Levels of Measurement

 Data are collected and coded into numbers

 Levels define what the numbers assigned to variables represent

 There are 4 levels or scales

o Nominal: numbers represent assigned or named categories (e.g., 1 = male, 2 =

female)

o Ordinal: numbers represent ranked or ordered categories that are not necessarily

equal in size (e.g., 1 = low, 2 = medium, 3 = high)

o Interval: numbers represent values of equal units (e.g., temperature, age in years).

Note: temperature of 0°C is not the same as 0°F and 0° on both scales does not mean there is

no temperature; age in years is not ratio because 0 years old is anywhere between birth and

the day before the first year.

o Ratio: numbers represent values of equal units and there is a set zero point

(height, weight, blood pressure)

Note: with ratio data ONLY, values can be compared as ratios

(e.g., a risk factor doubled the odds of disease, a diet supplement resulted in a 5% weight

loss)

Rules:

 Higher level data can be converted to a lower level

Examples:

o ratio data for weight loss can be arranged in 5 lb. interval groups;

o interval age in years can be converted to ordinal age groups such as 5-17, 18-44,

45-64, >65 years;

o ordinal ranks can be combined in nominal categories as in 1 = agree and strongly

agree, 2 = disagree and strongly disagree, 3 = no opinion, (where there is no

specific order)

 Lower level data cannot be converted to a higher level

Data types:

 There are 3 data types

o Categorical: nominal and ordinal data; numbers represent categories

(examples: gender, race/ethnicity)

o Ordinal: categorical data that are ranked; not everyone makes this distinction

(examples: low, medium, high)

o Continuous: interval and ratio data; numbers represent numerical values

(examples: age, height, weight)

Rules (extension of the rules for levels of measurement):

o Continuous data can be transformed to categorical data

o Categorical data cannot be transformed to continuous data

Descriptive Statistics

 Descriptive statistics describe the d