Opt.sig.t.test: Optimal significance level calculation for t-tests of means...

In OptSig: Optimal Level of Significance for Regression and Other Statistical Tests

Optimal significance level calculation for t-tests of means (one sample, two samples and paired samples)

Description

Computes the optimal significance level for the test for t-tests of means

Usage

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

Arguments

ncp	Non-centrality parameter
d	Effect size
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
type	Type of t test : one- two- or paired-sample
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, with the value of n.

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 (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

Opt.sig.t.test(d=0.2,n=60,type="one.sample",alternative="two.sided")

OptSig documentation built on July 3, 2022, 5:05 p.m.