# Understanding types of variables

In statistical research, a variable is defined as an attribute of an object of study. Choosing which variables to measure is central to good experimental design.

###### Example

If you want to test whether some plant species are more salt-tolerant than others, some key variables you might measure include the amount of salt you add to the water, the species of plants being studied, and variables related to plant health like growth and wilting.

You need to know which types of variables you are working with in order to choose appropriate statistical tests and interpret the results of your study.

You can usually identify the type of variable by asking two questions:

## Types of data: Quantitative vs categorical variables

Data is a specific measurement of a variable – it is the value you record in your data sheet. Data is generally divided into two categories:

• Quantitative data represents amounts.
• Categorical data represents groupings.

A variable that contains quantitative data is a quantitative variable; a variable that contains categorical data is a categorical variable. Each of these types of variable can be broken down into further types.

### Quantitative variables

When you collect quantitative data, the numbers you record represent real amounts that can be added, subtracted, divided, etc. There are two types of quantitative variables: discrete and continuous.

Discrete vs continuous variables
Type of variableWhat does the data represent?Examples
Discrete variables (aka integer variables)Counts of individual items or values.
• Number of students in a class
• Number of different tree species in a forest
Continuous variables (aka ratio variables)Measurements of continuous or non-finite values.
• Distance
• Volume
• Age

### Categorical variables

Categorical variables represent groupings of some kind. They are sometimes recorded as numbers, but the numbers represent categories rather than actual amounts of things.

There are three types of categorical variables: binary, nominal, and ordinal variables.

Binary vs nominal vs ordinal variables
Type of variableWhat does the data represent?Examples
Binary variables (aka dichotomous variables)Yes/no outcomes.
• Heads/tails in a coin flip
• Win/lose in a football game
Nominal variablesGroups with no rank or order between them.
• Species names
• Colors
• Brands
Ordinal variablesGroups that are ranked in a specific order.
• Finishing place in a race
• Rating scale responses in a survey

### Example data sheet

To keep track of your salt-tolerance experiment, you make a data sheet where you record information about the variables in the experiment, like salt addition and plant health.

To gather information about plant responses over time, you can fill out the same data sheet every few days until the end of the experiment. This example sheet is color-coded according to the type of variable: nominal, continuous, ordinal, and binary. ## Parts of the experiment: Independent vs dependent variables

Experiments are usually designed to find out what effect one variable has on another – in our example, the effect of salt addition on plant growth.

You manipulate the independent variable (the one you think might be the cause) and then measure the dependent variable (the one you think might be the effect) to find out what this effect might be.

You will probably also have variables that you hold constant (control variables) in order to focus on your experimental treatment.

Independent vs dependent vs control variables
Type of variableDefinitionExample (salt tolerance experiment)
Independent variables (aka treatment variables)Variables you manipulate in order to affect the outcome of an experiment.The amount of salt added to each plant’s water.
Dependent variables (aka response variables)Variables that represent the outcome of the experiment.Any measurement of plant health and growth: in this case, plant height and wilting.
Control variablesVariables that are held constant throughout the experiment.The temperature and light in the room the plants are kept in, and the volume of water given to each plant.

### Example data sheet

In this experiment, we have one independent and three dependent variables.

The other variables in the sheet can’t be classified as independent or dependent, but they do contain data that you will need in order to interpret your dependent and independent variables. When you do correlational research, the terms “dependent” and “independent” don’t apply, because you have not performed any sort of controlled experiment. In these cases, it is usually sufficient to simply say whether two variables are statistically related, without trying to distinguish between cause and effect.

However, there might be cases where one variable clearly precedes the other (for example, rainfall leads to mud, rather than the other way around). In these cases you may call the preceding variable (i.e. the rainfall) the predictor variable and the following variable (i.e. the mud) the outcome variable.

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## Other common types of variables

Once you have defined your independent and dependent variables and determined whether they are categorical or quantitative, you will be able to choose the correct statistical test.

But there are many other ways of describing variables that help with interpreting your results. Some useful types of variable are listed below.

Type of variableDefinitionExample (salt tolerance experiment)
Confounding variablesA variable that hides the true effect of another variable in your experiment. This can happen when another variable is closely related to a variable you are interested in, but you haven’t controlled it in your experiment.Pot size and soil type might affect plant survival as much or more than salt additions. In an experiment you would control these potential confounders by holding them constant.
Latent variablesA variable that can’t be directly measured, but that you represent via a proxy.Salt tolerance in plants cannot be measured directly, but can be inferred from measurements of plant health in our salt-addition experiment.
Composite variablesA variable that is made by combining multiple variables in an experiment. These variables are created when you analyze data, not when you measure it.The three plant health variables could be combined into a single plant-health score to make it easier to present your findings. 