## Case Study Dependent And Independent Variables

A variable is something that can be changed or varied, such as a characteristic or value. Variables are generally used in psychology experiments to determine if changes to one thing result in changes to another.

Variables play a critical role in the psychological research process. By systematically varying some variables and measuring the effects on other variables, researchers can determine if changes to one thing result in changes in something else.

### The Dependent and Independent Variables

In a psychology experiment:

- The
**independent variable**is the variable that is controlled and manipulated by the experimenter. For example, in an experiment on the impact of sleep deprivation on test performance, sleep deprivation would be the independent variable. - The
**dependent variable**is the variable that is measured by the experimenter. In our previous example, the scores on the test performance measure would be the dependent variable.

### Extraneous and Confounding Variables

It is important to note that the independent and dependent variables are not the only variables present in many experiments. In some cases, extraneous variables may also play a role. This type of variable is one that may have an impact on the relationship between the independent and dependent variables.

For example, in our previous description of an experiment on the effects of sleep deprivation on test performance, other factors such as age, gender, and academic background may have an impact on the results.

In such cases, the experimenter will note the values of these extraneous variables so this impact on the results can be controlled for.

There are two basic types of extraneous variables:

**Participant Variables:**These extraneous variables are related to individual characteristics of each participant that may impact how he or she responds. These factors can include background differences, mood, anxiety, intelligence, awareness and other characteristics that are unique to each person.

**Situational Variables:**These extraneous variables are related to things in the environment that may impact how each participant responds. For example, if a participant is taking a test in a chilly room, the temperature would be considered an extraneous variable. Some participants may not be affected by the cold, but others might be distracted or annoyed by the temperature of the room.

In many cases, extraneous variables are controlled for by the experimenter. In the case of participant variables, the experiment might select participants that are the same in background and temperament to ensure that these factors do not interfere with the results. If, however, a variable cannot be controlled for, it becomes what is known as a **confounding variable**. This type of variable *can* have an impact on the dependent variable, which can make it difficult to determine if the results are due to the influence of the independent variable, the confounding variable or an interaction of the two.

### Operationally Defining a Variable

Before conducting a psychology experiment, it is essential to create firm operational definitions for both the independent variable and dependent variable. An operational definition describes how the variables are measured and defined within the study.

For example, in our imaginary experiment on the effects of sleep deprivation on test performance, we would need to create very specific operational definitions for our two variables. If our hypothesis is "Students who are sleep deprived will score significantly lower on a test," then we would have a few different concepts to define. First, what do we mean by *students*? In our example, let’s define students as participants enrolled in an introductory university-level psychology course.

Next, we need to operationally define the *sleep deprivation* variable. In our example, let’s say that sleep deprivation refers to those participants who have had less than five hours of sleep the night before the test.

Finally, we need to create an operational definition for the test variable. For this example, the test variable will be defined as a student’s score on a chapter exam in the introductory psychology course.

Students often report problems with identifying the independent and dependent variables in an experiment. While the task can become more difficult as the complexity of an experiment increases, there are a few questions you can ask when trying to identify a variable.

What is the experimenter manipulating? The things that change, either naturally or through direct manipulation from the experimenter, are generally the independent variables. What is being measured? The dependent variable is the one that the experimenter is measuring.

Sources:

Evans, AN & Rooney, BJ. Methods in Psychological Research. Thousand Oaks, CA: SAGE Publications; 2014.

Kantowitz, BH, Roediger, HL, & Elmes, DG. Experimental Psychology. Stamfort, CT: Cengage Learning; 2015.

Generally speaking, in any given model or equation, there are two types of variables:

- Independent variables - The values that can be changed or controlled in a given model or equation. They provide the "input" which is modified by the model to change the "output."
- Dependent variables - The values that result from the independent variables.

## Using Independent and Dependent Variables

The definition of an independent or dependent variable is more or less universal in both statistical or scientific experiments and in mathematics; however, the way the variable is used varies slightly between experimental situations and mathematics.

### Example of Variables in Scientific Experiments

If a scientist conducts an experiment to test the theory that a vitamin could extend a person’s life-expectancy, then:

- The independent variable is the amount of vitamin that is given to the subjects within the experiment. This is controlled by the experimenting scientist.

- The dependent variable, or the variable being affected by the independent variable, is life span.

The independent variables and dependent variables can vary from person to person, and the variances are what are being tested; that is, whether the people given the vitamin live longer than the people not given the vitamin. The scientist might then conduct further experiments changing other independent variables -- gender, ethnicity, overall health, etc. -- in order to evaluate the resulting dependent variables and to narrow down the effects of the vitamin on life span under different circumstances.

Here are some other examples of dependent and independent variables in scientific experiments:

- A scientist studies the impact of a drug on cancer. The independent variables are the administration of the drug - the dosage and the timing. The dependent variable is the impact the drug has on cancer.
- A scientist studies the impact of withholding affection on rats. The independent variable is the amount of affection. The dependent variable is the reaction of the rats.
- A scientist studies how many days people can eat soup until they get sick. The independent variable is the number of days of consuming soup. The dependent variable is the onset of illness.

### Example of Variables in Mathematics

In mathematics, the "x" and "y" values in an equation or a graph are referred to as "variables."

- If an equation shows a relationship between x and y in which the value of y is dependent upon the value of x, y is known as the dependent variable and is sometimes referred to as ‘function(x)’ or f(x).
- The final solution of the equation, y, depends on the value of x, the independent variable which can be changed.

## Graphing Dependent and Independent Variables

In both math and science, dependent and independent variables can be plotted on the x and y axes of a graph. The convention is to use the independent variable as the x-axis and the dependent variable as the y-axis. There is typically a clear and obvious relationship between x and y shown on the graph.

An example of this would be Boyle’s Gas Law where the pressure of a gas is inversely proportional to its volume as long as the temperature remains constant.

- Using the equation (y = kx), one can plot a graph that will yield a theoretical value for y when given any value for x, allowing one to accurately predict the affect the independent variable will have on the dependent variable.

In order to have come up with the equation for what is now Boyle’s Law, Boyle himself would have had to conduct a series of experiments that measured the effect that altering the independent variable (pressure) had on the dependent variable (volume). This would have put both independent and dependent variables into a real life, practical context. Boyle was then able to devise his equation based on his observations of the independent and dependent variables.

Knowing the differences between independent and dependent variables will help as you sharpen your problem solving skills and explore new concepts within the fields of mathematics and the science

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