91Ó°ÊÓ

In a study of whether taking a garlic supplement reduces the risk of getting a cold, 146 participants were randomly assigned to either a garlic supplement group or to a group that did not take a garlic supplement ("Garlic for the Common Cold," Cochrane Database of Systematic Reviews, 2009). Based on the study, it was concluded that the proportion of people taking a garlic supplement who get a cold is lower than the proportion of those not taking a garlic supplement who get a cold. a. What claim about the effect of taking garlic is supported by the data from this study? b. Is it possible that the conclusion that the proportion of people taking garlic who get a cold is lower than the proportion for those not taking garlic is incorrect? Explain. c. If the number of people participating in the study had been \(50,\) do you think that the chance of an incorrect conclusion would be greater than, about the same as, or lower than for the study described?

Step by step solution

01

a. Identify the claim supported by the study.

The claim supported by the data from this study is that the proportion of people taking a garlic supplement who get a cold is lower than the proportion of those not taking a garlic supplement who get a cold.

02

b. Possible incorrect conclusion

Yes, it is possible that the conclusion that the proportion of people taking garlic who get a cold is lower than the proportion for those not taking garlic is incorrect. The study contains a sample of participants, and it is always possible that the result is due to sampling error or some other confounding factors. To minimize the chance of an incorrect conclusion, the study should be repeated with different random samples, and the results should be compared to see if the observed effect persists.

03

c. Comparing probability of incorrect conclusion with fewer participants

If the number of people participating in the study had been 50, the chance of an incorrect conclusion would be greater. This is because the smaller the sample size, the greater the impact of sampling error and other potential confounding factors on the results. A larger sample size typically provides more accurate and consistent results, as it becomes more reflective of the overall population.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

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

Random Assignment

Random assignment is a crucial element in the design of an experiment, especially when determining cause-and-effect relationships as in this garlic study. It ensures that each participant has an equal chance of being placed into either group: those taking the garlic supplement or those not taking it. This kind of assignment helps balance out unknown variations between participants. Therefore, differences in outcomes can be more confidently traced back to the garlic supplement itself rather than other factors.
Using random assignment adds credibility and reliability to a study's findings. It helps to mitigate bias by preventing researchers from unconsciously assigning healthier participants to a particular group. This randomness is essential in supporting the claims of reduced cold occurrence among garlic supplement users since any observed effect is less likely due to differences in group composition.

Sample Size

The sample size in an experiment significantly affects the potential accuracy of its conclusions. In this case, the study involved 146 participants. A larger sample size, such as this one, generally enhances the reliability of the results. This is because larger samples are better at approximating the true characteristics of the entire population.
With more participants, the impact of an outlier or an unusual result is minimized, providing a more stable base for analysis.
If the study had instead only included 50 participants, the conclusions would be less reliable. This is because smaller samples can lead to greater variability in results, thereby increasing the risk of reaching an incorrect conclusion. It’s generally more challenging to confidently generalize findings from smaller groups, which increases uncertainty in predicting similar outcomes in larger populations.

Sampling Error

Sampling error refers to the difference between the results obtained from a sample and the true characteristics of the population. Even with perfectly random selection, this error can occur because a sample represents only a subset of the entire population.
In the garlic study, sampling error might lead to an incorrect conclusion about the garlic supplement's effectiveness if the sample selected by chance does not accurately reflect the broader population.
This type of error is usually unavoidable, but its effect can be minimized by using a larger sample size. Larger samples tend to provide a more precise estimate of the population characteristics, thereby reducing sampling error and enhancing the trustworthiness of the study's findings.

Confounding Factors

Confounding factors are variables that may affect the outcome of an experiment without being accounted for, potentially skewing the results. These are outside influences that upset the causal relationship the study is investigating.
In this study on garlic and colds, confounding factors might include participants' overall health, diet, or stress levels, which could also influence cold incidence. If these variables are unevenly distributed between groups, they might falsely suggest that the garlic supplement is more or less effective than it truly is.
Recognizing and controlling for confounding factors is vital. Researchers can use various statistical techniques or design adjustments to mitigate their influence, helping ensure the observed outcomes more accurately reflect a direct effect of the garlic supplement on cold frequency.