Question

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?

Short answer

The estimated difference in the proportions of cardiologists and internists who were unaware of the effects of carbohydrates on triglycerides, can be computed using the formula described in step-3. Potential bias might include non-response bias due to the low response rate and the fact that the set of physicians were not randomly selected from the total population of physicians.

Step-by-step solution

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 \(222/419 = 0.5298\).

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.

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.

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.