What are Dependent and Independent Variables?

Teacher Guide to Quantities Measured & Manipulated in Experiments

Nov 2, 2009

In experiments, independent variables are quantities that are varied by researchers. Dependent variables are quantities whose response can be measured by the researchers.

In an experiment or analysis of a data set, a variable is a parameter or quantity that can be measured. Examples include numbers of individuals, frequencies of occurrence, amounts of material or money, distances or lengths, and time periods. What these parameters have in common is that they can be quantified in some way.

The purpose of most experiments or research studies is to understand how systems work. This is done by investigating how a change in one variable might affect a different variable. If changing one parameter produces a systematic variation in another, it demonstrates that the two variables are related. Such relationships can sometimes point to cause and effect.

What are Independent Variables?

The independent variable in an experiment is a quantity that is selected, manipulated or varied by the researcher. It is unaffected by changes in other variables. Time is an example of common independent variable selected for experiments. Regardless of whether or not the trial is conducted, time marches on. Changes in other variables can be measured as a function of the progression of time.

In other cases, independent variables are quantities that are decided upon by the researcher. For example, a study might involve adding different amounts of fertilizer to plants to see how growth rates are affected. The volume of fertilizer is the independent variable, manipulated by the researcher.

What are Dependent Variables?

A dependent variable is the factor studied and expected to change in response to variations in the independent variable. There can be more than one dependent variable for any system. For example, adding different volumes of fertilizer to plants might be expected to produce variations in plant height, plant biomass, and amount or quality of fruit produced. Any of these may be chosen as dependent variables in a study.

What are Controlled Variables?

A controlled variable is any other parameter that might otherwise influence the dependent variable if it were not fixed. These other variables must be kept the same (i.e., controlled) in each trial of an experiment to make sure that the relationship between the dependent and independent variables is not obscured. This is known as a “fair test.” Controlled variables are those parameters that could be selected as independent variables in a different experiment designed to answer a different question.

The Difference Between Causation and Correlation

Researchers design experiments to determine whether a change in the independent variable is the precise cause of corresponding change in a dependent variable. Correlations are identified graphically by plotting data, or numerically by statistical analysis of the values of dependent and independent variables.

A strong correlation may imply a causal relationship. However, if a causal mechanism is not actually identified, then the researcher can only say that a correlation between two variables was observed. Statistical analysis of data acquired from experiments or observational studies are used to support arguments for causation.

How to Plot Graphs of Dependent and Independent Variables

When plotting a graph of experimental results, the convention is to plot the independent variable as the abscissa (the x coordinate). A dependent variable is plotted as the ordinate (y coordinate). Thus, y=f(x) or y is a function of x.

For example, plotting the average weight of adults vs. the average height of adults might give you a graph as shown below. The independent variable is average height. The dependent variable is weight. Think of it this way: does being taller cause a person to weigh more, or does being heavier cause a person to be taller?

The assignment of dependent and independent variables depends on the specific purpose of the study. For example, height might be an independent variable in the context stated above but a dependent variable in a study on the effect of nutrition on growth rates.

To summarize, the independent variable is the quantity chosen by the researcher to be varied, and is unaffected by other variables. Changes in dependent variables occur because of the process.

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