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Category: Confidence intervals. A confidence interval provides a range of plausible values for an estimate that accounts for sampling error. Articles are arranged by date with the most recent entries at the top. You can find the theme and closely related categories, links to spreadsheets, and other resources at the bottom of this page.
Stats: Confidence interval for a rate (October 10, 2007). Dear Professor Mean, How do you calculate a confidence interval for a rate?
Stats: Is my confidence interval wide? (September 11, 2007). Dear Professor Mean, I have a case-control design. Among the cases, 271 were exposed and 317 were unexposed. Among the controls, 125 were exposed and 976 were unexposed. After adjustments for covariates, this produced an odds ratio of 7.4 with a 95% confidence interval of 5.7 to 9.5. Is this a wide interval?
Stats: Is a 10% shortfall in sample size critical? (October 23, 2006). Dear Professor Mean, I'm reviewing a paper where they did a power calculation based on 60 patients per group, but in the research study, they ended up only getting 55/58 per group. Since their sample size was much less than what they originally planned for, does this mean that the study had inadequate power?
Stats: Is my confidence interval too wide? (September 21, 2006). Dear Professor Mean, Is there a rule of the thumb to judge if a 95% CI is wide or narrow?
Stats: An exact confidence interval for a binomial proportion (August 18, 2006). A researcher came into my office this morning with some data that was strongly negative. Out of 15 patients, none showed a detectable improvement after the use of a controversial treatment. That sounds like a strong negative result to me, but a reviewer asked a legitimate question: How do you know that you are not having problems with a Type II error?
Stats: Confidence interval for a correlation coefficient (July 11, 2005). In many exploratory research studies, the goal is to examine associations among multiple demographic variables and some outcome variables. How can you justify the sample size for such an exploratory study? There are several approaches, but one simple way that I often use is to show that any correlation coefficients estimated by this research study will have reasonable precision. It may not be the most rigorous way to select a sample size, but it is convenient and easy to understand.
Stats: Examples of confidence intervals (June 28, 2005). The following abstracts, all from open source journals, provide good teaching examples of how confidence intervals are used in research publications.
Stats: Confidence intervals around a safety level (May 11, 2005). Someone asked me about an environmental clean up. The government told them that the location was cleaned up to a 90% confidence level of the standard. Would this give the residents an assurance that everything was safe? I don't have the background to answer all of this question, but can comment on the Statistical aspects.
Stats: Where is the confidence interval? (March 31, 2005). A recent letter to the editor, Child Psychopharmacology, Effect Sizes, and the Big Bang. Mathews M, Adetunji B, Mathews J, Basil B, George V, Mathews M, Budur K, Abraham S. Am J Psychiatry 2005: 162(4); 818. complains about an article claiming that a drug, citalopram, can reduce depressive symptoms A randomized, placebo-controlled trial of citalopram for the treatment of major depression in children and adolescents. Wagner KD, Robb AS, Findling RL, Jin J, Gutierrez MM, Heydorn WE. Am J Psychiatry 2004: 161(6); 1079-83. The letter writers dispute (among other things) the claim of a statistically and clinically significant reduction.
Stats: Confidence intervals (November 29, 2004). Dear Professor Mean: Can you give me a simple explanation of what a confidence interval is?
Stats: Rates versus proportions (September 15, 2004). Many people use the words "rates" and "proportions" interchangeably, but there is an important distinction that I draw. A proportion represents a situation where the numerator and denominator both represent counts, and the numerator is a subset of the denominator. Rates represent a situation where the numerator is a count, but the denominator is in different units (such as the number of patient years of risk) or where the numerator is not a subset of the denominator (such as number of automobiles in a town divided by the number of adults living in that town).
Stats: Confidence intervals for proportions (July 8, 2004). One of the fellows at the hospital asked me about confidence intervals for proportions. I wrote a couple of simple spreadsheets to do these calculations. It's important to avoid comparing two separate confidence intervals to see if they overlap.
Stats: Why 95% confidence limits (May 6, 2002). Dear Professor Mean:, I've been working with small data sets for some neuroimaging research that have five (5) treatment and five (5) control participants. It is not unusual to have such small samples in this kind of work. My 95% confidence interval (CI) included zero; yet, the 85% confidence interval did not include zero. I know that the 95% CI is the common one, but I also know that others are used, but I don't know when to use them. Therefore, I'd like to know why we use 95% confidence limits all the time? When is it appropriate to use other CIs and the logic behind making such decisions?
Stats: Asymmetric confidence intervals (September 3, 1999). Dear Professor Mean, I found a journal article with a confidence interval that was asymmetric. For example, the authors reported a mortality difference of 5% and a 95% confidence interval of -1.2% to 12%. I can't understand how the CI can be unequally distributed if it uses the form ESTIMATE +/- 1.96*STANDARD ERROR.
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This webpage was written by Steve Simon on 2007-06-07, edited by Steve Simon, and was last modified on 2008-07-14. Send feedback to ssimon at cmh dot edu or click on the email link at the top of the page.