Chapter 3: Levels of Measurement

levels of measurement: NOIR

(least → most detailed)

categorical

• nominal

• ordinal

scale:

• interval

• ratio

nominal

• data organized into UNRANKED categories

• categories mutually exclusive/exhaustive (no SATA questions, all possibilities included → other category)

• ex: ethnicity, gender, hair color, zip codes, SSN, favorite sport

ordinal

• data organized into RANKED categories

• categories are mutually exclusive/exhaustive (no SATA questions, all possibilities included → other category)

• categories can be used to include ranges of scores

• ex: data measured on Likert-type scale, year in school, rank in finishing a race, income level (low, medium, high), education level

interval

• data measured on a numeric scale

• intervals between measurements have equal distances

• can be discrete (whole #) or continuous

• can treat an ordinal scale as interval if it is large enough (at least 10 points)

• zero is an arbitrary value on the scale

• can add or subtract values

• ex: scores on standardized assessments (depression, inventory, IQ test), satisfaction measured on scale of 1-10, time of day

ratio

• data is measured on a numeric scale

• intervals between measurements have equal distances

• can be discrete or continuous

• zero is meaningful and nonarbitrary (ex. zero = no amount of the variable)

• can add, subtract, multiply, or divide numbers

• ex: weight (lbs, kg, oz), height (in, ft), amount of time (years, months)

interval variable ex: temperature

• no true zero is present

• daily winter temperatures in degrees Fahrenheit

  • -17, -11, -9, -4, -2, -1, 4, 5 , 6, 8, 18

ratio variable example: income

• has true/absolute zero (zero = no income)

• income in thousands of dollars:

  • $27k, 34k, 38, 39k, 43k, 47k, 64k, 68k, 77k, 88k, 107k