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Vitamin B A New York Times article (March 12, 2006) described two studies in which subjects who had recently had a heart attack were randomly assigned to one of four treatments: placebo and three different doses of vitamin B. In each study, after years of study, the differences among the proportions having a heart attack were judged to be not statistically significant. Identify the (a) response variable, (b) explanatory variable, (c) experimental units, (d) treatments, and (e) explain what it means to say that differences "were judged to be not statistically significant."

Short Answer

Expert verified
(a) having another heart attack, (b) type of treatment, (c) individuals who had a heart attack, (d) placebo and vitamin B doses, (e) differences likely due to chance.

Step by step solution

01

Identify the Response Variable

The response variable is the primary outcome that the study is measuring. In this case, it is whether or not the subject has another heart attack after undergoing the treatment.
02

Identify the Explanatory Variable

The explanatory variable is what is manipulated by the researchers to examine its effect on the response variable. Here, the explanatory variable is the type of treatment received (placebo or one of the three different doses of vitamin B).
03

Identify the Experimental Units

Experimental units are the smallest division of subjects to which treatments are assigned. In this context, the experimental units are the individual subjects who have recently had a heart attack.
04

Identify the Treatments

Treatments refer to the different conditions applied to the experimental units. The treatments in this study are the placebo and three different doses of vitamin B given to the subjects.
05

Explain 'Not Statistically Significant'

When the differences among treatment outcomes are 'not statistically significant,' it means that any observed differences in the proportions of those who had another heart attack are likely due to chance rather than a real effect of the treatments.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Response Variable
In any study, the response variable is the primary outcome that researchers are interested in measuring. It reflects the effect of experimental conditions or treatments. In the context of the vitamin B study, the response variable is whether or not each subject experiences another heart attack after the treatment.

This variable is crucial because it gives researchers insight into the effectiveness of the treatment applied. If a certain treatment resulted in fewer recurring heart attacks, it would be considered potentially effective. The response variable, therefore, helps in evaluating the success of the intervention within the study.
Explanatory Variable
The explanatory variable is what the researchers manipulate or change to investigate its impact on the response variable. In this study, the type of treatment is the explanatory variable, consisting of either a placebo or one of three different doses of vitamin B.

Researchers use explanatory variables to understand how different treatments can affect outcomes. By controlling the explanatory variables, they can see if changes in the treatment lead to changes in the response variable. This helps in establishing a potential cause-effect relationship within the study.
While the response variable indicates what happened, the explanatory variable explains why it might have happened.
Statistical Significance
Statistical significance is a term used to describe how likely it is that an observed effect in a study is due to chance rather than the treatment itself. When results are said to be 'not statistically significant,' as in the vitamin B study, it implies that the observed differences are probably due to random variation rather than actual treatment effects.

In practical terms, this means that the treatments might not have had any real effect on reducing heart attacks compared to the placebo. Researchers typically use a significance level, often set at 5%, to determine this. If the p-value derived from the data is higher than this threshold, the result is deemed not statistically significant.
It's important to remember that not statistically significant doesn't prove the treatment has no effect; it simply suggests that any effect observed could easily have arisen by chance.
Experimental Units
Experimental units are the individuals or entities to which treatments are applied in a study. In the vitamin B study, each person who had recently experienced a heart attack acts as an experimental unit. These individuals are randomly assigned to different treatment groups, ensuring that the effects observed can be more confidently attributed to the treatments rather than any other factors.

The concept of experimental units is foundational to experimental design because it helps in ensuring the reliability and validity of the results. By carefully selecting and assigning treatments to these units, researchers can reduce biases and increase the credibility of their findings.
Random assignment is key, as it helps in distributing any known or unknown characteristics equally among treatment groups, minimizing the chance for skewed results.

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