Independent Variables = Grouping VariablesObjectives:
Dependent Variable = Outcome Measures
- Be able to identify the independent and dependent variables of a study from its title or abstract.
- Be able to define the term "extraneous variable."
- Be able to identify the features of independent and dependent variables
What is a variable - and what's not?
A variable is a characteristic or feature that varies, or changes within a study. The opposite of variable is constant: something that doesn't change. In math, the symbols "x" , "y" or "b" represent variables in an equation, while "pi" is a constant. In an experimental example, if a study is investigating the differences between males and females, gender would be a variable (some subjects in the study would be men, and others would be women). If a study has only female subjects, gender would not be a variable, since there would be only women. If a study includes both males and females as subjects, but is not interested in differences between men and women - and does not compare them, gender would not be a variable in that study.
If a study compares three different diets, but keeps all 3 diets the same in the amount of sodium, then sodium isn't a variable in that study - it's a constant. Other features of the diets would be variables of interest - maybe the calories or carbohydrates or fat content.
In this course, we will study independent variables, dependent variables, and confounding or intervening variables. In this section, we will focus on how to identify and distinguish Independent from Dependent variables, and the roles these variables play in a research study.
In experimental research, an investigator manipulates one variable and measures the effect of that manipulation on another variable. The variable that the researcher manipulates is called the independent, or grouping variable. The independent variable is the variable that is different between the groups compared: all the members of one group will have the same level of the independent variable, a second group will have a different level of that same variable, and the same for a 3rd or 4th group, if present.
For example, let's take a study in which the investigators want to determine how often an exercise must be done to increase strength. Stop for a minute and think about how they might organize a study so they could figure this out. There are usually several possible studies that could be done to address a question.
These investigators decided to compare 3 groups, one group participate in a set of specific exercises 4 times per week; a second group would do the same exercises, but only twice per week, and a control group would participate in stretching exercises that would have no impact on strength. The variable that differs between these 3 groups that are compared is an Independent Variable. This particular independent variable has 3 LEVELS of the SINGLE independent variable - in this example: type of exercise.
Some non-experimental studies also have independent variables, but they may not be determined or manipulated by the investigators. For example, a study may compare test performance between men and women; so gender would be the independent variable. However, since investigators didn't determine or specify which individuals would be men and which would be women (!), it is not considered to be an active independent variable. Because gender does define the variable used for comparison, it is still an independent variable, even though it has lost some of its power. We'll look at this in more detail in the next chapter.
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The outcome variable measured in each subject, which may be influenced by manipulation of the independent variable is termed the dependent variable. In experimental studies, where the independent variables are imposed and manipulated, the dependent variable is the variable thought to be changed or influenced by the independent variable.
Example: study title: Effects of a new tooth paste (YummyTooth) on incidence of caries in 1st grade children. The intervention group was given YummyTooth toothpaste, while the control group was given an identical toothpaste that did not contain the secret ingredient in YummyTooth. Subjects were observed brushing their teeth 3x per day with the assigned toothpaste (by teacher or parent). 6 months later, dental appointments were scheduled, and the number of dental caries present in each child was reported.
In this study, the toothpaste was the independent variable; it was different between the two groups: one level was the YummyTooth toothpaste itself, and the second level (a control group) was the identical non-YummyTooth toothpaste (a placebo). The outcome measure (dependent variable) - that "depended" upon the type of toothpaste, was the number of dental caries.
Frequently a single research study may have many dependent variables. However, since most analyses only consider one dependent variable at a time (called univariate analyses), each dependent variable analysis is considered a separate study for the purposes of statistical analysis.
Independent Variables in Observational Studies and Some Quasi-Experimental Studies: When Independent Variables are not Manipulated
Observational and some quasi-experimental studies lack active interventions - their independent variables are not specifically imposed by the investigators. They may study variables that cannot physically impose the intervention (e.g., gender, country of birth, family history of heart disease) or cannot manipulate it ethically (smoking, exposure to risk factors). While these studies cannot tell us whether one variable causes changes, they can tell us how strong a relationship exists between variables.
Identifying the Independent variables in these studies is a bit trickier than in true experiments, where the investigators control them. Observational studies may collect all of the data from a single questionnaire or set of medical records, so all information comes from a single assessment. Since they don't impose a change, they cannot tell us what would happen if we changed something. They tell us about relationships among variables in populations. In many cases, a single set of data can be analyzed in several ways, so it is important to determine exactly how the particular study probed the data: what questions did they ask?
In these studies, independent variables are still the grouping variables, so key in on statements that indicate comparisons. In a tooth-brushing study, the investigators might ask the parents how frequently the children brushed their teeth (check 0, 1, 2, 3), and collect the caries data from dental records from the schools. In this case, the investigators are not imposing a tooth-brushing regime, but are simply inquiring about existing habits, and then comparing those groups to determine the strength of the relationship. Here, as before, the independent variable is tooth-brushing, but now it is the comparison of groups of children in each category (#times brushed per day). The dependent (outcome measure) variable, is still the number of caries.
Another example from a study title:
Impact of smoking status on long-term mortality in patients with acute myocardial infarction
The independent variable is smoking status (undoubtedly not imposed, not active)- could be reporting just smoking/non-smoking/quit categories. The dependent variable would be long-term mortality.
Confounding or Extraneous Variables
In the best circumstances, the only consistent feature that differs between the intervention and control groups is the intervention level itself. The groups that are compared should be similar in every other way, and only differ in the independent variable level. In the YummyTooth toothpaste example above, this would mean that the groups receiving the two types of toothpaste should be similar. If children with a history of many more caries were systematically put into the control group, this would introduce bias. When the two groups start out the same (have the same incidence of prior caries), then introduce a single intervention difference, any difference in later number of caries reflects only the influence of the intervention. If there are other differences between the two groups of children, such as a bias that put children with more caries in the control group, then we can no longer have that confidence. In this situation, even if the YummyTooth group of children have significantly fewer caries, we won't be able to tell whether it was the toothpaste, or the history of caries, or some combination, that caused the different number of caries between the groups. These biasing variables are called confounding or extraneous variables.
The confounding variables are differences between groups other than the independent variables. That means that most members of a group are alike on a variable, but different from the other group, e.g., if the control group was mostly smokers and the experimental group mostly non-smokers. These variables interfere with assessment of the effects of the independent variable because they, in addition to the independent variable, potentially affect the dependent variable. Since they cannot be separated from the independent variable, they are said to be confounding variables. These variables produce differences between groups that cannot be attributed to the independent variable. In these situations,the independent variable is not the only difference that exists between the groups. Therefore, there may be many other variables contributing to the differences observed between the groups compared. Thus, we cannot conclude that the independent variable is the cause of the difference or change seen. These other factors that may influence the dependent variable are termed "extraneous", "intervening" or "confounding" variables. Usually this type of confounding variable is avoided by randomly assigning subjects to groups, so not all of one kind of subject goes into one group.
Identifying Independent & Dependent Variables
Let's say that a study reports "The effects of kicking on the position of the ball." Just from this title of the study, we can tell that the outcome measure (the dependent variable) will be the position of the ball (or the distance traveled). The variable thought to influence the distance, the independent variable, would be the kicking. We would assume that in the study, some balls were kicked (intervention or experimental group), and others were not kicked; or had something else done to them; so there were at least 2 levels of the independent variable.
You can use this typical form to determine the independent and dependent variables from the title of the study. If the study title is in the form "The effects of X on Y in Z". X is the independent variable and Y is the dependent variable - the outcome, and Z is the type of subjects represented.
A simple example would be: The effects of tomatoes on risk of prostate cancer in Scandinavian men. The "tomatoes" is in the X position, so it is the independent variable - it is the variable being compared between groups (and the variable possibly manipulated - it also implies that there's another level - a comparison group of some sort). The Y position is "risk of prostate cancer" - that's the dependent variable, which is measured as the outcome. The target population: Scandinavian men is the sample in which the study was done - however, the results may be more generalizable. (back to top)
Here's another example:
A randomized trial of breast cancer risk counseling: the impact on self-reported mammography use.
From this title, you can tell that the independent variable is type of counseling (with 2 or more levels, risk counseling and no counseling or standard care). The dependent variable is self-reported mammography use.
|Independent Variable||Dependent Variable|
|manipulated/measured||"manipulated" or "imposed" by researchers in an experiment||measured as outcome variable|
|groups different/groups the same||grouping variable: different levels for different groups in observational studies||all subjects in all groups are measured the same way|
|each study may have several independent variables||each study likely has several to many dependent variables|
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