conf.limits.nct {MBESS}R Documentation

Confidence limits for a noncentrality parameter from a t-distribution

Description

Function to determine the noncentrality parameters necessary to form a confidence interval around the population noncentrality parameter and related parameters. Due to the difficulties in estimating the necessary values, three different methods are implemented within the present function (conf.limits.nct.M1, conf.limits.nct.M2, and conf.limits.nct.M3) and the best set of results are taken.

Usage

conf.limits.nct(ncp, df, conf.level = 0.95, alpha.lower = NULL, 
alpha.upper = NULL, t.value, tol = 1e-09, sup.int.warns = TRUE, 
method = "all", ...)

Arguments

ncp the noncentrality parameter (e.g., observed t-value) of interest.
df the degrees of freedom.
conf.level the level of confidence for a symmetric confidence interval.
alpha.lower the proportion of values beyond the lower limit of the confidence interval (cannot be used with conf.level).
alpha.upper the proportion of values beyond the upper limit of the confidence interval (cannot be used with conf.level).
t.value alias for ncp
tol is the tolerance of the iterative method for determining the critical values.
sup.int.warns Suppress internal warnings (from internal functions): TRUE or FALSE
method which of the three methods should be used: "all", "1", "2", "3" ("all" is default).
... allows one to potentially include parameter values for inner functions

Details

Function for finding the upper and lower confidence limits for a noncentral parameter from a noncentral t-distribution with df degrees of freedom. This function is especially helpful when forming confidence intervals around standardized mean differences (i.e., Cohen's d; Glass's g; Hedges g'), standardized regression coefficients, and coefficients of variations. The Lower.Limit and the Upper.Limit values correspond to the noncentral parameters of a t-distribution with df degrees of freedom whose upper and lower tails contain the desired proportion of the curves, respectively. When ncp is zero, the Lower.Limit and Upper.Limit are simply the desired quantiles of the central t-distribution with df degrees of freedom.

See the documentation and code for each of the three methods (if interested). Each of the three methods should reach the same values for the confidence limits. However, due to the iterative nature of the functions, one function may arrive at a more optimal solution. Furthermore, in some situations one (or more) functions could fail to find the optimum values, which necessitates the use of multiple methods to (essentially) ensure that optimal values are found.

Value

Lower.Limit Value of the distribution with Lower.Limit noncentral value that has at its specified quantile F.value
Prob.Less.Lower Proportion of the distribution beyond (i.e., less than) Lower.Limit
Upper.Limit Value of the distribution with Upper.Limit noncentral value that has at its specified quantile F.value
Prob.Greater.Upper Proportion of the distribution beyond (i.e., larger than) Upper.Limit

Warning

At the present time, the largest ncp that R can accurately handle is 37.62.

Author(s)

Ken Kelley (University of Notre Dame; KKelley@ND.Edu)

References

Cumming, G. & Finch, S. (2001) A primer on the understanding, use, and calculation of confidence intervals that are based on central and noncentral distributions, Educational and Psychological Measurement, 61, 532–574.

Kelley, K. (2005) The effects of nonnormal distributions on confidence intervals around the standardized mean difference: Bootstrap and parametric confidence intervals, Educational and Psychological Measurement, 65, 51–69.

Steiger, J. & Fouladi, T. (1997) Noncentrality interval estimation and the evaluation of statistical models. In L. Harlow, S. Muliak, & J. Steiger (Eds.), What if there were no significance tests?. Mahwah, NJ: Lawrence Erlbaum.

See Also

pt, qt, ci.smd, ci.smd.c, ss.aipe, conf.limits.ncf, conf.limits.nc.chisq

Examples


# Suppose observed t-value based on 'df'=126 is 2.83. Finding the lower 
# and upper critical values for the population noncentrality parameter 
# with a symmetric confidence interval with 95% confidence is given as:
conf.limits.nct(ncp=2.83, df=126, conf.level=.95)

# Modifying the above example so that nonsymmetric confidence intervals 
# can be formed:
conf.limits.nct(ncp=2.83, df=126, alpha.lower=.01, alpha.upper=.04,
conf.level=NULL)

[Package MBESS version 2.0.0 Index]