### Confidence limits and confidence intervals (error bars)

Confidence limits provide a range of values estimated from a study group that is highly likely to include the true, but unknown, value (“confidence limit” applies to the results of a statistical analysis). They are usually displayed as error bars on a graph.

A 95% confidence limit means that there is only a 5% chance that the true value is NOT included within the span of the error bar. This is a way of visualizing uncertainty in summary points plotted in a graph.

The length of the error bar expresses the amount of uncertainty. If the number of cases is small, the error bar will be long, reflecting the fact that the results based on a small number of cases are more uncertain and might not be applicable to the full population. For example, 1 occurrence out of a sample of 100 and 100 occurrences out of a sample of 10,000 both produce a frequency of 0.01, but the confidence interval is much wider with the former. This may be simply understood as follows: if we repeated the study, in a sample of 100 we might observe 0 or 2 occurrences (frequency of 0.00 or 0.02), but with a sample of 10,000 it would be very unlikely to see 0 or 200 occurrences; it would be more likely to see 99 or 101 occurrences (frequency of 0.0099 or 0.0101). The likely error in the frequency is much smaller with the larger sample size.