Opt.sig.norm.test {OptSig}

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

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

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 (2019). 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

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