Confidence limits for the standardized mean difference using the control group standard deviation as the divisor.


Function to calculate the confidence limits for the standardized mean difference using the control group standard deviation as the divisor (Glass's g).


ci.smd.c(ncp = NULL, smd.c = NULL, n.C = NULL, n.E = NULL, 
conf.level = 0.95, alpha.lower = NULL, alpha.upper = NULL, 
tol = 1e-09, ...)



is the estimated noncentrality parameter, this is generally the observed t-statistic from comparing the control and experimental group (assuming homogeneity of variance)


is the standardized mean difference (using the control group standard deviation in the denominator)


is the sample size for the control group


is the sample size for experimental group


is the confidence level (1-Type I error rate)


is the Type I error rate for the lower tail


is the Type I error rate for the upper tail


is the tolerance of the iterative method for determining the critical values


Potentially include parameter for inner functions



The lower bound of the computed confidence interval


The standardized mean difference based on the control group standard deviation


The upper bound of the computed confidence interval


This function uses conf.limits.nct, which has as one of its arguments tol (and can be modified with tol of the present function). If the present function fails to converge (i.e., if it runs but does not report a solution), it is likely that the tol value is too restrictive and should be increased by a factor of 10, but probably by no more than 100. Running the function conf.limits.nct directly will report the actual probability values of the limits found. This should be done if any modification to tol is necessary in order to ensure acceptable confidence limits for the noncentral-t parameter have been achieved.


Ken Kelley (University of Notre Dame; KKelley@ND.Edu)


Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum.

Cumming, G. & Finch, S. (2001). A primer on the understanding, use, and calculation of confidence intervals that are based on central and noncentral distributions, Educational and Psychological Measurement, 61, 532–574.

Glass, G. V. (1976). Primary, secondary, and meta-analysis of research. Educational Researcher, 5, 3–8.

Hedges, L. V. (1981). Distribution theory for Glass's Estimator of effect size and related estimators. Journal of Educational Statistics, 2, 107–128.

Kelley, K. (2007). Constructing confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20 (8), 1–24.

Steiger, J. H., & Fouladi, R. T. (1997). Noncentrality interval estimation and the evaluation of statistical methods. In L. L. Harlow, S. A. Mulaik, & J. H. Steiger (Eds.), What if there were no significance tests? (pp. 221–257). Mahwah, NJ: Lawrence Erlbaum.

See Also

smd.c, smd, ci.smd, conf.limits.nct


ci.smd.c(smd.c=.5, n.C=100, n.E=100, conf.level=.95)

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