OptSig.Chisq: Optimal Significance Level for a Chi-square test

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

Optimal Significance Level for a Chi-square test

Description

The function calculates the optimal level of significance for a Ch-square test

Usage

OptSig.Chisq(w=NULL, N=NULL, ncp=NULL, df, p = 0.5, k = 1, Figure = TRUE)

Arguments

w	Effect size, Cohen's w
N	Total number of observations
ncp	a value of the non-centality paramter
df	the degrees of freedom
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
Figure	show graph if TRUE (default); No graph if FALSE

Details

See Kim and Choi (2020)

Value

alpha.opt	Optimal level of significance
crit.opt	Critical value at the optimal level
beta.opt	Type II error probability at the optimal level

Note

Applicable to any Chi-square test Either ncp or w (with N) should be given.

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

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>

See Also

Leamer, E. 1978, Specification Searches: Ad Hoc Inference with Nonexperimental Data, Wiley, New York.

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum.

Kim, JH and Ji, P. 2015, Significance Testing in Empirical Finance: A Critical Review and Assessment, Journal of Empirical Finance 34, 1-14. <DOI:http://dx.doi.org/10.1016/j.jempfin.2015.08.006>

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

# Optimal level of Significance for the Breusch-Pagan test: Chi-square version
data(data1)                 # call the data: Table 2.1 of Gujarati (2015)

# Extract Y and X
y=data1$lnoutput; x=cbind(data1$lncapital,data1$lnlabor)

# Restriction matrices for the slope coefficents sum to 1
Rmat=matrix(c(0,1,1),nrow=1); rvec=matrix(1,nrow=1)

# Model Estimation
M=R.OLS(y,x,Rmat,rvec); print(M$coef)

# Breusch-Pagan test for heteroskedasticity
e = M$resid[,1]                  # residuals from unrestricted model estimation

# Restriction matrices for the slope coefficients being 0
Rmat=matrix(c(0,0,1,0,0,1),nrow=2); rvec=matrix(0,nrow=2)

# Model Estimation for the auxilliary regression
M1=R.OLS(e^2,x,Rmat,rvec); 

# Degrees of Freedom and estimate of non-centrality parameter 
df1=nrow(Rmat); NCP=M1$ncp

# LM stat and p-value
LM=nrow(data1)*M1$Rsq[1,1]
pval=pchisq(LM,df=df1,lower.tail = FALSE)

OptSig.Chisq(df=df1,ncp=NCP,p=0.5,k=1, Figure=TRUE)

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