Performs a sensitivity analysis when planning sample size from the Accuracy in Parameter Estimation (AIPE) Perspective for the standardized ANOVA contrast.

1 2 3 |

`true.psi` |
population standardized contrast |

`estimated.psi` |
estimated standardized contrast |

`c.weights` |
the contrast weights |

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

`selected.n` |
selected sample size to use in order to determine distributional properties of at a given value of sample size |

`assurance` |
parameter to ensure that the obtained confidence interval width is narrower than the desired width with a specified degree of certainty (must be NULL or between zero and unity) |

`certainty` |
an alias for |

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

`G` |
number of generations (i.e., replications) of the simulation |

`print.iter` |
to print the current value of the iterations |

`detail` |
whether the user needs a detailed ( |

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

`psi.obs` |
observed standardized contrast in each iteration |

`Full.Width` |
vector of the full confidence interval width |

`Width.from.psi.obs.Lower` |
vector of the lower confidence interval width |

`Width.from.psi.obs.Upper` |
vector of the upper confidence interval width |

`Type.I.Error.Upper` |
iterations where a Type I error occurred on the upper end of the confidence interval |

`Type.I.Error.Lower` |
iterations where a Type I error occurred on the lower end of the confidence interval |

`Type.I.Error` |
iterations where a Type I error happens |

`Lower.Limit` |
the lower limit of the obtained confidence interval |

`Upper.Limit` |
the upper limit of the obtained confidence interval |

`replications` |
number of replications of the simulation |

`True.psi` |
population standardized contrast |

`Estimated.psi` |
estimated standardized contrast |

`Desired.Width` |
the desired full width of the obtained confidence interval |

`assurance` |
the value assigned to the argument |

`Sample.Size.per.Group` |
sample size per group |

`Number.of.Groups` |
number of groups |

`mean.full.width` |
mean width of the obtained full conficence intervals |

`median.full.width` |
median width of the obtained full confidence intervals |

`sd.full.width` |
standard deviation of the widths of the obtained full confidence intervals |

`Pct.Width.obs.NARROWER.than.desired` |
percentage of the obtained full confidence interval widths that are narrower than the desired width |

`mean.Width.from.psi.obs.Lower` |
mean lower width of the obtained confidence intervals |

`mean.Width.from.psi.obs.Upper` |
mean upper width of the obtained confidence intervals |

`Type.I.Error.Upper` |
Type I error rate from the upper side |

`Type.I.Error.Lower` |
Type I error rate from the lower side |

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

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. (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. P*sychological Methods, 11* (4), 363–385.

Lai, K., & Kelley, K. (2007). Sample size planning for standardized ANCOVA and ANOVA
contrasts: Obtaining narrow confidence intervals. *Manuscript submitted for publication*.

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 where
no significance tests?* (pp. 221–257). Mahwah, NJ: Lawrence Erlbaum.

`ss.aipe.sc`

, `ss.aipe.c`

, `conf.limits.nct`

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

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