conf.limits.nct {MBESS}

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.

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, 
...)

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

...

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 respective noncentral t-distribution. 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.

Note that the confidence interval limit(s) are found twice, using two different methods. The first method uses the optimize function, whereas the second method uses the nlm function. The best of the two methods, if not equal and numerically exact, is taken. This does not concern the user.

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; [e-mail])

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.

Kelley, K. (2007). Constructing confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20 (8), 1–24.

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 a nonsymmetric 95% confidence interval
# can be formed:
conf.limits.nct(ncp=2.83, df=126, alpha.lower=.01, alpha.upper=.04,
conf.level=NULL)

# Modifying the above example so that a single-sided 95% confidence interval
# can be formed:
conf.limits.nct(ncp=2.83, df=126, alpha.lower=0, alpha.upper=.05,
conf.level=NULL)