Question 2: What do they mean by '95% confidence interval 0.45 to 0.99' and 'P=0.04'? Are these two things consistent?
We are using the babies in this trial as a sample to estimate the relative risk in the larger population of babies. A 95% confidence interval is a range of values which we estimate will contain the relative risk in the larger population from which these babies come. It is calculated in such a way that the confidence intervals calculated from 95% of possible samples will include the relative risk in the population. We estimate that the relative risk in the population will be between 0.45 and 0.99.
'P = 0.04' is the result of a significance test. They are testing the null hypothesis that the relative risk in the population is equal to 1.0, against the alternative hypothesis that the relative risk in the population is not equal to 1.0. P is the probability of getting a sample relative risk as far from 1.0 as the one observed, if the null hypothesis were true. P = 0.04, so a relative risk as extreme as this would occur in only 4 out of 100 samples. The data are not consistent with the null hypothesis and we have evidence that the relative risk in the population is not 1.0. The difference is significant.
As the confidence interval for the relative risk is 0.45 to 0.99, it does not include 1.0 and the data are inconsistent with a relative risk = 1.0 in the population. This is the same conclusion as we would draw from the significance test, so the two calculations are consistent.
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