Lesson 2: Summarizing Data
Section 2: Types of Variables
Look again at the variables (columns) and values (individual entries in each column) in Table 2.1. If you were asked to summarize these data, how would you do it?
First, notice that for certain variables, the values are numeric; for others, the values are descriptive. The type of values influence the way in which the variables can be summarized. Variables can be classified into one of four types, depending on the type of scale used to characterize their values (Table 2.2).
Table 2.2 Types of Variables
Nominal “categorical” or “qualitative” | disease status ovarian cancer | yes / no Stage I, II, III, or IV |
Interval “continuous” or “quantitative” | date of birth tuberculin skin test | any date from recorded time to current 0 – ??? of induration |
- A nominal-scale variable is one whose values are categories without any numerical ranking, such as county of residence. In epidemiology, nominal variables with only two categories are very common: alive or dead, ill or well, vaccinated or unvaccinated, or did or did not eat the potato salad. A nominal variable with two mutually exclusive categories is sometimes called a dichotomous variable.
- An ordinal-scale variable has values that can be ranked but are not necessarily evenly spaced, such as stage of cancer (see Table 2.3).
- An interval-scale variable is measured on a scale of equally spaced units, but without a true zero point, such as date of birth.
- A ratio-scale variable is an interval variable with a true zero point, such as height in centimeters or duration of illness.
Nominal- and ordinal-scale variables are considered qualitative or categorical variables, whereas interval- and ratio-scale variables are considered quantitative or continuous variables. Sometimes the same variable can be measured using both a nominal scale and a ratio scale. For example, the tuberculin skin tests of a group of persons potentially exposed to a co-worker with tuberculosis can be measured as “positive” or “negative” (nominal scale) or in millimeters of induration (ratio scale).
Table 2.3 Example of Ordinal-Scale Variable: Stages of Breast Cancer*
| Less than 2 cm | No | No |
| Between 2 and 5 cm | No or in same side of breast | No |
| More than 5 cm | Yes, on same side of breast | No |
| Not applicable | Not applicable | Yes |
* This table describes the stages of breast cancer. Note that each stage is more extensive than the previous one and generally carries a less favorable prognosis, but you cannot say that the difference between Stages 1 and 3 is the same as the difference between Stages 2 and 4.
For each of the variables listed below from the line listing in Table 2.1, identify what type of variable it is.
- Nominal
- Ordinal
- Interval
- Ratio
- ____ Date of diagnosis
- ____ Town of residence
- ____ Age (years)
- ____ Sex
- ____ Highest alanine aminotransferase (ALT)
Check your answer.
A variable is any characteristics, number, or quantity that can be measured or counted. A variable may also be called a data item. Age, sex, business income and expenses, country of birth, capital expenditure, class grades, eye colour and vehicle type are examples
of variables. It is called a variable because the value may vary between data units in a population, and may change in value over time. For example; 'income' is a variable that can vary between data units in a population (i.e. the people or businesses being studied may not have the same incomes) and can also vary over time for each data unit (i.e. income can go up or down).
What are the types of variables?
There are different ways variables can be described according to the ways they can be studied, measured, and presented.Numeric variables have values that describe a measurable quantity as a number, like 'how many' or 'how much'.
Therefore numeric variables are quantitative variables.Numeric variables may be further described as either continuous or discrete:- A continuous variable is a numeric variable. Observations can take any value between a certain set of real numbers. The value given to an observation for a continuous variable can include values as small as the instrument of measurement allows. Examples of continuous variables include height, time, age, and temperature.
- A discrete variable is a numeric variable. Observations can take a value based on a count from a set of distinct whole values. A discrete variable cannot take the value of a fraction between one value and the next closest value. Examples of discrete variables include the number of registered cars, number of business locations, and number of children in a family, all of of which measured as whole units (i.e. 1, 2, 3 cars).
The data collected for a numeric variable are quantitative data.
Categorical variables have values that describe a 'quality' or 'characteristic' of a data unit, like 'what type' or 'which category'.
Categorical variables fall into mutually exclusive (in one category or in another) and exhaustive (include all possible options) categories. Therefore, categorical variables are qualitative variables and tend to be represented by a non-numeric value.Categorical variables may be further described as ordinal or nominal:- An ordinal variable is a categorical variable. Observations can take a value that can be logically ordered or ranked. The categories associated with ordinal variables can be ranked higher or lower than another, but do not necessarily establish a numeric difference between each category. Examples of ordinal categorical variables include academic grades (i.e. A, B, C), clothing size (i.e. small, medium, large, extra large) and attitudes (i.e. strongly agree, agree, disagree, strongly disagree).
- A nominal variable is a categorical variable. Observations can take a value that is not able to be organised in a logical sequence. Examples of nominal categorical variables include sex, business type, eye colour, religion and brand.
The data collected for a categorical variable are qualitative data.
Types of variables flowchart:
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