| OptSig-package {OptSig} | R Documentation |
Optimal Level of Significance for Regression and Other Statistical Tests
Description
The optimal level of significance is calculated 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 and Choi (2020) <doi:10.1111/abac.12172>, and Kim (2021) <doi:10.1080/00031305.2020.1750484>.
Details
The DESCRIPTION file:
| Package: | OptSig |
| Type: | Package |
| Title: | Optimal Level of Significance for Regression and Other Statistical Tests |
| Version: | 2.2 |
| Imports: | pwr |
| Date: | 2022-06-29 |
| Author: | Jae H. Kim <jaekim8080@gmail.com> |
| Maintainer: | Jae H. Kim <jaekim8080@gmail.com> |
| Description: | The optimal level of significance is calculated 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 and Choi (2020) <doi:10.1111/abac.12172>, and Kim (2021) <doi:10.1080/00031305.2020.1750484>. |
| License: | GPL-2 |
Index of help topics:
Opt.sig.norm.test Optimal significance level calculation for the
mean of a normal distribution (known variance)
Opt.sig.t.test Optimal significance level calculation for
t-tests of means (one sample, two samples and
paired samples)
OptSig-package Optimal Level of Significance for Regression
and Other Statistical Tests
OptSig.2p Optimal significance level calculation for the
test for two proportions (same sample sizes)
OptSig.2p2n Optimal significance level calculation for the
test for two proportions (different sample
sizes)
OptSig.Boot Optimal Significance Level for the F-test using
the bootstrap
OptSig.BootWeight Weighted Optimal Significance Level for the
F-test based on the bootstrap
OptSig.Chisq Optimal Significance Level for a Chi-square
test
OptSig.F Optimal Significance Level for an F-test
OptSig.Weight Weighted Optimal Significance Level for the
F-test based on the assumption of normality in
the error term
OptSig.anova Optimal significance level calculation for
balanced one-way analysis of variance tests
OptSig.p Optimal significance level calculation for
proportion tests (one sample)
OptSig.r Optimal significance level calculation for
correlation test
OptSig.t2n Optimal significance level calculation for two
samples (different sizes) t-tests of means
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
data1 Data for the U.S. production function
estimation
The package accompanies the paper: Kim and Choi, 2020, Choosing the Level of Significance: A Decision-theoretic Approach. Abacus. Wiley.
It oprovides functions for the optimal level of significance for the test for linear restiction in a regeression model.
Other basic statistical tests, including those for population mean and proportion, are also covered using the functions from the pwr package.
Author(s)
Jae H. Kim <jaekim8080@gmail.com>
Maintainer: Jae H. Kim <jaekim8080@gmail.com>
References
Kim and Choi, 2020, Choosing the Level of Significance: A Decision-theoretic Approach: Abacus: a Journal of Accounting, Finance and Business Studies. Wiley. <https://doi.org/10.1111/abac.12172>
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum.
Stephane Champely (2017). pwr: Basic Functions for Power Analysis. R package version 1.2-1. https://CRAN.R-project.org/package=pwr
See Also
Leamer, E. 1978, Specification Searches: Ad Hoc Inference with Nonexperimental Data, Wiley, New York.
Kim, JH and Ji, P. 2015, Significance Testing in Empirical Finance: A Critical Review and Assessment, Journal of Empirical Finance 34, 1-14. <DOI:http://dx.doi.org/10.1016/j.jempfin.2015.08.006>
Kim, Jae H., 2020, Decision-theoretic hypothesis testing: A primer with R package OptSig, The American Statistician. <https://doi.org/10.1080/00031305.2020.1750484.>
Examples
data(data1)
y=data1$lnoutput; x=cbind(data1$lncapital,data1$lnlabor)
# Restriction matrices to test for constant returns to scale
Rmat=matrix(c(0,1,1),nrow=1); rvec=matrix(0.94,nrow=1)
# Model Estimation and F-test
M=R.OLS(y,x,Rmat,rvec)
# Degrees of Freedom and estimate of non-centrality parameter
K=ncol(x)+1; T=length(y)
df1=nrow(Rmat);df2=T-K; NCP=M$ncp
# Optimal level of Significance: Under Normality
OptSig.F(df1,df2,ncp=NCP,p=0.5,k=1, Figure=TRUE)