bus, Train, or Plane– Amer, United, Delta, …– Yes, No, Don’t Know

• Choices are mutually exclusive. The customer chooses only one of the options at a given choice occasion.