The interval has an upper bound and a lower bound (i.e. confidence limits).

Example We have gathered data on all sociology students at Stockholm University and find that their mean age is 26 years. Instead of highlighting this relatively non-informative fact, we can calculate the confidence interval (at the 95% level). In this case, it is 25-27. Therefore, we could make the more informative statement that: “with 95% confidence, we conclude that the mean age of sociology students is 25 to 27 years”.

Similar to p-values, confidence intervals have “confidence levels” that indicate how certain we can be that the interval includes the true population parameter.

As can also be noted in the example, confidence intervals are typically stated at the 95% level.

A 95% confidence level would thus mean that if we replicated a certain analysis in 100 samples of the population, we would expect that 95% of the intervals would include the true population parameter.

Note Strictly speaking, it is not correct to say that “with 95% probability, the true population parameter lies within this interval” (because the parameter either is or is not within the interval).

The most common application for confidence intervals as a way of significance testing is when we are interested in the difference between two samples.

Example Suppose that we have an upcoming election and just got the results from the latest poll. There are two parties in the race: the green party and the yellow party. The results from the poll show that the green party got 42% of the votes and the confidence interval is 40-44 (at the 95 % level). The yellow party got 58% of the votes and the confidence interval is 54-62 (at the 95% level). What does this tell us? First of all, we can conclude that the yellow party has a greater share of votes. Looking at the two confidence intervals, we see that the intervals do not overlap. Why is that important? Well, remember that all values in a confidence interval are plausible. Hence, if the confidence intervals do not overlap, it means that the estimates (in this case: the share of votes) are indeed different given the chosen confidence level (in this case: at the 95% level). However, it should be emphasized that while non-overlap always mirrors a significant difference, overlap is not always the same as a non-significant difference.