returnCutoffValue: Estimates The Statistic Cutoff For A Target Alpha

In dbEmpLikeNorm: Test for joint assessment of normality

Description

estimates the test statistic cutoff for significance

Usage

returnCutoffValue(numberOfgroups,
                  sample.size,
                  targetalpha=0.05,
                  MC.Method=TRUE,
                  Table.Method=FALSE,
                  Bayes.Method=FALSE,
                  num.mc=1000,
                  delta=0.05,
                  nsims=200,
                  v.threshold=NA)

Arguments

numberOfgroups	number of different groups or experiments
sample.size	number of observations
targetalpha	The significance level for the test.
MC.Method	logical indicating if value should be calculated based on Monte Carlo techniques
Table.Method	logical indicating if value should be calculated based on estimates from generated data table
Bayes.Method	logical indicating if value should be calculated using a Bayesian method incorporating elements of MC.Method and Table.Method
num.mc	number of simulations to estimate distribution of statistic in MC.Method
delta	an option for changing the minimizing range for the EL ratio test statistic for the distribution. Utilized in MC.Method
nsims	The number of simulations to generate and investigate in each turn of Bayesian approach
v.threshold	a numeric threshold for the variance. This threshold must be met to accept calculated value of Bayesian approach. If NA, a variance estimate is calculated and used as threshold.

Details

This function is designed to return the cut-off for significance for the statistics obtained from the density-based EL tests. The significance level for the associated cutoffs are specified by the user in 'targetalpha'.

The 'numberOfgroups' is a scalar denoting the number of groups or datasets being tested. The 'sample.size' should be a vector of length equal to the 'numberOfgroups' where sample.size[1] is the number of observations for group 1, sample.size[2] is the number of observations for group 2, etc. If only a single 'sample.size' is specified, it is assumed groups are of equal length.

MC.Method, Table.Method, and Bayes.Method are binary options. When MC.Method is TRUE, the cutoff is determined from a Monte-Carlo simulation where the number of resamplings is controlled by 'num.mc'. When Table.Method is TRUE, the cutoff is determined by imputation from a stored table of test statistics and significance levels for common sample sizes. When Bayes.Method is TRUE, the cutoff is determined through a Bayesian approach where the number of additional observations is controlled by nsims, and the threshold for acceptance is controlled by 'v.threshold'. See [Tsai 2013] for more details on the algorithm

The 'delta' value must be in the range [0,1]. Essentially this setting controls the range over which a minimum is taken to produce the EL ratio test statistic. The range is from 1 to n^(1-'delta') where 'n' represents the number of observations in 'x'.

Value

Returns a statistical cutoff value to assess significance at level 'targetalpha'. If more than one method is selected, a list with value for each method is returned. If only one method is selected, a single numeric value for that method is returned.

Author(s)

Lori A. Shepherd, Wan-Min Tsai, Albert Vexler, Jeffrey C. Miecznikowski

References

Tsai WM, Shepherd LA, Miecznikowski J, Hutson A, Vexler A. (2013). An EL based test for normality in multiple groups. Department of Biostatistics. University at Buffalo. Report 1204.

Examples

returnCutoffValue(3, c(10,15,40), MC.Method=TRUE)

returnCutoffValue(3, c(10,15,40), MC.Method=TRUE, Bayes.Method=TRUE, Table.Method=TRUE)

dbEmpLikeNorm documentation built on May 2, 2019, 3:45 p.m.