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Chapter 4: Problem 35

More duct tape \(\quad\) 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

Expert verified
The study's response variable is wart disappearance; the explanatory variable is the treatment type. Despite a 10% difference, the results were not statistically significant.

Step by step solution

01

Identify the Experimental Units

The experimental units in this study are the 103 patients in the Netherlands who participated in the experiment.
02

Identify the Response Variable

The response variable is whether or not the warts disappeared after six weeks of treatment.
03

Identify the Explanatory Variable

The explanatory variable is the type of treatment used, which includes duct tape and a placebo.
04

Identify the Treatments

In this study, the treatments are the application of duct tape and the application of a placebo to the warts.
05

Explain Statistical Significance

A result is "not statistically significant" if the observed difference between groups is likely due to random chance rather than a real effect of the treatment. Here, the difference in wart disappearance rates between the duct tape group (16%) and the placebo group (6%) was not large enough to conclude that duct tape is more effective than placebo beyond random variation.

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Key Concepts

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

Response Variable
In the study about patients with warts, the response variable is the outcome or the effect we are measuring. Here, the response variable is the disappearance of warts after six weeks. We are looking to see if the warts are gone or still present, which provides insight into the effectiveness of the treatment. This variable responds to the treatment being applied and therefore is crucial in assessing the impact of different interventions.
Explanatory Variable
The explanatory variable in an experimental setup is the variable that is manipulated to observe its effect on the response variable. In this study, the explanatory variable is the type of treatment used on the warts. Two treatments were compared: duct tape and a placebo. By varying this variable, researchers aim to explore its potential influence on the outcome, which is the disappearance of warts.
Statistical Significance
Statistical significance is a concept used to determine if the results of an experiment are due to the effect of the explanatory variable, or if they might have happened by chance. When we say a result is "not statistically significant," it signals that the observed difference between groups could just as likely be a result of random variation as it could be due to the actual treatments.
The study found a 10% difference in wart disappearance rates between the duct tape (16%) and placebo (6%) groups. However, this difference wasn't deemed statistically significant, meaning the results don't provide strong evidence that duct tape is indeed more effective than the placebo.
Treatments
In any experiment, treatments refer to the specific conditions applied to experimental units. In this particular case, treatments involve the use of duct tape and placebo on patients. Each group received a different treatment, one with actual duct tape and the other with a placebo (a ring covered by tape, with warts left clear).
Understanding which treatment gets applied allows researchers to compare their impacts. Doing so helps investigate whether there is a difference in outcomes (warts disappearing) between the two treatments and how they perform in promoting wart removal.

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