⟩ There is substantial overlap between two sets of confidence intervals on an error bar chart. The chart shows confidence intervals for boys and girls on a depression questionnaire. What could we make of this?
1. We can be 95% confident that the population means are within the intervals indicated on the chart. As there is much overlap between the two sets of confidence intervals we cannot be sure whether there is a difference in the population means. It seems likely that there is no difference but we cannot draw any firm conclusions.
2. We can be 95% confident that the population means are within the intervals indicated on the chart. As there is much overlap between the two sets of confidence intervals this would suggest that there is a real difference in the population means.
3. It would appear that 95% of girls are more depressed than boys according to the confidence intervals.
4. We can be 5% confident that the population means are within the intervals indicated on the chart. As there is much overlap between the two sets of confidence intervals we can be sure that there is a real difference in the population means.
Answer: We can be 95% confident that the population means are within the intervals indicated on the chart. As there is much overlap between the two sets of confidence intervals we cannot be sure whether there is a difference in the population means. It seems likely that there is no difference but we cannot draw any firm conclusions.
