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The authors of the paper "Inadequate Physician Knowledge of the Effects of Diet on Blood Lipids and Lipoproteins" (Nutrition Journal [2003]: 19-26) summarize the responses to a questionnaire on basic knowledge of nutrition that was mailed to 6000 physicians selected at random from a list of physicians licensed in the United States. Sixteen percent of those who received the questionnaire completed and returned it. The authors report that 26 of 120 cardiologists and 222 of 419 internists did not know that carbohydrate was the diet component most likely to raise triglycerides. a. Estimate the difference between the proportion of cardiologists and the proportion of internists who did not know that carbohydrate was the diet component most likely to raise triglycerides using a \(95 \%\) confidence interval. b. What potential source of bias might limit your ability to generalize the estimate from Part (a) to the populations of all cardiologists and all internists?

Step by step solution

01

Calculate the proportions

The proportion of cardiologists who didn't know is \(26/120 = 0.2167\) and the proportion of internists who didn't know is \(222/419 = 0.5298\).

02

Calculate the estimate of the standard error

The standard error is calculated as \(\sqrt{[(\hat{p1} (1-\hat{p1}))/n1] + [(\hat{p2} (1-\hat{p2}))/n2]}\), in this case \(\hat{p1}\) and \(\hat{p2}\) are the proportions of cardiologists and internists who didn't know respectively and \(n1\) and \(n2\) are the total number of cardiologists and internists respectively who took the survey.

03

Calculate the 95% confidence interval

The 95% confidence interval is calculated as \(\hat{p1} - \hat{p2} \pm Z * SE\) where \(Z\) is the z-value from the standard normal distribution corresponding to a 95% confidence level which is 1.96. The confidence interval thus obtained will estimate the difference in proportions between the two groups of doctors.

04

Identify potential bias

The potential source of bias could be the fact that the questionnaire was sent to selected physicians, meaning it may not represent all cardiologists and internists. The response rate of only 16% might mean the responses may not be representative of all physicians. Another bias could be because the questionnaire was mailed, which might introduce a non-response bias, if physicians who do not know the effect of diet on blood lipids were more likely to ignore the questionnaire.

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Key Concepts

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

Confidence Interval

A confidence interval provides a range of values within which we are confident that the true value lies. In medical research, understanding this concept helps to generalize findings from sample data to a broader population. Here, we are estimating the difference between two proportions with a 95% confidence level. This tells us that, 95% of the time, the true difference is likely within the calculated interval. To construct this interval, we calculate the difference between the two sample proportions and add and subtract the margin of error. The margin of error is derived using the standard error and the z-score associated with our confidence level, which is 1.96 for 95%. This ensures that even with unavoidable randomness, our interval estimation remains robust and reliable.

Proportion Calculation

Proportion calculation is crucial in assessing how often a particular event occurs within a study group. In our exercise, we want to determine the proportion of doctors unaware of the specific dietary fact. For cardiologists, it is calculated as the number of those who were unaware divided by the total surveyed cardiologists: \( \frac{26}{120} = 0.2167 \). Similarly, for internists, the proportion is \( \frac{222}{419} = 0.5298 \). These proportions provide a snapshot of each group’s knowledge level and serve as the basis for comparing the two groups. Being able to calculate and interpret these proportions is fundamental in research to draw meaningful conclusions about different study populations.

Bias in Survey Research

Bias in survey research can significantly skew results, limiting the conclusions we can draw. In this exercise, several forms of potential bias could affect our findings. The response bias is a major consideration, given that only 16% of those contacted responded, which might not reflect the views of the broader physician population. Furthermore, selection bias could occur since the sample may not represent the entire profession accurately. Lastly, non-response bias might exist if those uninterested in diet effects on blood lipids were less likely to respond, potentially skewing results. Being aware of these biases is essential in critically evaluating survey-based research and ensuring findings are as representative as possible.