Types of VariablesObjective:

Students should be able to identify the different types of variables, and know the characteristics of each type

Types of VariablesCategorical (data that are counted)

•Nominal•Ordinal

Quantitative or Numerical (data that are measured)•Interval•Ratio

Why is the type of variable important?The methods used to display, summarize, and analyze data depend on whether the variables are categorical or quantitative.

Types of Variables: Categorical

Nominal

Variables that are “named”, i.e. classified into one or more qualitative categories that describe the characteristic of interest

• no ordering of the different categories

• no measure of distance between values

• categories can be listed in any order without affecting the relationship between them

Nominal variables are the simplest type of variable

Nominal

In medicine, nominal variables are often used to describe the patient. Examples of nominal variables might include:

Gender (male, female)

Eye color (blue, brown, green, hazel)

Surgical outcome (dead, alive)

Blood type (A, B, AB, O)

Note: When only two possible categories exist, the variable is sometimes called dichotomous, binary, or binomial.

Ordinal

Variables that have an inherent order to the relationshipamong the different categories

• an implied ordering of the categories (levels)

• quantitative distance between levels is unknown

• distances between the levels may not be the same

• meaning of different levels may not be the same for different individuals

Note: The scale of measurement for most ordinal variables is called a Likert scale.

Ordinal

In medicine, ordinal variables often describe the patient’s characteristics, attitude, behavior, or status. Examples of ordinal variables might include:

Stage of cancer (stage I, II, III, IV)

Education level (elementary, secondary, college)

Pain level (mild, moderate, severe)

Satisfaction level (very dissatisfied, dissatisfied, neutral, satisfied, very satisfied)

Agreement level (strongly disagree, disagree, neutral, agree, strongly agree)

Types of Variables: Quantitative/Numerica

lInterval

Variables that have constant, equal distances between values, but the zero point is arbitrary.

Examples of interval variables:

Intelligence (IQ test score of 100, 110, 120, etc.)

Pain level (1-10 scale)

Body length in infant

Ratio

Variables have equal intervals between values, the zero point is meaningful, and the numerical relationships between numbers is meaningful.

Examples of ratio variables:

Weight (50 kilos, 100 kilos, 150 kilos, etc.)

Pulse rate

Respiratory rate

Levels of Measurement

Higher level variables can always be expressed at a lower level, but the reverse is not true.

For example, Body Mass Index (BMI) is typically measured at an interval-level such as 23.4. BMI can be collapsed into lower-level Ordinal categories

such as:• >30: Obese• 25-29.9: Overweight• <25: Underweight

or Nominal categories such as:• Overweight• Not overweight

Discrete Data

Quantitative or Numerical variables that are measured in each individual in a data set, but can only be whole numbers.

Examples are counts of objects or occurrences:

Number of children in household Number of relapses Number of admissions to a hospital

Continuous Data

Quantitative or Numerical variables that are measured in each individual in a data set.

Continuous variables can theoretically take on an infinite number of values - the accuracy of the measurement is limited only by the measuring instrument.

Note: Continuous data often include decimals or fractions of numbers.

Continuous Data

Examples of continuous variables: Height, weight, heart rate, blood pressure, serum cholesterol, age, temperature

A person’s height may be measured and recorded as 60 cm, but in theory the true height could be an infinite number of values:

height may be 60.123456789…………..cm or 59.892345678…………..cm

Classification of variables in The Bypass Angioplasty Revascularization Investigation

Variable

CABG (n=914)

PTCA (n=915)

Type of Variable

Age (years, mean SD) 61.1 3.2 61.8 3.7

Weight (kg, mean SD) 80.9 5.6 78.8 6.0

Gender [#, (%)] Males Females

676 (74%) 238 (26%)

668 (73%) 247 (27%)

Education [#, (%)] Grade School High School Some College College Graduate or >

192 (21%) 457 (50%) 165 (18%) 100 (11%)

192 (21%) 458 (50%) 165 (18%) 100 (11%)

Prior Hospitalizations (mean SD) 4.0 0.6 3.8 0.6

Post Treatment Mortality Alive at 5 Years Dead at 5 Years

902 (98.7%)

12 (1.3%)

898 (98.1%)

17 (1.9%)