Confidence interval methods for a normal mean and standard deviation are well known and simple to apply. However, the same cannot be said for important functions of these parameters. These functions include the normal distribution percentiles, the Bland–Altman limits of agreement, the coefficient of variation and Cohen's effect size. We present a simple approach to this problem by using variance estimates recovered from confidence limits computed for the mean and standard deviation separately. All resulting confidence intervals have closed forms. Simulation results demonstrate that this approach performs very well for limits of agreement, coefficients of variation and their differences.
EfronBTibshiraniRJ. An introduction to the bootstrap. New York: Chapman & Hall/CRC, 1993, pp.180–180.
13.
SchenkerN. Qualms about bootstrap confidence intervals. Journal of the American Statistical Association1985; 80: 360–361.
14.
ZouGYDonnerA. Construction of confidence limits about effect measures: A general approach. Statistics in Medicine2008; 27: 1693–1702.
15.
ZouGY. On the estimation of additive interaction by use of the four-by-two table and beyond. American Journal of Epidemiology2008; 168: 212–224.
16.
RamasundarahettigeCDonnerAZouGY. Confidence interval construction for a difference between two dependent intraclass correlation coefficients. Statistics in Medicine2009; 28: 1041–1053.
17.
PaytonMEGreenstoneMHSchenkerN. Overlapping confidence intervals or standard error intervals: what do they mean in terms of statistical significance?. Journal of Insect Science2003; 3: 34–39.
18.
CummingG. Inference by eye: confidence intervals and how to read pictures of data. American Psychologist2005; 60: 170–180.
19.
CummingG. Inference by eye: reading the overlap of independent confidence intervals. Statistics in Medicine2009; 28: 205–220.
HoweWG. Approximate confidence limits on the mean of X + Y where X and Y are two tabled independent random variable. Journal of the American Statistical Association1974; 69: 789–794.
22.
GraybillFAWangCM. Confidence intervals on nonnegative linear combinations of variances. Journal of the American Statistical Association1980; 75: 869–873.
23.
BurdickRKGraybillFA. Confidence intervals on variance components. New York: Marcel Dekker, 1992.
24.
NewcombeRG. Estimating the difference between differences: Measurement of additive scale interaction for proportions. Statistics in Medicine2001; 20: 2885–2893.
25.
GreenlandS. Quantitative methods in the review of epidemiologic literature. Epidemiologic Reviews1987; 9: 1–30.
26.
FiellerEC. Some problems in interval estimation. Journal of the Royal Statistical Society, Series B1954; 16: 175–185.
27.
WillianARO'BrienBJ. Confidence intervals for cost-effectiveness ratios: an application of Fieller's theorem. Health Economics1998; 5: 297–305.
28.
ZouGYDonnerA. A generalization of Fieller's Theorem for ratios of non-normal variables and some practical applications. In: SchusterHMetzgerW (eds) Biometrics: methods, applications and analyses. UK: Nova Publications, 2010, pp.197–216.
29.
StiglerSM. Kruskal's proof of the joint distribution of and S2. American Statistician1984; 38: 134–135.
30.
MillerGE. Asymptotic test statistics for coefficients of variation. Communication in Statistics–Theory and Methods1991; 20: 3351–3363.
31.
FungWTsangT. A simulation study comparing tests for the equality of coefficients of variation. Statistics in Medicine1998; 17: 2003–2014.
32.
ZouGYTalebanJHuoCY. Confidence interval estimation for lognormal data with application to health economics. Computational Statistics & Data Analysis2009; 53: 3755–3764.
33.
ZouGY. Toward using confidence intervals to compare correlations. Psychological Methods2007; 12: 399–413.
34.
ZouGYHuangWZhangX. A note on confidence interval estimation for a linear function of binomial proportions. Computational Statistics & Data Analysis2009; 53: 1080–1085.
35.
LipGYHLaneDVan WalravenCHartRG. Additive role of plasma von Willebrand factor levels to clinical factors for risk stratification of patients with atrial fibrillation. Stroke2006; 37: 2294–2300.
36.
RobinsonCNvan AswegenAJuliousSA. The relationship between administered radiopharmaceutical activity in myocardinal perfusion scintigraphy and imaging outcomes. European Journal of Nuclear Medicine and Molecular Imaging2008; 35: 329–335.
