Experimental Variables: Independent, Dependent, Control

In an experiment, the independent variable is the factor that the experimenter deliberately changes, the dependent variable is the factor that is measured to see the effect, and the control variables are all other factors that are kept constant. In brief: in a test of how temperature affects the rate at which sugar dissolves, temperature is the independent variable, the time to dissolve is the dependent variable, and the amount of sugar, volume of water and stirring are controlled.

Understanding variables is the basis of a fair test. If more than one factor changes at once, there is no way to know which one caused the result. This article defines each type of variable, shows how to identify them in an investigation, explains control groups and replication, gives a table of examples, works through the design of an experiment and gives the history of controlled experiments.

What are independent, dependent and control variables?

• Independent variable (manipulated variable): the one factor that you change on purpose. You choose its values, for example 10, 20, 30 and 40 °C.
• Dependent variable (responding variable): the factor that you measure. Its values depend on the independent variable. Examples are the volume of gas produced, mass, time or a temperature change.
• Control variables (controlled variables): all other factors that could affect the result, which are kept the same in each trial. Examples are the volume of solutions, the mass of solid, the apparatus used and the temperature (when it is not the independent variable).

How do you identify the variables?

Rewrite the aim of the investigation in the form “How does X affect Y?”. X is the independent variable and Y is the dependent variable. For instance: “How does the concentration of hydrochloric acid affect the rate of reaction with magnesium?” The concentration is independent and the rate (measured as time or volume of hydrogen) is dependent. Then list everything else that could change the result, and decide how to keep each factor constant.

Examples of variables in chemistry experiments

What is a control group?

A control group is a sample that is treated in the same way as the others, except that the independent variable is not applied or is at a baseline value. It shows what happens without the change and gives a reference for comparison. In testing whether a fertilizer helps plants grow, plants given only water are the control group. In chemistry, a control or blank might be a solution that contains everything except the substance of interest, and it helps to reveal the effect of the reagents or the environment.

How do you design a fair test?

1. State a clear question and a testable prediction (hypothesis).
2. Choose one independent variable and decide on a suitable range and number of values, typically at least five.
3. Select a dependent variable that can be measured accurately, and choose an instrument with suitable precision.
4. List the control variables, and decide how to keep each constant.
5. Plan repeated trials, ideally at least three at each value, to check consistency and calculate averages.
6. Write a step-by-step method, including safety precautions.
7. Make a data table in advance.

Worked example: reaction rate and concentration

A student investigates how the concentration of sodium thiosulfate affects the time taken for a cross under the flask to disappear when hydrochloric acid is added.

1. Independent variable. Concentration of sodium thiosulfate: 0.050, 0.100, 0.150, 0.200 and 0.250 mol/L, made by diluting a stock solution.
2. Dependent variable. Time for the cross to disappear, measured with a stopwatch to 0.1 s.
3. Control variables. Volume of thiosulfate (50.0 mL), volume and concentration of hydrochloric acid (5.0 mL of 1.0 mol/L), temperature (25 °C, in a water bath), the same flask and cross, and the same person judging the end point.
4. Repeats. Three trials for each concentration.

The mean time decreases as the concentration increases. A way to compare is the rate, defined as 1 ÷ time: at 0.050 mol/L it is 1 ÷ 98 = 0.0102 s⁻¹, and at 0.250 mol/L it is 1 ÷ 20 = 0.0500 s⁻¹. The concentration is five times larger, and the rate is 0.0500 ÷ 0.0102 = 4.9 times larger, so the rate is approximately proportional to the concentration under these conditions. The data show a clear trend, and the repeated trials differ by only a few seconds, which suggests that the controls worked.

How do variables appear in graphs?

By convention, the independent variable is plotted on the horizontal axis (x) and the dependent variable on the vertical axis (y). Each axis is labeled with the quantity and the unit. For categories, such as brands, a bar chart is used, and for numerical independent variables, a scatter plot or line graph is used. The graph should have a title, and the points should be plotted accurately with a line or curve of best fit.

Where does the controlled experiment come from?

The idea of a controlled comparison goes back to early scientists. Ibn al-Haytham (Alhazen), in the 11th century, wrote about testing hypotheses by experiments. In the 17th century Francis Bacon promoted systematic experimentation. Robert Boyle’s experiments on air pressure in the 1660s changed one variable at a time and recorded results. In the 20th century Ronald Fisher developed statistical design of experiments, which is the basis of modern experimental design.

Which mistakes are common?

Mistake 1: Changing more than one variable at once

If both temperature and concentration are changed, you cannot say which caused the change.

Mistake 2: Confusing the dependent and independent variables on a graph

The one you control goes on the x-axis, and the one you measure goes on the y-axis.

Mistake 3: Naming a control variable without keeping it constant

Listing “temperature” as controlled is not enough. State how you keep it constant, for example with a water bath.

Mistake 4: Using only one trial

A single result may be an accident. Repeat the experiment and use the mean.