OptSig.2p2n {OptSig} | R Documentation |
Optimal significance level calculation for the test for two proportions (different sample sizes)
Description
Computes the optimal significance level for the test for two proportions
Usage
OptSig.2p2n(ncp=NULL,h=NULL,n1=NULL,n2=NULL,p=0.5,k=1,alternative="two.sided",Figure=TRUE)
Arguments
ncp |
Non-centrality parameter |
h |
Effect size, Cohen's h |
n1 |
Number of observations (1st sample) |
n2 |
Number of observations (2nd sample) |
p |
prior probability for H0, default is p = 0.5 |
k |
relative loss from Type I and II errors, k = L2/L1, default is k = 1 |
alternative |
a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less" |
Figure |
show graph if TRUE (default); No graph if FALSE |
Details
Refer to Kim and Choi (2020) for the details of k and p
Either ncp or h value should be specified.
For h, refer to Cohen (1988) or Chapmely (2017)
Assume X ~ N(mu,sigma^2); and let H0:mu = mu0; and H1:mu = mu1;
ncp = sqrt(n)(mu1-mu0)/sigma
Value
alpha.opt |
Optimal level of significance |
beta.opt |
Type II error probability at the optimal level |
Note
Also refer to the manual for the pwr package
The black curve in the figure is the line of enlightened judgement: see Kim and Choi (2020). The red dot inticates the optimal significance level that minimizes the expected loss: (alpha.opt,beta.opt). The blue horizontal line indicates the case of alpha = 0.05 as a reference point.
Author(s)
Jae H. Kim (using a function from the pwr package)
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
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
OptSig.2p2n(h=0.30,n1=80,n2=245,alternative="greater")