Hello, I have a question on questions c and d shown in the picture attached. Can

Question

Hello,

I have a question on questions c and d shown in the picture attached. Can you please help me with these problems? How do we solve this using the properties of Simpson's paradox?

Thanks for your help! I have attached a picture of the problem and the text (see typed below) about Simpson's paradox.

Simpson‘s paradox—heart disease patients Today we are going to look at common numerical arguments often used in newspapers and in television. Often when newspapers and other media provide statistics, we do not know how data was gathered, or the different ways data was manipulated before being presented to us. This lesson will look at how, on the surface, the numbers may tell us one thing; but as we dig deeper, the numbers may tell us something entirely different. The following example is a generalized case of what happened several years ago in the United States. A large drug manufacturer presented information from their study suggests that their drug reduced the number of heart attacks in patients with heart disease. Patients were randomly selected from several hospitals and administered the new drug. The rest of the patients continued to receive normal heart care. The table shows the results. From the table, we can calculate the proportion of patients that had heart attacks from both the normal and the new drug treatments.

The news media started talking about the new wonder drug and berating the medical community for not supplying this drug to all of its heart patients, since the new treatment was about the same price as the normal treatment. The medical community held a press conference to respond. They produced the following tables Low Blood Pressure High Blood Pressure Normal New Drug Normal New Drug Dear Aback Heart Attack No Heart Attack see Tata Tea Tse me in Anace and so I Total Tseases 420 Pooled Results Normal New Drug Heart Attack 20 TOD No Heart Attack Me the res Total Tsao Tas Page 104 C. Calculate the proportions of heart attacks for both the low and high blood pressures for the treatments d, Do you still agree with your choice when we only had the pooled results? Make sure to support your answer,

Explanation / Answer

c) Proportion of heart attack for low blood pressure with normal drug = 220 / 4200 = 0.052

  Proportion of heart attack for low blood pressure with new drug = 30 / 530 = 0.057

Thus , the difference in normal drug and new drug is of 0.004 . So if we give normal care to patients rather than giving new drug is appropriate too .

Proportion of heart attack for high blood pressure with normal drug = 700 / 5600 = 0.125

  Proportion of heart attack for high blood pressure with new drug = 40 / 265 = 0.151

Thus , the difference in normal drug and new drug is of 0.026 . So if we give normal care to patients rather than giving new drug is appropriate too .

d)

Proportion of heart attack for normal drug = 920 / 9800 = 0.094

  Proportion of heart attack for new drug = 70 / 835 = 0.084

Thus , the difference in normal drug and new drug is of 0.010 . So if we give normal care to patients rather than giving new drug is appropriate too .

So the pooled data also gives the same information that heart attacks proportion is almost same for new drug and normal drug .

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