The assessment of diet is an important exposure for many disease outcomes. However, there is often much imprecision in dietary recall. In one study, 70-to 79-year-old women were asked about the preschool diet of their children (ages 2−4) using a food frequency questionnaire (FFQ). A unique aspect of the study is that simultaneous diet record data exist on the same children recorded in real time by their mothers when they were ages 2−4 and their mothers were 20 to 40 years old. The data in Table 11.36 were available on average servings of margarine per week. ID FFQ DR 340 7 0 399 7 0.5 466 0 0 502 0 0 541 0 0 554 7 2.5 558 7 3 605 7 0.5 611 21 3.7 618 0 2.5 653 21 4.1 707 7 8.5 The Pearson correlation between intake from the two re-cording methods was 0.448. Assume that FFQ and DR margarine intake are normally distributed.
The assessment of diet is an important exposure for many disease outcomes. However, there is often much imprecision in dietary recall. In one study, 70-to 79-year-old women were asked about the preschool diet of their children (ages 2−4) using a food frequency questionnaire (FFQ). A unique aspect of the study is that simultaneous diet record data exist on the same children recorded in real time by their mothers when they were ages 2−4 and their mothers were 20 to 40 years old. The data in Table 11.36 were available on average servings of margarine per week.
| ID | FFQ | DR |
| 340 | 7 | 0 |
| 399 | 7 | 0.5 |
| 466 | 0 | 0 |
| 502 | 0 | 0 |
| 541 | 0 | 0 |
| 554 | 7 | 2.5 |
| 558 | 7 | 3 |
| 605 | 7 | 0.5 |
| 611 | 21 | 3.7 |
| 618 | 0 | 2.5 |
| 653 | 21 | 4.1 |
| 707 | 7 | 8.5 |
The Pearson
Question: Provide a 95% confidence interval for ρ.
#95% CI for z
r <- 0.448
#Fisher's transformation of r
z <- 0.5*log((1+r)/(1-r)); z
z + c(-1,1)*qnorm(0.975)*sqrt(1/(n-3))
95% CI for z = (-0.1711261, 1.1355166)
#95% CI for ρ
rlower <- (exp(2*-0.1711261)-1)/(exp(2*-0.1711261)+1); rlower
rupper <- (exp(2*1.1355166)-1)/(exp(2*1.1355166)+1); rupper
My answer: 95% CI = (-0.169475, 0.8128989)
Is my answer correct?
The dataset is given as:
| 340 | 7 | 0 |
| 399 | 7 | 0.5 |
| 466 | 0 | 0 |
| 502 | 0 | 0 |
| 541 | 0 | 0 |
| 554 | 7 | 2.5 |
| 558 | 7 | 3 |
| 605 | 7 | 0.5 |
| 611 | 21 | 3.7 |
| 618 | 0 | 2.5 |
| 653 | 21 | 4.1 |
| 707 | 7 | 8.5 |
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I thought CI around Pearson's r is not symmetrical and we would need to transform it to z, calculate the CI then undo Fisher's transformation to obtain the population
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