Social Research Glossary   A B   Citation reference: Harvey, L., 2012-20, Social Research Glossary, Quality Research International, http://www.qualityresearchinternational.com/socialresearch/ This is a dynamic glossary and the author would welcome any e-mail suggestions for additions or amendments. Page updated 19 December, 2019 , © Lee Harvey 2012–2020. A fast-paced novel of conjecture and surprises

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Confidence interval

core definition

A confidence interval (or confidence limits) refers to a range of values within which a particular population parameter (e.g. mean, standard deviation, etc.) has a specified probability of lying, as estimated from sample data.

explanatory context

Confidence intervals are determined from statistical sampling theory; see significance testing.

For example, using the characteristics of the normal distribution we can say with 95% level of confidence that any population value lies within the range of approx. 2 standard erorrs in either direction from our sample estimate.

analytical review

Easton and McColl (undated) in Statistics Glossary state:

Confidence Interval: A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data. If independent samples are taken repeatedly from the same population, and a confidence interval calculated for each sample, then a certain percentage (confidence level) of the intervals will include the unknown population parameter. Confidence intervals are usually calculated so that this percentage is 95%, but we can produce 90%, 99%, 99.9% (or whatever) confidence intervals for the unknown parameter.

The width of the confidence interval gives us some idea about how uncertain we are about the unknown parameter (see precision). A very wide interval may indicate that more data should be collected before anything very definite can be said about the parameter.

Confidence intervals are more informative than the simple results of hypothesis tests (where we decide "reject H0" or "don't reject H0") since they provide a range of plausible values for the unknown parameter.

Confidence Limits: Confidence limits are the lower and upper boundaries / values of a confidence interval, that is, the values which define the range of a confidence interval.

The upper and lower bounds of a 95% confidence interval are the 95% confidence limits. These limits may be taken for other confidence levels, for example, 90%, 99%, 99.9%.

The NHS Health News Glossary, (NHS, undated) states:

A confidence interval (CI) expresses the precision of an estimate and is often presented alongside the results of a study (usually the 95% confidence interval). The CI shows the range within which we're confident that the true result from a population will lie 95% of the time. The narrower the interval, the more precise the estimate. There's bound to be some uncertainty in estimates because studies are conducted on samples and not entire populations.

By convention, 95% certainty is considered high enough for researchers to draw conclusions that can be generalised from samples to populations. If we're comparing 2 groups using relative measures, such as relative risks or odds ratios, and see that the 95% CI includes the value of one in its range, we can say there's no difference between the groups.

This confidence interval tells us that, at least some of the time, the ratio of effects between the groups is one. Similarly, if an absolute measure of effect, such as a difference in means between groups, has a 95% CI that includes 0 in its range, we can conclude there's no difference between the groups.

associated issues

related areas

significance test

Sources

Easton, V.J. and McColl, J.H. (undated) 'Confidence intervals' in Statistics Glossary available at http://www.stats.gla.ac.uk/steps/glossary/confidence_intervals.html, accessed 2 February 2013, still available 1 June 2019.

NHS, undated, Health News Glossary, available at https://www.nhs.uk/news/health-news-glossary/, accessed 1 June 2019.