View source: R/conf.limits.nct.R

conf.limits.nct | R Documentation |

Function to determine the noncentrality parameters necessary to form a confidence interval around the population noncentrality parameter and related parameters.

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

`ncp` |
the noncentrality parameter (e.g., observed |

`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 |

`alpha.upper` |
the proportion of values beyond the upper limit of the confidence interval (cannot be used with |

`t.value` |
alias for |

`tol` |
is the tolerance of the iterative method for determining the critical values. |

`sup.int.warns` |
Suppress internal warnings (from internal functions): |

`...` |
allows one to potentially include parameter values for inner functions |

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.

`Lower.Limit` |
Value of the distribution with |

`Prob.Less.Lower` |
Proportion of the distribution beyond (i.e., less than) |

`Upper.Limit` |
Value of the distribution with |

`Prob.Greater.Upper` |
Proportion of the distribution beyond (i.e., larger than) |

At the present time, the largest `ncp`

that R can accurately handle is 37.62.

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

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.

`pt`

, `qt`

, `ci.smd`

, `ci.smd.c`

, `ss.aipe`

, `conf.limits.ncf`

, `conf.limits.nc.chisq`

```
# 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)
```

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