| OptSig.Chisq {OptSig} | R Documentation |
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)