OptSig (version 2.1)

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

Description

Computes the optimal significance level for the mean of a normal distribution (known variance)

Usage

Opt.sig.norm.test(ncp=NULL,d=NULL,n=NULL,p=0.5,k=1,alternative="two.sided",Figure=TRUE)

Arguments

ncp

Non-centrality parameter

d

Effect size, Cohen's d

n

Sample size

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 d value should be given.

In a general term, if X ~ N(mu,sigma^2); let H0:mu = mu0; and H1:mu = mu1;

ncp = sqrt(n)(mu1-mu0)/sigma

d = (mu1-mu0)/sigma: Cohen's d

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 {
Opt.sig.norm.test(d=0.2,n=60,alternative="two.sided")
# }