# Sample size planning for Accuracy in Parameter Estimation (AIPE) of the standardized mean

### Description

A function to calculate the appropriate sample size for the standardized mean such that the width of the confidence interval is sufficiently narrow.

### Usage

1 | ```
ss.aipe.sm(sm, width, conf.level = 0.95, assurance = NULL, certainty=NULL, ...)
``` |

### Arguments

`sm` |
the population standardized mean |

`width` |
the desired full width of the obtained confidence interval |

`conf.level` |
the desired confidence interval coverage, (i.e., 1 - Type I error rate) |

`assurance` |
parameter to ensure that the obtained confidence interval width is
narrower than the desired width with a specified degree of certainty (must be |

`certainty` |
an alias for |

`...` |
allows one to potentially include parameter values for inner functions |

### Value

`n ` |
the necessary sample size in order to achieve the desired degree of accuracy (i.e., the sufficiently narrow confidence interval) |

### Author(s)

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

### References

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.

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. (2005). The effects of nonnormal distributions on confidence intervals around the standardized mean
difference: Bootstrap and parametric confidence intervals, *Educational and Psychological Measurement, 65*, 51–69.

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

Kelley, K., & Rausch, J. R. (2006). Sample size planning for the standardized mean difference:
Accuracy in Parameter Estimation via narrow confidence intervals. *Psychological Methods, 11(4)*, 363–385.

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

`conf.limit.nct`

, `ci.sm`

### Examples

1 2 3 4 5 6 7 8 | ```
# Suppose the population mean is believed to be 20, and the population
# standard deviation is believed to be 2; thus the population standardized
# mean is believed to be 10. To determine the necessary sample size for a
# study so that the full width of the 95 percent confidence interval
# obtained in the study will be, with 90% assurance, no wider than 2.5,
# the function should be specified as follows.
# ss.aipe.sm(sm=10, width=2.5, conf.level=.95, assurance=.90)
``` |