
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. 


