Your research study could measure the length of stay needed following a particular procedure -- say an appendectomy. The length of time spent in the hospital would be the dependent variable. The independent variable could be the ages of the patients. An extraneous variable could be something that no one has control over -- say the number of visitors or the general health of the patient before the surgery.
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It might help to review the classical epxerimental method.
An independent variable is the potential stimulus or cause, usually directly manipulated by the experimenter, so it could also be called a manipulative variable.
A dependent variable is the response or measure of results.
Extraneous variables — other than the independent variable — potentially can affect the dependent variable, so they must be controlled. If possible, you try to keep them constant between the experimental and control group.
The experimental group receives the independent variable.
The control group is similar to experimental, except it does not receive the independent variable. Extraneous variables are balanced between experimental and control groups.
Types of experiments
1. Single blind gives the control group a placebo — a substance that is inert, it has no physical effect. Subjects don't know if they are in experimental or control group to reduce placebo effect, a change in behavior solely due to believing that you are getting the independent variable.
2. Double blind keeps both subjects and experimenter ignorant of group setup. Distribution of the independent variable and placebo is controlled by third party. This controls for experimenter bias and self-fulfilling prophecy. This means that experimenters with particular expectations are likely to consciously or unconsciously to bias the experiment and influence it to conform to their expectations.
As an example, suppose you want to find out if fluorides reduce dental cavities. You would find two groups, trying to control the extraneous variables. Extraneous variables are found by surveying previous research in the area. In this case, you would match the groups in terms of previous history of cavities, diet and dental hygiene habits including how and how often they brush their teeth.
The experimental group would get toothpaste with the independent variable, the fluoride, while the control group would not have the fluoride in their toothpaste. The toothpaste without the fluoride would be the placebo.
The dependent variable would be the number of cavities after participating in the experiment for a time. The dependent variable indicates the results, but it is not the results. At the end of the experiment, both groups could have no change in cavities or one of the groups could have a greater reduction in cavities. (Of course, if the fluoride increased cavities, you wouldn't want to use it.) All of these varied results would be indicated in terms of the dependent variable.
If only the subjects do not know who is getting the fluoride, it is a single blind experiment. If both the subjects and experimenter do not know, it is a double blind.
I hope this helps a little more. Thanks for asking.