Two independent variables

The controlled variable

The scientific method requires that only one variable be set (the independent) and one be measured (the dependent), while any other factors that can influence the result must be held constant during the course of the experiment. But what if you want to know how the experimental system is influenced by two different factors? How do you apply the scientific method and understand the influence of both parameters independently?

The most straightforward method to do this is run multiple experiments, with one of the parameters you are interested in investigating as an independent variable being set to a known, fixed value. Because you are setting and investigating the influence of this parameter on the system, it is an independent variable, but because it is not varying during each run of the experiment, it is also a control variable. We introduce a new term is identify this type of variable:

Controlled variable

This is the factor in the experiment that you set to a known value but do not alter during the course of one experiment. It may be changed to another, known value and the experiment repeated.

To conduct an experiment which determines the relationship between two factors and a dependent variable, one variable is determined to be the controlled variable and can be set to a fixed value. The experiment is run adjusting the other variable, which would be the independent variable, and measuring the dependent variable. This can be repeated for different, fixed values of the controlled variable, producing a number of “series” of data.

An example of using a controlled variable

Let’s apply this idea to finding the efficiency of a centrifugal water pump, which is a rotating device that increases the pressure of water. Let’s pretend the efficiency of the pump varies with both the water flow rate, between 0 and 20 litres per minute, and the speed that pump spins between 0 and 3,000 revolutions per minute. We pick the speed of the pump to be the controlled variable. In the first experiment, the speed of the pump (controlled variable) can be set to a value of 500 rpm. Measurements of efficiency (dependent variable) are made at different settings of flow rate (independent variable) to determine the relationship between these to factors. The experiment is then repeated a second time, with the controlled variable speed set to 1,000 rpm, and a third time at 1,500 rpm...etc, up to the top value of 3000 rpm.

Presenting controlled variables

If the results are numerical, the best way to present this information is with a number of series on a single pair of axes. The relationship between the independent and dependent for each experiment can be plotted as a unique set of data points, remembering to identify what each set of points represents with appropriate labelling or key/legend.

The same process can be conducted for more than two parameters, but if you find yourself needing to do a full, multiple parametric analysis, there are more sophisticated (and also more complicated) methods available, for example here

Summary: When you want to investigate the influence of two parameters on the measured output of a system the scientific method, of altering one parameter and measuring another, need to still be adopted. The way to investigate the influence of a second parameter, referred to as a controlled variable, is to set it to known value and run an experiment by setting the independent variable and measuring the dependent variable. The experiment can be run multiple times with different values for the controlled variable.

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