Description Usage Arguments Author(s) References Examples

Hypothesis test to determine whether an observed empirical detection rate, coupled with a given robustness interval, statistically differs from the population value. Uses the methods described by Serlin (2000) as well to generate critical values (similar to confidence intervals, but define a fixed window of robustness). Critical values may be computed without performing the simulation experiment (hence, can be obtained a priori).

1 | ```
Serlin2000(p, alpha, delta, R, CI = 0.95)
``` |

`p` |
(optional) a vector containing the empirical detection rate(s) to be tested. Omitting this input will compute only the CV1 and CV2 values, while including this input will perform a one-sided hypothesis test for robustness |

`alpha` |
Type I error rate (e.g., often set to .05) |

`delta` |
(optional) symmetric robustness interval around |

`R` |
number of replications used in the simulation |

`CI` |
confidence interval for |

Phil Chalmers rphilip.chalmers@gmail.com

Chalmers, R. P., & Adkins, M. C. (2020). Writing Effective and Reliable Monte Carlo Simulations
with the SimDesign Package. `The Quantitative Methods for Psychology, 16`

(4), 248-280.
doi: 10.20982/tqmp.16.4.p248

Serlin, R. C. (2000). Testing for Robustness in Monte Carlo Studies.
*Psychological Methods, 5*, 230-240.

Sigal, M. J., & Chalmers, R. P. (2016). Play it again: Teaching statistics with Monte
Carlo simulation. `Journal of Statistics Education, 24`

(3), 136-156.
doi: 10.1080/10691898.2016.1246953

1 2 3 4 5 6 7 8 9 10 11 12 | ```
# Cochran's criteria at alpha = .05 (i.e., 0.5 +- .01), assuming N = 2000
Serlin2000(p = .051, alpha = .05, delta = .01, R = 2000)
# Bradley's liberal criteria given p = .06 and .076, assuming N = 1000
Serlin2000(p = .060, alpha = .05, delta = .025, R = 1000)
Serlin2000(p = .076, alpha = .05, delta = .025, R = 1000)
# multiple p-values
Serlin2000(p = c(.05, .06, .07), alpha = .05, delta = .025, R = 1000)
# CV values computed before simulation performed
Serlin2000(alpha = .05, R = 2500)
``` |

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