OptSig (version 2.1)

OptSig.2p2n: 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

Value

alpha.opt

Optimal level of significance

beta.opt

Type II error probability at the optimal level

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

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

# NOT RUN {
OptSig.2p2n(h=0.30,n1=80,n2=245,alternative="greater")
  
# }