TERMINOLOGY 101 Confidence intervals: Part 1 MAHER M. EL-MASRI, RN, PHD, IS AN ASSOCIATE PROFESSOR AND RESEARCH LEADERSHIP CHAIR IN THE FACULTY OF NURSING, UNIVERSITY OF WINDSOR, IN WINDSOR, ONT. Confidence interval: The range of values, consistent with the data, that is believed to encompass the actual or "true" population value Source: Lang, T.A., & Secic, M. (2006). How to Report Statistics in Medicine. (2nd ed.). Philadelphia: American College of Physicians To draw conclusions about a study population, the sample. This sample mean value is probably a researchers use samples that they assume truly more reliable estimate of the true mean value of represent the population. The confidence the population than a sample mean value with a interval (CI) is among the most reliable wider CI of, for example, 110-210 mmHg. With indicators of the soundness of their assumption. such a wide CI, the population mean could be as A CI is the range of values within which the high as 210 mmHg, which is far from the sample population value being studied is believed to fall. mean of 120 mmHg. In fact, a very wide CI in a CIs are reported in the results section of study should be a red flag: it indicates that more published research and are often calculated data should have been collected before any either for mean or proportion data (calculation serious conclusions were drawn about the details are beyond the scope of this article). population. Remember, the narrower the CI, the A 95% CI, which is the most common level used more likely it is that the sample value represents (others are 90% and 99%), means that if the population value. researchers were to sample numerous times from the same population and calculate a range of estimates for these samples, 95% of the intervals within the lower and upper limits of this range will include the population value. NurseONE resources To illustrate the 95% CI of a mean value, say that a sample of patients with hypertension has ON THIS TOPIC a mean blood pressure of 120 mmHg and that EBSCO-MEDLINE FULL-TEXT ARTICLES the 95% CI for this mean was calculated to range from 110 to 130 mmHg. This might be reported Hildebrandt, M., Vervolgyi, E., & Bender, R. (2009). as: mean 120 mmHg, 95% CI 110-130 mmHg. Calculation of NNTs in RCTs with time-to-event outcomes: A literature review. BMC Medical Research Methodology, It indicates that if other samples from the same 9. 21. population of patients were generated and Hildebrandt, M., Bender, R., Gehrmann, U., & Blettner, intervals for the mean blood pressure of these M. (2006). Calculating confidence intervals for impact samples were estimated, 95% of the intervals numbers. BMC Medical Research Methodology, 6, 32. ILLUSTRATION: VANNI LORIGGIO between the lower limit of 110 mmHg and the Altman, D. G. (1998). Confidence intervals for the number upper limit of 130 mmHg would include the true needed to treat. BMJ (Clinical Research Ed), 317(7168). mean blood pressure of the population. 1309-1312. Notice that the width of the CI range is a very MYILIBRARY important indicator of how reliably the sample value represents the population in question. Campbell, M. J., Machin, D., & Walters, S. J. (2010). Medical If the CI is narrow, as it is in our example of statistics: A textbook for the health sciences (4th ed). Mateo, M. A., & Kirchhoff, K. T. (Eds.). (2009). Research for 110-130 mmHg, then the upper and lower limits advanced practice nurses: From evidence to practice. of the CI will be very close to the mean value of Webb, C., & Roe, B. (Eds.). (2007). Reviewing research evidence for nursing practice: Systematic reviews. 17TERMINOLOGY 101 THE RESEARCH FILE Confidence intervals: Part 2 MAHER M. EL-MASRI, RN, PhD, IS AN ASSOCIATE PROFESSOR AND RESEARCH LEADERSHIP CHAIR IN THE FACULTY OF NURSING, UNIVERSITY OF WINDSOR, IN WINDSOR, ONT. Confidence interval: The range of values, consistent with the data, that is believed to encompass the actual or "true" population value Source: Lang, T.A., & Secic, M. (2006). How to Report Statistics in Medicine. (2nd ed.). Philadelphia: American College of Physicians Part 1, which appeared in the February 2012 to zero. Some researchers choose to provide the issue, introduced the concept of confidence CI for the difference of two mean scores instead intervals (CIs) for mean values. This article of providing a separate CI for each of the mean explains how to compare the CIs of two mean scores. In that case, the difference in the mean scores to draw a conclusion about whether or scores is said to be statistically significant if its not they are statistically different. Two mean CI does not include zero (e.g., if the lower limit is scores are said to be statistically different if their 10 and the upper limit is 30). If the CI includes respective CIs do not overlap. Overlap of the CIs zero (e.g., if the lower limit is -10 and the upper suggests that the scores may represent the same limit is 30), we conclude that the observed "true" population value; in other words, the true difference is not statistically significant. difference in the mean scores may be equivalent To illustrate this point, let's say that we want to compare the mean blood pressure (BP) of exercising and sedentary patients. The mean BP NurseONE resources is 120 mmig (95% CI 110-130 mmHg) for the exercising group and 140 mmHg (95% CI ON THIS TOPIC 120-160 mmHg) for the non-exercising group. We notice that the mean BP values of the two EBSCO-MEDLINE FULL-TEXT ARTICLES groups differ by 20 mmig, and we want to . Hildebrandt, M., Vervolgyi, E., & Bender, R. (2009). determine whether this difference is statistically Calculation of NNTs in RCTs with time-to-event significant. Notice that the range of values outcomes: A literature review. BMC Medical between 120 and 130 mmHg falls within the CIs Research Methodology, 9, 21. Hildebrandt, M., Bender, R., Gehrmann, U.. for both groups (i.e., the CIs overlap). Thus, we & Blettner, M. (2006). Calculating confidence conclude that the 20 mmHg difference between intervals for impact numbers. BMC Medical the mean BP values is not statistically Research Methodology, 6, 32. significant. Now, say that the mean BP is . Altman, D. G. (1998). Confidence intervals for the 120 mmHg (95% CI 110-130 mmHg) for the number needed to treat. BMJ (Clinical Research exercising group and 140 mmHg (95% CI Ed.), 317(7168), 1309-1312. 136-144 mmHg) for the sedentary group. In this case, the two CIs do not overlap; none of the MYiLIBRARY values within the first CI fall within the range . Campbell, M. J., Machin, D., & Walters, S. J. (2010). of values of the second CI. Thus, we conclude Medical statistics: A textbook for the health that the mean BP difference of 20 mmHg is sciences (4th ed). . Mateo, M. A., & Kirchhoff, K. T. (Eds.). (2009). statistically significant. Research for advanced practice nurses: Remember, we can use either the CIs of two From evidence to practice. mean scores or the CI of their difference to draw . Webb, C., & Roe, B. (Eds.). (2007). Reviewing conclusions about whether or not the observed research evidence for nursing practice: difference between the scores is statistically Systematic reviews. significant. 10 CANADIAN-NURSE.COMConfidence Interval Estimate for the Mean Data Sample Standard Deviation 17.68777 Sample Mean 26.2 Sample Size 50 Confidence Level 80% Intermediate Calculations Standard Error of the Mean 2.50143 Degrees of Freedom 49 t Value 1.2991 Interval Half Width 3.2495 Confidence Interval Interval Lower Limit 22.950 Interval Upper Limit 29.450