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

### Description

A function to calculate the appropriate sample size per group for the standardized contrast in ANOVA such that the width of the confidence interval is sufficiently narrow.

### Usage

1 2 | ```
ss.aipe.sc(psi, c.weights, width, conf.level = 0.95,
assurance = NULL, certainty = NULL, ...)
``` |

### Arguments

`psi` |
population standardized contrast |

`c.weights` |
the contrast weights |

`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 NULL or between zero and unity) |

`certainty` |
an alias for |

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

### Value

`n` |
necessary sample size |

### 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.

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

### See Also

`ci.sc`

, `conf.limits.nct`

, `ss.aipe.c`

### Examples

1 2 3 4 5 6 7 8 9 | ```
# Suppose the population standardized contrast is believed to be .6
# in some 5-group ANOVA model. The researcher is interested in comparing
# the average of means of group 1 and 2 with the average of group 3 and 4.
# To calculate the necessary sample size per gorup such that the width
# of 95 percent confidence interval of the standardized
# contrast is, with 90 percent assurance, no wider than .4:
# ss.aipe.sc(psi=.6, c.weights=c(.5, .5, -.5, -.5, 0), width=.4, assurance=.90)
``` |

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