## Understanding confidence intervals helps you make better clinical decisions

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By: Zhaomin He, PhD, and Ellen Fineout-Overholt, PhD, RN, FNAP, FAAN

PERHAPS YOU DIDNâ€™T LEARNÂ about the confidence intervalÂ (CI) in your formal educationÂ or you donâ€™tÂ hear the term inÂ daily conversation.Â ConfidenceÂ intervalÂ just doesnâ€™t rollÂ of the tongue of a staffÂ nurse quite like blood pressureÂ or urine output does.

But knowing the importance of the CIÂ allows you to interpret research for its impactÂ on your practice. Evidence-based decision making isÂ central to healthcare transformation. To make goodÂ decisions, you must know how to interpret and useÂ research and practice evidence. Evaluating researchÂ means determining its validity (were the researchersâ€™Â methods good ones?) and reliability (can cliniciansÂ get the same results the researchers got?).

# CI and the degree of uncertainty

In a nutshell, the CI expresses the degree of uncertaintyÂ associated with a sample statistic (also called aÂ study estimate). The CI allows clinicians to determineÂ if they can realistically expect results similar to thoseÂ in research studies when they implement those studyÂ results in their practice. Specifically, the CI helps cliniciansÂ identify a range within which they can expectÂ their results to fall most of the time.

Used in quantitative research, the CI is part of theÂ stories that studies tell in numbers. These numericÂ stories describe the characteristics, or parameters, ofÂ a population; populations can be made up of individuals,Â communities, or systems. Collecting informationÂ from the whole population to find answers to clinicalÂ questions is practically impossible. For instance, weÂ canâ€™t possiblyÂ collect informationÂ from all cancerÂ patients. Instead, we collectÂ information from smaller groups within the largerÂ population, called samples. We learn about populationÂ characteristics from these samples through aÂ process called inference.

To differentiate sample values from those of theÂ population (parameters), the numeric characteristicsÂ of a sample most commonly are termed statistics, butÂ also may be called parameter estimates becauseÂ theyâ€™re estimates of the population. Inferring informationÂ from sample statistics to population parametersÂ can lead to errors, mainly because statistics may differÂ from one sample to the next. Several other termsÂ are related to this opportunity for errorâ€”probability,Â standard error (SE), and mean. (See What are probability,Â standard error, and mean?)

# Calculating the CI

Used in the formula to calculate the upper and lowerÂ boundaries of the CI (within which the population parameter is expected to fall), the SE reveals howÂ accurately the sample statistics reflect populationÂ parameters. Choosing a more stringent probability,Â such as 0.01 (meaning a CI of 99%), would offerÂ more confidence that the lower and upper boundariesÂ of the CI contain the true value of the populationÂ parameter.

Not all studies provide CIs. For example, when weÂ prepared this article, our literature search found studyÂ after study with a probability (p) value) but no CI.Â However, studies usually report SEs and means. If theÂ study youâ€™re reading doesnâ€™t provide a CI, hereâ€™s theÂ formula for calculating it:

95% CI: X= Xâ€ľÂ Â± (1.96 x SE),Â where X denotes the estimate and Xâ€ľÂ denotes the mean of the sample.

To find the upper boundary of the estimate, add 1.96 times the SE to Xâ€ľ. To find the lower boundary of the estimate, subtract 1.96 times the SE fromXâ€ľ. Note: 1.96 is how many standard deviations from the mean are required for the range of values to contain 95% of the values.

Be aware that values found with this formula arenâ€™t reliable with samples of less than 30. But donâ€™t despair; you can still calculate the CIâ€” although explaining that formula is beyond the scope of this article. Watch the video at https://goo.gl/AuQ7Re to learn about that formula.

# Real-world decision-making: Where CIs really count

Now letâ€™s apply your new statistical knowledge to clinical decision making. In everyday terms, a CI is the range of values around a sample statistic within which clinicians can expect to get results if they repeat the study protocol or intervention, including measuring the same outcomes the same ways. As you critically appraise the reliability of research (â€śWill I get the same results if I use this research?â€ť), you must address the precision of study findings, which is determined by the CI. If the CI around the sample statistic is narrow, study findings are considered precise and you can be confident youâ€™ll get close to the sample statistic if you implement the research in your practice. Also, if the CI does not contain the statistical value that indicates no effect (such as 0 for effect size or 1 for relative risk and odds ratio), the sample statistic has met the criteria to be statistically significant.

The following example can help make the CI concept come alive. In a systematic review synthesizing studies of the effect of tai chi exercise on sleep quality, Du and colleagues (2015) found tai chi affected sleep quality in older people as measured by the Pittsburgh Sleep Quality Index (mean difference of -0.87; 95% CI [-1.25, -0.49]). Hereâ€™s how clinicians caring for older adults in the community would interpret these results: Across the studies reviewed, older people reported better sleep if they engaged in tai chi exercise. The lower boundary of the CI is -1.25, the study statistic is -0.87, and the upper boundary is -0.49. Each limit is 0.38 from the sample statistic, which is a relatively narrow CI. Keep in mind that a mean difference of 0 indicates thereâ€™s no difference; this CI doesnâ€™t contain that value. Therefore, the sample statistic is statistically significant and unlikely to occur by chance. Because this was a systematic review and tai chi exercise has been established as helping people sleep, based on the sample statistics and the CI, clinicians can confidently include tai chi exercises among possible recommendations for patients who have difficulty sleeping.

Now you can apply your knowledge of CIs to make wise decisions about whether to base your patient care on a particular research finding. Just rememberâ€”when appraising research, consistently look for the CI. If the authors report the mean and SE but donâ€™t report the CI, you can calculate the CI using the formula discussed earlier.

The authors work at the University of Texas at Tyler. Zhaomin He is an assistant professor and bioÂ­statistician of nursing. Ellen Fineout-Overholt is the Mary Coulter Dowdy Distinguished Professor of Nursing.

Selected references

Du S, Dong J, Zhang H, et al. Taichi exerciseÂ for self-rated sleep quality in older people:Â a systematic review and meta-analysis.Â Int J Nurs Stud. 2015;52(1):368-79.

Fineout-Overholt E. EBP, QI, and research:Â strange bedfellows or kindred spirits? In:Â Hedges C, Williams B, eds. Anatomy of ResearchÂ for Nurses. Indianapolis, IN: SigmaÂ Theta Tau International; 2014:23-44.

Fineout-Overholt E, Melnyk BM, Stillwell SB,Â Williamson KM. Evidence-based practice,Â step by step: critical appraisal of the evidence:Â part II: digging deeperâ€”examiningÂ the â€śkeeperâ€ť studies.Â Am J Nurs. 2010;110(9):Â 41-8.

Kahn Academy. Small sample size confidenceÂ intervals

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Melnyk BM, Fineout-Overholt E. ARCC (AdvancingÂ Research and Clinical practiceÂ through close Collaboration): a model forÂ system-wide implementation and sustainabilityÂ of evidence-based practice. In: Rycroft-Malone J, Bucknall T, eds. Models andÂ Frameworks for Implementing Evidence-Based Practice: Linking Evidence to Action.Â Indianapolis, IN: Wiley-Blackwell & SigmaÂ Theta Tau International; 2010.

Oâ€™MathĂşna DP, Fineout-Overholt E. CriticallyÂ appraising quantitative evidence for clinicalÂ decision making. In: Melnyk BM, Fineout-Overholt E, eds. Evidence-Based Practice inÂ Nursing and Healthcare: A Guide to BestÂ Practice. 3rd ed. Philadelphia: LippincottÂ Williams and Wilkins; 2015:81-134.

Plichta, SB, Kelvin E. Munroâ€™s StatisticalÂ Methods for Health Care Research. 6th ed.Â Philadelphia, PA: Lippincott, Williams &Â Wilkins; 2013.