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"Doctors Praise Device That Aids Ailing Hearts" (Associated Press, November 9,2004 ) is the headline of an article describing a study of the effectiveness of a fabric device that acts like a support stocking for a weak or damaged heart. People who consented to treatment were assigned at random to either a standard treatment consisting of drugs or the experimental treatment that consisted of drugs plus surgery to install the stocking. After two years, \(38 \%\) of the 57 patients receiving the stocking had improved, and \(27 \%\) of the 50 patients receiving the standard treatment had improved. The researchers used these data to determine if there was evidence to support the claim that the proportion of patients who improve is higher for the experimental treatment than for the standard treatment.

Step by step solution

01

Identify the proportions

First identify the proportions of patients who improved in each group. For the experimental treatment group, 38% of 57 patients improved, which is approximately 0.38 × 57 = 21.66, which simplifies to about 22 patients. For the standard treatment group, 27% of 50 patients improved, which is approximately 0.27 × 50 = 13.5, which simplifies to about 14 patients.

02

Calculate the difference between proportions

Next, calculate the difference between the two proportions. Subtract the proportion of patients who improved with standard treatment from the proportion who improved with the experimental treatment. The difference is 0.38 - 0.27 = 0.11 or 11%.

03

Interpret the result

The difference in proportions indicates the relative effectiveness of the treatments. A positive difference of 11% suggests that the experimental treatment (device plus drugs) is more effective than the standard treatment (only drugs). An increase of 11% in the improvement rate implies that approximately 11 more patients out of every 100 patients would improve with the experimental treatment compared to the standard one. However, this alone doesn't provide evidence of statistical significance. Further analysis using confidence intervals or hypothesis testing should be performed to reach a statistically valid conclusion.

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Key Concepts

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

Experimental Design

Experimental design is a critical component of any scientific study, ensuring that the findings are reliable and valid. In the context of this heart support stocking study, an experimental design was used to compare two groups of patients. Each group was assigned randomly to either the standard treatment (drugs alone) or the experimental treatment (drugs plus the heart stocking device). This random assignment is crucial.

• Random assignment helps eliminate biases that might occur if patients are consciously selected for specific treatments.
• By controlling for variables, researchers can more confidently determine whether the differences in patient outcomes are due to the treatment itself and not some other factor.

This article discusses the setup of an experiment where one group received the standard treatment and the other received an additional surgical procedure. Such designs help in judging new interventions accurately, allowing researchers to make informed claims regarding their effectiveness.

Confidence Intervals

Confidence intervals are statistical tools that help us determine the precision of an estimate. They provide a range of values that likely includes the true population parameter. In this case, the researchers would calculate the confidence interval for the difference in improvement rates between the two treatment groups.

• A 95% confidence interval, for example, would suggest that if the same experiment were conducted 100 times, the calculated range would contain the true difference in improvement rates in 95 of those experiments.
• This interval gives researchers an idea of how much the improvement might actually vary in the wider population. It helps establish whether the observed difference (11% in this case) is statistically significant or might have occurred by random chance.

Using confidence intervals, we can quantify the uncertainty around our sample estimate and assess its reliability, aiding in robust decision-making regarding treatment efficacy.

Proportion Comparison

Proportion comparison is the backbone of this study, as it evaluates the effectiveness of two treatment methods. By comparing proportions, researchers can determine if one treatment is superior to the other based on the observed improvement rates among patients.

• In this study, 38% of patients in the experimental group improved, compared to 27% in the standard treatment group.
• This results in a difference of 11% in favor of the experimental treatment.

To further substantiate this finding, statistical hypothesis testing or confidence intervals are employed. They help ascertain whether this 11% difference is likely due to the experimental treatment itself, or it might be a result of random variation. Through the process of statistical testing and analysis, researchers can make evidence-based conclusions about treatment effectiveness.