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

1 2 3 |

`ncp` |
is the estimated noncentrality parameter, this is generally the observed |

`smd.c` |
is the standardized mean difference (using the control group standard deviation in the denominator) |

`n.C` |
is the sample size for the control group |

`n.E` |
is the sample size for experimental group |

`conf.level` |
is the confidence level (1-Type I error rate) |

`alpha.lower` |
is the Type I error rate for the lower tail |

`alpha.upper` |
is the Type I error rate for the upper tail |

`tol` |
is the tolerance of the iterative method for determining the critical values |

`...` |
Potentially include parameter for inner functions |

`Lower.Conf.Limit.smd.c` |
The lower bound of the computed confidence interval |

`smd.c` |
The standardized mean difference based on the control group standard deviation |

`Upper.Conf.Limit.smd.c` |
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.

`smd.c`

, `smd`

, `ci.smd`

, `conf.limits.nct`

1 |

Questions? Problems? Suggestions? Tweet to @rdrrHQ or email at ian@mutexlabs.com.

All documentation is copyright its authors; we didn't write any of that.