1. Types of Variables Objective:
Students should be able to identify the different types of variables, and know the characteristics of each type
This module explains the different types of variables that you will encounter and use in statistical analysis. The learning objective for this module is that students should be able to identify the different types of variables, and know the characteristics of each type of variable.

2. Why is the type of variable important?
Types of Variables
Categorical (data that are counted)
Nominal
Ordinal
Quantitative or Numerical (data that are measured)
Interval
Ratio
To begin with, a variable is simply what is being observed or measured. Variables take on one of a number of specific values.
Variables are divided into four levels, that are grouped into two classifications. The first classification, categorical data, are those that are counted and include nominal and ordinal level data. The next two levels of variables are classified as quantitative or numerical, and include interval and ratio level data. These data are measured, rather than counted.
Understanding the type of variable is critically important to understanding appropriate statistical testing procedure. The type of variable determines how the data is displayed, summarized, and which statistical tests are appropriate.
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.

3. 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
Let’s begin with a discussion of each of the four levels of data, or what some call levels of measurement. Nominal level data are the simplest type of data and consist of named categories, with no implied order among the categories. In other words, the data either exist, or do not exist, within the category
Nominal variables are the simplest type of variable

4. Eye color (blue, brown, green, hazel) Surgical outcome (dead, alive)
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)
An example of nominal data is gender – a person is either male or female. Another example is surgical outcome – an individual is either dead or alive following surgery. Nominal variables do not have to be dichotomous, they can have any number of categories, as in the case of eye color or blood type.
Note: When only two possible categories exist, the variable is sometimes called dichotomous, binary, or binomial.

5. Variables that have an inherent order to the relationship
Ordinal
Variables that have an inherent order to the relationship
among 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
Ordinal data are also categorical data, but the categories are ordered or hierarchical. However, the differences or distances between categories is not equal.
Ordinal variables are often measured using a Likert Scale – on surveys, this might be worded as, “How often do you exercise?” with response categories of Always, Sometimes, Rarely, or Never. There is an obvious order or hierarchy to the categories, but the difference between Always and Sometimes is not the same as the difference between Rarely and Never.
Note: The scale of measurement for most ordinal variables is called a Likert scale.

6. 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)
In medicine, ordinal variables are often used to describe the patient and his or her characteristics, attitude, behavior, or status. Some commonly-used examples of ordinal level data are stage of cancer, education level, pain level, satisfaction, and agreement.

7. Types of Variables: Quantitative/Numerical
Interval
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
Interval level data is classified as quantitative or numerical data. Interval data are measured and have constant, equal distances between values, but the zero point is arbitrary. The zero isn’t meaningful, it doesn’t mean a true absence of something. An example of interval level data is intelligence, as measured on some IQ test. We know that the scoring difference between a 100 and a 110 is equal to the scoring distance between 120 and 130, but there is no true zero on this test and an IQ of 140 is not twice as high as an IQ of 70.
Another example is asking a patient to describe their pain on a 1-10 scale where 1 means minimal pain and 10 means the worst pain the person has ever suffered. Even though the distances between numbers on the scale are constant and equal, a pain score of 8 does not mean that the pain is twice as bad as a score of 4.

8. Examples of ratio variables:
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
Ratio level data are those which have equal intervals between values, and the zero is meaningful. Some laboratory tests are good examples of ratio level data. A person who weighs 100 kilos is twice as heavy as a person who weighs 50 kilos, and a measure of zero kilos is meaningful. Other examples include pulse rate and respiratory rate.
One point to note is that although we differentiate interval and ratio level data for definitional purposes, in practical application, they are often treated the same in statistical analysis.

9. 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
: Overweight
<25: Underweight
or Nominal categories such as:
Overweight
Not overweight
One thing to remember is that higher level variables can always be expressed at a lower level, but the reverse is not true. You can convert ordinal-level data to nominal-level data, but you cannot do the reverse. For example, Body Mass Index, or BMI, is often measured at the interval level and is given a score such as This interval-level BMI data can be collapsed into ordinal categories such as obese, overweight, and underweight, or it can be reduced to nominal-level categories such as overweight and not overweight. This is why we often try to measure data at the highest level of measurement possible.

10. 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
Variables are also described as being discrete or continuous. Discrete variables are those which can only be counted or observed as whole numbers, such as the number of children in a household, the number of relapses a patient experiences, or the number of hospital admissions.

11. Note: Continuous data often include decimals or fractions of numbers.
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.
Continuous variables can theoretically take on any value, within a range defined by the measuring instrument. Continuous data often include decimals or fractions of numbers.
Note: Continuous data often include decimals or fractions of numbers.

12. Examples of continuous variables:
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 …………..cm
or …………..cm
Many variables measured in medicine are continuous, interval or ratio level data such as height, weight, heart rate, blood pressure, serum cholesterol, age, and temperature. For example, a person’s height can theoretically be an infinite number of values, but it is measured and recorded based on a designated measurement tool, such as centimeters.

13. Classification of variables in The Bypass Angioplasty Revascularization Investigation
This chart demonstrates a variety of different types of variables. The variables Age and Weight, are both quantitative/numerical and continuous because they are variables that are measured, and they can take on any value within a defined range. The variable Gender however, is nominal because the data consist of named categories and have only one of a limited set of values. Education is an ordinal level variable because the categories are ordered or hierarchical. The variable Prior Hospitalizations is a ratio level variable since 4 hospitalizations is twice as much as 2 hospitalizations, and discrete because it is measured as a whole number count. Post Treatment Mortality is a nominal level variable because a person can only be categorized into one of the two groups.
Now that we have examined the different types of variables, we will now move on to a discussion of displaying data. Remember, that the appropriate display of data is dependent upon understanding what type of variable is being used.