Question

In a study of 1,040 subjects, researchers found that the prevalence of coronary heart disease increased as the number of cups of coffee consumed per day increased. \({ }^{31}\) (a) What is the explanatory variable? (b) What is the response variable? (c) What are the observational units?

Short answer

The explanatory variable is the number of cups of coffee consumed per day, the response variable is the prevalence of coronary heart disease, and the observational units are the 1,040 subjects in the study.

Step-by-step solution

Identify the Explanatory Variable

In a research study, the explanatory variable is the one that may explain or cause a change in the response variable. In this study, since the number of cups of coffee consumed is believed to potentially affect the prevalence of coronary heart disease, the explanatory variable is the number of cups of coffee consumed per day.

Identify the Response Variable

The response variable is the outcome of interest that is measured to see if it is affected by the explanatory variable. Here, it is the prevalence of coronary heart disease, as it is the condition whose variation is being studied across the subjects with respect to coffee consumption.

Identify the Observational Units

The observational units are the entities being measured or observed in a study. In this scenario, each of the 1,040 subjects being studied becomes an observational unit, as data about coffee consumption and heart disease prevalence is recorded for each of these individuals.

Key concepts

Explanatory Variable

Imagine you are sleuthing for clues to solve a mystery. In the world of research, the explanatory variable is akin to an intriguing clue. It's that one piece of the puzzle that could lead you to understand why something is happening. In our coffee and heart disease study, think of the number of cups of coffee consumed daily as a potential key to unlock the mystery of coronary heart disease prevalence.

An explanatory variable, also known as an independent variable, is what researchers manipulate or observe to see if it has an effect on something else. It is the suspected cause in the cause-and-effect relationship under investigation. Essentially, it's the 'if' in the 'if-then' scenario we often contemplate when trying to understand the world around us. In simple experiments, it is the variable that is changed or varied in order to assess its impact.

For instance, in evaluating whether studying habits influence exam scores, the number of hours spent studying would be the explanatory variable. The aim is to observe if changes in this variable explain variations in the scores, hence the name 'explanatory'. In our example, the researchers are putting the coffee consumption under the microscope to determine if it’s a factor that needs to be adjusted.

Response Variable

Now, the response variable is the effect observed in the grand experiment of life—or, more technically, in an actual research study. After investigators zero in on the explanatory variable (or variables), they turn their attention to the response variable to decode the story it tells. In the coffee consumption study, our response variable is the prevalence of coronary heart disease, the puzzle's outcome.

Think of the response variable as the answer to a burning question. It's the data you collect that may have changed because of the explanatory variable's influence. This variable is sometimes called the dependent variable because its value may depend on the effect of the explanatory variable. It's the result, the 'then', in our 'if-then' investigation.

Taking the example of a science fair project - if a student hypothesizes that fertilizer will make plants grow taller, the height of the plants would be the response variable. Researchers or scientists measure the response variable to grasp the extent to which it is altered by the explanatory variable. Back to our study, by looking into the heart disease patterns, researchers endeavour to untangle how coffee impacts heart health.

Observational Units

The concept of observational units is like focusing on individual characters in a novel. Each character may have a different story, but together they weave the tapestry of the plot. In the realm of research, observational units are the individual entities we examine or measure in a study. These are the 'who' or 'what' that provide us with the data.

In many studies, these units are people, but they might also be schools, communities, medical records, or even countries in different kinds of research. They are the foundational blocks of data collection and integral to the study's structure. In the case of our heart disease research, each of the 1,040 subjects represents an observational unit. Each person's data on coffee intake and heart condition contributes a critical narrative to the study's overall findings.

Observational units are essential not just because they hold the data but because researchers must understand the context and variability that each unit brings. Acknowledging the uniqueness of each observational unit ensures that conclusions drawn from the study are robust and reflective of the population at large. When you hear about a new finding on how exercise affects mood, remember, every participant in that study was an observational unit that played a part in the final conclusion.