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In a follow-up study, 103 patients in the Netherlands having warts were randomly assigned to use duct tape or a placebo, which was a ring covered by tape so that the wart itself was kept clear \((\) Arch. Pediat. Adoles. Med. \(2006 ; 160: 1121-1125)\) a. Identify the response variable, the explanatory variable, the experimental units, and the treatments. b. After six weeks, the warts had disappeared for \(16 \%\) of the duct tape group and \(6 \%\) of the placebo group. However, the difference was declared to be "not statistically significant." Explain what this means.

Short Answer

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a. Response: Wart disappearance; Explanatory: Type of treatment; Units: 103 patients; Treatments: Duct tape vs. placebo. b. The difference in results could be due to random chance.

Step by step solution

01

Identify the Response and Explanatory Variables

In any experiment, the **response variable** is what you measure to see the effects of the treatment. In this study, the response variable is the disappearance of the warts after treatment. The **explanatory variable**, which is the variable that might explain changes in the response variable, is the type of treatment administered: either duct tape or placebo.
02

Recognize the Experimental Units

The **experimental units** are the subjects or objects that receive the treatment. In this study, the 103 patients who were randomly assigned to one of the treatments serve as the experimental units.
03

Determine the Treatments

The **treatments** in this experiment are the different approaches applied to the experimental units. Here, the treatments are the application of duct tape and the application of a placebo ring covered by tape.
04

Explain the Meaning of 'Not Statistically Significant'

When the results are declared "not statistically significant," it means the difference in wart disappearance rates between the duct tape group (16%) and the placebo group (6%) is not large enough to rule out chance as a possible explanation. In other words, we do not have strong enough evidence to say the duct tape treatment is definitively more effective than the placebo.

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Key Concepts

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

Response Variable
In this particular study dealing with wart treatment, the response variable is pivotal in understanding the outcome. A response variable, also known as a dependent variable, is the one that is measured in an experiment to assess the effect of the treatments applied.
For this research, the response variable is the disappearance of the warts after six weeks of applying the treatments. Essentially, it's what the researchers are keeping a close eye on to assess the treatments' effectiveness. They recorded the percentage of wart disappearances in the two groups—those treated with duct tape and those with the placebo.
  • This variable helps in understanding whether the treatment had the intended effect.
  • By focusing on the response variable, conclusions can be drawn about the effectiveness of each treatment condition.
Thus, it's essential to accurately measure the response variable to ensure the reliability of the experiment's conclusions.
Explanatory Variable
The explanatory variable plays a crucial role in understanding why the response variable changes. It is often referred to as the independent variable because it explains or influences the outcome. In this warts study, the explanatory variable is the type of treatment administered to the patients—duct tape versus a placebo.
This variable is what researchers manipulate to determine if it will cause a change in the response variable.
  • For the experiment at hand, the explanatory variable sets up the different treatments: applying duct tape to warts and applying a placebo.
  • This allows researchers to compare the effects of both treatments on the disappearance rate of the warts.
Understanding the explanatory variable is imperative as it helps in setting the foundation for the experimental design, helping researchers to align their observations with the research question.
Experimental Units
In experiments, the term "experimental units" refers to the individuals or items subjected to treatments. Here, 103 patients from the Netherlands serve as experimental units. These individuals are randomly assigned one of the two treatments: duct tape or a placebo.
The concept of experimental units is foundational because it defines the scope and scale of the investigation.
  • Each patient receives one treatment formula, ensuring the trial can measure genuine differences attributable to the treatments, not individual differences.
  • The random assignment of participants to different treatments helps in minimizing bias.
Properly identifying experimental units is vital as it ensures that the results are applicable to the larger population from which the sample is drawn.
Statistical Significance
The term "statistical significance" is used to infer the strength of the results obtained in an experiment. In this wart study, despite a higher percentage of warts disappearing in the duct tape group compared to the placebo group, this difference was termed "not statistically significant."
This means the observed difference (16% for duct tape and 6% for placebo) isn't enough to prove that duct tape is definitively more effective at a certain confidence level, considering the possibility of the observed effect being due to random chance.
  • When an experiment's results are not statistically significant, it suggests there is insufficient evidence to validate the treatment's efficacy over the placebo.
  • The term highlights the importance of using probability to distinguish true effects from those arising by chance.
Therefore, the declaration of "not statistically significant" encourages researchers to be cautious in their conclusions and promotes the need for further studies to provide more definitive answers.

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