# OptSig v1.0

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## Optimal Level of Significance for Regression and Other Statistical Tests

Calculates the optimal level of significance based on a decision-theoretic approach.
The optimal level is chosen so that the expected loss from hypothesis testing is minimized.
A range of statistical tests are covered, including the test for the population mean, population proportion, and a linear restriction in a multiple regression model.
The details are covered in Kim, Jae H. and Choi, In, Choosing the Level of Significance: A Decision-Theoretic Approach (December 18, 2017), available at SSRN: <https://ssrn.com/abstract=2652773> or <doi:10.2139/ssrn.2652773>.
See also Kim and Ji (2015) <doi:10.1016/j.jempfin.2015.08.006>.

## Functions in OptSig

Name | Description | |

Opt.sig.chisq.test | Optimal significance level calculation for chi-squared tests | |

Opt.sig.norm.test | Optimal significance level calculation for the mean of a normal distribution (known variance) | |

Opt.Sig.Chisq | Optimal Significance Level for a Chi-square test | |

Opt.Sig | Optimal Significance Level for an F-test | |

Opt.SigWeight | Weighted Optimal Significance Level for the F-test based on the assumption of normality in the error term | |

Opt.sig.2p.test | Optimal significance level calculation for the test for two proportions (same sample sizes) | |

Opt.sig.2p2n.test | Optimal significance level calculation for the test for two proportions (different sample sizes) | |

Opt.sig.anova.test | Optimal significance level calculation for balanced one-way analysis of variance tests | |

Opt.SigBoot | Optimal Significance Level for the F-test using the bootstrap | |

Opt.SigBootWeight | Weighted Optimal Significance Level for the F-test based on the bootstrap | |

data1 | Data for the U.S. production function estimation | |

Opt.sig.t.test | Optimal significance level calculation for t-tests of means (one sample, two samples and paired samples) | |

Opt.sig.t2n.test | Optimal significance level calculation for two samples (different sizes) t-tests of means | |

Opt.sig.p.test | Optimal significance level calculation for proportion tests (one sample) | |

Opt.sig.r.test | Optimal significance level calculation for correlation test | |

OptSig-package | OptSig | |

Power.Chisq | Function to calculate the power of a Chi-square test | |

Power.F | Function to calculate the power of an F-test | |

R.OLS | Restricted OLS estimation and F-test | |

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