What happens to the dependent variable when the independent variable increases?

In analytical health research there are generally two types of variables. Independent variables are what we expect will influence dependent variables. A Dependent variable is what happens as a result of the independent variable. For example, if we want to explore whether high concentrations of vehicle exhaust impact incidence of asthma in children, vehicle exhaust is the independent variable while asthma is the dependent variable.  

A confounding variable, or confounder, affects the relationship between the independent and dependent variables. A confounding variable in the example of car exhaust and asthma would be differential exposure to other factors that increase respiratory issues, like cigarette smoke or particulates from factories. Because it would be unethical to expose a randomized group of people to high levels of vehicle exhaust,[1] a study comparing two populations with differential exposure to vehicle exhaust would rely on a natural experiment, or a situation in which this already occurs due to factors unrelated to the researchers. In this natural experiment, a community living near higher concentrations of car exhaust may also live near factories that pollute or have higher rates of smoking.

When running a study or analyzing statistics, researchers try to remove or account for as many of the confounding variables as possible in their study design or analysis. Confounding variables lead to bias, or a factor that may cause an estimate to differ from the true population value. Bias is a systematic error in study design, subject recruitment, data collection, or analysis that results in a mistaken estimate of the true population parameter.[2]

Although there are many types of bias, two common types are selection bias and information bias.  Selection bias occurs when the procedures used to select subjects and others factors that influence participation in the study produce a result that is different from what would have been obtained if all members of the target population were included in the study.[2]  For example, an online website that rates the quality of primary care physicians based on patients’ input may produce ratings that suffer from selection bias.  This is because individuals that had a particularly bad (or good) experience with the physician may be more likely to go to the website and provide a rating. 

Information bias refers to a “systematic error due to inaccurate measurement or classification of disease, exposure, or other variables.”[3]  Recall bias, a type of information bias, occurs when study participants do not remember the information they report accurately or completely.  The subject of confounding and bias relates to a larger discussion of the relationship between correlation and causation.  Although two variables may be correlated, this does not imply that there is a causal relationship between them. 

One way to determine whether a relationship between variables is causal is based on three criteria for research design: temporal precedence meaning that the hypothesized cause happens before the measured effect; covariation of the cause and effect meaning that there is an established relationship between the two variables regardless of causation; and a lack of plausible alternative explanations. Plausible alternative explanations are other factors that may cause the dependent variable under observation.[4]. These alternative explanations are closely related to the concept of internal validity.  

[1]Trochim, W.M.K. “Establishing Cause and Effect.” Research Methods Knowledge Base, 10/20/2006. Web 1/24/2017.
[2] “Bias, Confounding and Effect Modification” Stat 507, Epidemiological Research Methods, Penn State Eberly College of Science, 2017 Web 1/24/17.
[3] Aschengrau A. and G.R. Seage. (2014) Epidemiology in public health. 3rd ed. Burlington, MA: Jones & Bartlett Learning.
[4]. Due to a long history of unethical research in health and social sciences, researchers have many ethical obligations when conducting research, particularly with human subjects. These obligations were first codified in the Nuremburg Code in 1946, which specified that the benefits of research must outweigh the foreseeable risks. Ethical obligations continue to evolve to protect human subjects, including confidentiality and anonymity unless waived and informed consent. Increasingly, communities that have a stake in the outcomes of research are involved in its design and informed of the outcomes of the study. All federally funded research in the United States is subject to review by an Institutional Review Board (IRB).

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PreLab: Sketching a Graph of Your Hypothesis

Now that you have formed a hypothesis concerning relationship of the independent variable(s) and dependent variable, it might be a good idea to sketch out what this relationship might be. These sketches can be on grid or plain paper. They should only take a minute to draw. Notice in the examples below that no tick marks are measured out on scales nor are specific points plotted on the graph. The graph's purpose is to express a rough idea of what you think the trend in the data will be.

The first decision you need to make is whether you think there is a relationship between the variable or not. That is, will changes in the value of the independent variable affect the value of the dependent variable? If you think there is a relationship, then the next decision may be to decide whether this relationship is linear or governed by a higher order (curved) relationship.

No Relationship

If you think there is no relationship, then changes in value of the independent (x) variable will not affect the value of the dependent variable. The dependent variable value might be zero, a constant positive value, or constant negative value. It might be that there are other factors/variables that affect the dependent variable values, but it will be up to you to rule these out.

Linear Relationships

Another possibility is that you have hypothesized a linear relationship between the independent and dependent variables. If there is a positive relationship, then increases in the independent variable would lead to a proportional increase in the dependent variable. Your graph might look like the one above.

If you think that there will be a negative relationship between the variables, then increases in the independent variable will lead to decreases in the dependent variable. Your graph might look like the one above.

Higher Order (curved) Relationship

If you think that there is a higher order relationship (e.g., the dependent variable increases with the square of the independent variable increase) between the independent and dependent variables, then you will need to express the relationship in the graph as a curve. The exact shape of the curve will depend on the mathematical relationship between the variables, but there are a few basic curve shapes.

With this shaped curve, positive increases in the independent variable lead to increasingly larger growth in the dependent variable. The curve may or may not get to the point that the curve is essentially vertical. At this point the curve would express that an infinitesimally small increase in X will lead to an infinitely large increase in Y. A curve that approaches vertical but never gets there is said to be asymptotic.

Another possibility is the reverse of the previously situation. Here increases in the independent variable lead to increasingly larger decreases in the dependent variable.

Another common type of asymptotic curve is one where the independent variable as less and less of an effect on the dependent variable. In this case the curve becomes closer and closer to horizontal as the independent variable gets larger, as it does above.

The reverse could also be true. In the curve above, as the independent variable grows, the dependent variable decreases less and less as it approaches a constant Y value.

Next Step

If you have more than one independent variable you have the choice of sketching multiple graphs for each pair of independent and dependent variable, or sketching all the lines on a single graph. In this case you will have to label or code the individual lines. Both approaches have their merits. In the first case, you can focus in on each pairing of variables. In the latter case, you can see the relationship of the curves to each other as the independent variables are changed.

With a graph or graphs sketched out, you can begin to collect data from the lab with some prediction of how you think the data will map onto a graph. It is important that you don't attempt to manipulate the data you collect to fit some predefined line. Rather, this pre-graphing exercise helps further cement in your mind what you think the implications your hypothesis are to the data you are about to collect.

When the dependent variable increases when the independent variable increases?

What happens to the dependent variable when we change the independent variable?

What is the relationship between two variables when the dependent variable increases as the independent variable increases?