Problem 33 - BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

Question

A researcher studies the effect of fiber supplements on heart disease. The researcher identified 175 people who take fiber supplements and 175 people who do not take fiber supplements. The study found that those who took the supplements had \(19.6 \%\) fewer heart attacks. The researcher concludes that taking fiber supplements reduces the chance of heart attacks. a. Explain why the researcher's conclusion may not be valid. b. Describe how the researcher could have conducted the study differently to produce valid results.

Step-by-Step Solution

Answer

The researcher's conclusion may not be valid due to lack of consideration for other potential factors affecting heart disease, mistaking correlation for causation, and potential selection bias. A randomized controlled trial with the consideration of other confounding factors could produce more valid results.

Step 1: Analyze the Research Method

Review the research conclusion. From the information given, it seems that the researcher did not consider other factors that could influence heart disease such as lifestyle factors, diet, heredity, and physical activity levels among others. This is a case of correlation being mistaken for causation. Just because the group taking fiber supplements had fewer heart attacks, it does not necessarily mean that the supplements are the direct cause of the decrease in heart attacks.

Step 2: Suggest for The Designer's Bias

The study can also be flawed due to selection bias. Take into consideration that those who opt to take fiber supplements may generally be more health-conscious and might be doing other things that lower their risk of heart diseases such as regular exercise, maintaining a balanced diet etc. These factors might not be present among those who did not take fiber supplements that can attribute to the differences observed.

Step 3: Suggest Improvement in Methodology

The study could have been designed in a way to consider and control other confounding variables. Ideally, a randomized controlled trial could be more suitable as it can randomly assign people into two groups, one receiving the supplements and the other a placebo, reducing biases. Both groups should be followed over time to detect any differences. This can provide a more definitive answer as to whether the fiber supplements indeed reduce the chance of heart attacks by comparing the two groups after a period of time. Also, the researcher could consider a larger sample size to validate the findings and increase the reliability of the result.

Key Concepts

Selection Bias

Selection bias arises when the sample collected is not representative of the overall population. In the context of the fiber supplement study, the researcher selected 175 people who take fiber supplements and matched them with 175 people who do not. However, these two groups may not be comparable due to inherent differences. For instance:

• Individuals opting for supplements might generally have healthier lifestyles.
• There could be differences in socio-economic status, as those who can afford supplements might also have access to better healthcare.

These points indicate that selection bias can skew the results of the study. It leads to false conclusions about causation. To avoid this, a study needs careful planning, ensuring that the selected groups are truly comparable.

Confounding Variables

Confounding variables are external influences that stifle the clear relationship between the independent and dependent variables. In the fiber supplement study, various factors like diet, exercise, and genetic predispositions to heart disease were not controlled. Consider the following:

• If people taking fiber supplements also eat healthy food, their reduced rate of heart attacks might be less about the supplements and more about their overall diet.
• Likewise, these individuals might exercise more frequently, which is a known factor in reducing heart disease.

Omitting such confounding variables leads to confusion about what is actually causing the observed effects. Adequately managing these variables is crucial to clarify the direct relationship and ensure the study's validity.

Randomized Controlled Trial

A randomized controlled trial (RCT) is a study design that can minimize biases and confounding variables by randomly assigning participants into different groups. In the context of the fiber supplement study, an RCT could be structured as follows:

• Randomly assign individuals to either a group receiving the fiber supplement or a placebo group.
• Neither the participants nor the researchers know who is receiving the supplements or placebo (double-blind).

This approach ensures that both known and unknown factors are evenly distributed across the groups. Doing so, it mitigates the risk of selection bias and controls confounding variables, leading to more reliable results. An RCT allows researchers to determine whether fiber supplements truly have a causal effect on reducing heart attacks.