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What Does a 95% Confidence Interval Really Mean?
News from National: A report from the February 2025 Chapter Advisory Council meeting
Announcements
Join us for our first social event of the year on March 29th from 5-7 pm at Bolé Ethiopian Cuisine in Saint Paul (1341 Pascal Street North, Saint Paul 55108)! Come expand your professional network; strengthen the medical writing community; and enjoy delicious, delicious food while swapping favorite obscure guidelines from the AMA Manual of Style. If you haven’t already, please RSVP to Angie Herron (angelayherron@gmail.com) no later than March 22nd.
To all Chapter members, we welcome your upcoming contributions. If you are interested in writing for the newsletter, please contact Dora Miedaner (dora.miedaner@gmail.com). Submissions are due at the beginning of the last week of each month and may require a round of editorial revision before being published.
The AMWA North-Central Chapter is always welcoming volunteers. We have a variety of roles that you can take on individually or team up with another AMWA member. If you are not sure a particular role is the right fit, you can “try it out” for a period of time while being paired up with a senior member in the role of your interest. If you would like to join us or have any questions regarding open roles, please reach out to bod@amwanorthcentral.org.
Adam Fix, PhD
A confidence interval (CI) is a key output of biostatistics. However, the information a CI provides is sometimes misinterpreted. This article reviews the definition of a CI, unpacks this common misinterpretation, and discusses how properly interpreting a CI can help medical writers accurately communicate about biostatistics.
Definition
A CI is a range of possible values for a population parameter (e.g., blood pressure reduction from baseline during a clinical trial) that is likely to contain the true value of that parameter. The confidence level of a CI is conventionally set at 95%, meaning that we are 95% confident the true parameter lies within that CI. Other confidence levels such as 90% or 99% are sometimes used.
Formula
A CI is calculated as:
CI = m ± z⋅SEM
where m is the sample mean, SEM is the standard error of the mean, and z is the z-score. While m and SEM are calculated from the sample data, z is normally looked up from a z-score table. For a 95% CI, z = 1.96.
Example
Suppose we conduct a randomized controlled trial investigating the efficacy of a new blood pressure medication. At 12 weeks, mean blood pressure reduction from baseline in the treatment group was 5.2 mmHg, while the control group showed no reduction. Suppose SEM = 1.1. Our 95% CI is:
CI = 5.2 ± 1.96⋅1.1
or,
CI = 5.2 ± 2.2
or,
CI = [3.0, 7.4].
Misinterpretation
A 95% CI is often interpreted as the range in which the true parameter must lie with 95% probability. However, this is not quite accurate. A CI is a fixed interval that either does or does not contain the true parameter; there’s no probability involved.1,2
Consider our example. Suppose repeated trials consistently find no significant reduction in blood pressure resulting from the medication. With this new information, we suspect that the true parameter is 0 or close to 0. In that case, it would not be accurate to write that the true parameter has a 95% probability of lying within [3.0, 7.4], even though this interval is technically a 95% CI. We begin to suspect that our CI is a statistical outlier that does not contain the true parameter.
Proper interpretation
What does the “95% probability” associated with a CI actually mean? To answer this, we must view a CI in the context of repeated sampling. We must consider all possible CIs that would be calculated if the trial were repeated many times. As a BMJ publication explains (emphasis mine):
Imagine taking repeated samples of the same size from the same population. For each sample calculate a 95% confidence interval. Since the samples are different, so are the confidence intervals. We know that 95% of these intervals will include the population parameter. However, without any additional information we cannot say which ones! Thus with only one sample, and no other information about the population parameter, we can say there is a 95% chance of including the parameter in our interval.3
That is, 95% of all possible 95% CIs contain the true parameter. All else being equal, any individual 95% CI has a 95% probability of being one of those CIs containing the true parameter. Crucially, this is true only if no information suggests otherwise. If additional information on the true parameter arises, we must be cautious in interpreting that CI.
Imagine that all possible 95% CIs are in a drawstring bag. You reach in and grab one at random. There is a 95% chance of grabbing a CI containing the true parameter. Therefore, you are 95% confident that the true parameter lies within that CI because the act of grabbing it was perfectly random. However, this does not preclude us from reevaluating this assumption later.
Consider our example. We were initially 95% confident that our CI of [3.0, 7.4] was one of the many possible CIs containing the true parameter, because we had no information to suggest otherwise (our CI was grabbed from the bag at random). But once new information arose suggesting that the true parameter was 0, we began to suspect that [3.0, 7.4] is among the 5% of possible CIs that does not contain the true parameter. In this case, a reevaluation of the data may be necessary.
Conclusion
The probability associated with a CI reflects not one individual CI but rather the long-run frequency of multiple CIs capturing the true parameter across repeated sampling. A given 95% CI is computed using a procedure that, in repeated trials, captures the true parameter 95% of the time. However, for any specific CI, we do not know whether or not it contains the true parameter. If additional information (e.g., contradictions with other data) suggests that the CI may be unreliable, its validity should be reassessed. Properly interpreting a CI in the context of repeated sampling—especially in cases where the CI may be unreliable—is essential for medical writers to accurately communicate the outputs of biostatistics.
References
Tan SH, Tan SB. The correct interpretation of confidence intervals. Proceedings of Singapore Healthcare. 2010;19(3):276-278. doi:10.1177/201010581001900316
D'Arrigo G, El Hafeez SA, Mezzatesta S, et al. Common mistakes in biostatistics. Clin Kidney J. Jul 2024;17(7):sfae197. doi:10.1093/ckj/sfae197
Swinscow TDV. Statements of probability and confidence intervals. In: Campbell M, ed. Statistics at Square One. 9 ed. BMJ Publishing Group; 1997.
Naomi Ruff, CAC Representative
Hello North Central Chapter! As a reminder, the mission of the CAC is as follows:
The CAC serves to maintain a connection between chapter leaders and the AMWA Board of Directors by advising the AMWA board on the organization’s strategic direction as it affects the chapters and acting as a sounding board about issues that have an impact on chapters and the national organization.
It also serves as a way to bring news from the national organization to chapter members and for the chapter (and its members) to bring issues of concern to the national board. Have an issue that you want discussed? Let the chapter board know: bod@amwanorthcentral.org.
Notable news
2025 Medical Writing & Communication Conference
a. November 5–8, 2025, Phoenix, Arizona
b. The deadline to submit a proposal for an education session has passed, but there is still time to propose a Roundtable or Poster—that deadline is March 31
c. Chapter dinners will be held on the Thursday night of the conference
Strategic Planning Initiative
a. The strategic planning process was begun in 2024 and will continue in 2025 as a way to update and improve how AMWA works
b. This process provides AMWA with an opportunity to reimagine chapters to improve both members' and volunteers' experience
c. What do you want from the chapter? Would a different structure—based on something other than wide geographic regions—suit your needs better? Make sure to let the chapter leaders know what you are looking for! You can reach the chapter board at bod@amwanorthcentral.org.
Are you looking for work? You know someone who’s hiring? Please reach out! The job board will be updated in every issue of the monthly newsletter. If you’d like to add your name to this list, please contact Dora Miedaner (dora.miedaner@gmail.com).