Question

Infections Can Lower IQ A headline in June 2015 proclaims "Infections can lower IQ." 1 The headline is based on a study in which scientists gave an IQ test to Danish men at age \(19 .\) They also analyzed the hospital records of the men and found that \(35 \%\) of them had been in a hospital with an infection such as an STI or a urinary tract infection. The average IQ score was lower for the men who had an infection than for the men who hadn't. (a) What are the cases in this study? (b) What is the explanatory variable? Is it categorical or quantitative? (c) What is the response variable? Is it categorical or quantitative? (d) Does the headline imply causation? (e) Is the study an experiment or an observational study? (f) Is it appropriate to conclude causation in this case?

Short answer

a) The cases in this study are the Danish men. b) The explanatory variable is whether the men have had an infection and it is categorical. c) The response variable is the IQ score and it is quantitative. d) The headline does imply causation. e) It's an observational study. f) It is improper to conclude causation based on this study.

Step-by-step solution

Identify the cases in the study

The cases in this study are the Danish men who were tested at the age of 19.

Identify the explanatory variable and its type

The explanatory variable is the men's hospitalization for an infection (like an STI or a urinary tract infection). This is a categorical variable indicating if the person has had an infection or not.

Identify the response variable and its type

The response variable is the IQ score of the Danish men. This is a quantitative variable as IQ scores can be measured on a numerical scale.

Analyze the headline for implied causation

The headline 'Infections can lower IQ.' does imply causation as it suggests that infections directly cause a lower IQ.

Determine the type of the study

The study is an observational study. The researchers did not manipulate any variables or randomly assign participants to different groups but instead, studied the outcome as it naturally occurred.

Discuss the appropriateness of determining causation

No, it's not appropriate to conclude causation in this case. Even though the study found a correlation between infection and lower IQ scores, this does not necessarily mean the infection caused the lower IQ. Other third variables might be influencing this correlation. The claim of causation especially from an observational study requires a very thorough examination and careful interpretation.

Key concepts

Explanatory Variable

When delving into the realm of research and statistics, the term explanatory variable often surfaces. This concept is pivotal as it represents the potential influence or cause in a study. For example, if researchers want to discern if studying habits impact test scores, the amount of time spent studying would be considered the explanatory variable.

In the context of the provided exercise, the explanatory variable is the hospitalization for an infection, such as an STI or a urinary tract infection. This variable is categorical, meaning it divides the cases into categories – in this scenario, those who have been hospitalized for an infection versus those who have not. It is essential to clearly define and understand the explanatory variable, for it frames the direction the study takes and guides the analytical interpretation.

Response Variable

Complementing the explanatory variable is the response variable, also known as the dependent variable. It is the outcome researchers are interested in dissecting or predicting. It typically answers the question 'What changes?' when the explanatory variable is altered. Imbuing clarity and preciseness during its designation is crucial for reliable and interpretable results.

In the exercise, the IQ score of the Danish men is identified as the response variable. This is because the IQ score is the outcome being measured after considering whether the individuals had an infection. IQ scores are quantitative variables, as they are expressed numerically, and hence, can be measured and meaningfully ordered or ranked.

Causation in Observational Studies

Understanding causation in observational studies can be like navigating a labyrinth due to the complexities and nuances involved. Causation implies that one event is the result of the occurrence of the other event; i.e., there is a cause and effect relationship. However, merely observing an association between two variables doesn't prove that one causes the other. Confounding factors may exist that contribute to or confuse the relationship.

Returning to our exercise example, while the headline implies that infections can lower IQ, implying a causal relationship, the format of an observational study makes that conclusion unreliable. Observational studies are inherently limited in their ability to prove causation because they don't control for all potential confounding variables, nor do they involve random assignment which is necessary to establish cause and effect. Therefore, even though an association was observed, declaring that infections cause a decrease in IQ could be misleading without further experimental evidence.

Quantitative and Categorical Variables

Distinguishing between quantitative and categorical variables is at the heart of statistical analysis, as they are the building blocks of data.

Quantitative Variables are numerical and measurable. They represent a measurable quantity and allow for mathematical operations – examples include height, weight, and, in our exercise, IQ score.

Categorical Variables, on the other hand, describe characteristics or qualities and are sorted into groups or categories. These variables are not necessarily numerical and often include demographic information like gender, race, or the presence of an infection as displayed in the exercise.

Identifying whether a variable is quantitative or categorical will dictate the type of statistical analysis that is suitable for interpreting the data and will ultimately influence the findings of a study.