# Exercise: Estimation, standard error and confidence intervals

## Preterm births

A UK study of factors affecting the outcome of pregnancy among 1513 women reported that the overall incidence of preterm births was 7.5%, SE=0.68%, 95% CI 6.1 to 8.8% (Peacock et al., 1995).

1. What is meant by SE=0.68%? What kind of diagram is this?

2. What is meant by 95% CI 6.1 to 8.8%?

3. How would the confidence interval change if 90% limits were used?

4. How would the confidence interval change if 99% limits were used?

Another study conducted at about the same time in Denmark and including 51851 women, reported that the overall incidence of preterm birth was 4.5% (95% CI 4.3 to 4.7%).

1. Explain why this 95% confidence interval is narrower than that reported in the UK study. Do you think that there is a real difference in preterm birth rates between the two populations being studied?

## Exercise, bone density and falls

In a study of bone density and falls in older women, 118 volunteers were randomized to receive either calcium supplements plus a program of exercise classes or to calcium alone for two years. Twelve subjects dropped out from the calcium group and 14 from the calcium group taking exercise, leaving 92 subjects who completed the two year project. The percentage change in bone mineral content and bone mineral density in two years was calculated for each individual. The authors reported that for the ultradistal forearm the change in bone mineral content was –2.6 (95% confidence interval –4.6 to –0.6) in the calcium only group and 1.14 (95% confidence interval –0.8 to 3.1) in the calcium group taking exercise (McMurdo et al., 1997).

### Questions about exercise, bone density and fallsn

1. What do the confidence intervals for the change in bone mineral content mean? To what population do they refer?

2. Confidence intervals are presented for each group separately. Suggest a more informative confidence interval. To which population would this relate?