ci_r2: Confidence interval for R^2 (exported helper)
In MOTE: Effect Size and Confidence Interval Calculator

ci_r2

R Documentation

Confidence interval for R^2 (exported helper)

Description

Compute a confidence interval for the coefficient of determination (R^2). This implementation follows MBESS (Ken Kelley) and is exported here to avoid importing many dependencies. It supports cases with random or fixed predictors and can be parameterized via either degrees of freedom or sample size (n) and number of predictors (p/k).

Usage

ci_r2(
  r2 = NULL,
  df1 = NULL,
  df2 = NULL,
  conf_level = 0.95,
  random_predictors = TRUE,
  random_regressors = random_predictors,
  f_value = NULL,
  n = NULL,
  p = NULL,
  k = NULL,
  alpha_lower = NULL,
  alpha_upper = NULL,
  tol = 1e-09
)

Arguments

`r2`	Numeric. The observed R^2 (may be 'NULL' if 'f_value' is supplied).
`df1`	Integer. Numerator degrees of freedom from F.
`df2`	Integer. Denominator degrees of freedom from F.
`conf_level`	Numeric in (0, 1). Two-sided confidence level for a symmetric confidence interval. Default is '0.95'. Cannot be used with 'alpha_lower' or 'alpha_upper'.
`random_predictors`	Logical. If 'TRUE' (default), compute limits for random predictors; if 'FALSE', compute limits for fixed predictors.
`random_regressors`	Logical. Backwards-compatible alias for 'random_predictors'. If supplied, it overrides 'random_predictors'.
`f_value`	Numeric. The observed F statistic from the study.
`n`	Integer. Sample size.
`p`	Integer. Number of predictors.
`k`	Integer. Alias for 'p' (number of predictors). If supplied along with 'p', they must be equal.
`alpha_lower`	Numeric. Lower-tail noncoverage probability (cannot be used with 'conf_level').
`alpha_upper`	Numeric. Upper-tail noncoverage probability (cannot be used with 'conf_level').
`tol`	Numeric. Tolerance for the iterative method determining critical values. Default is '1e-9'.

Details

If 'n' and 'p' (or 'k') are provided, 'df1' and 'df2' are derived as 'df1 = p' and 'df2 = n - p - 1'. Conversely, if 'df1' and 'df2' are provided, 'n = df1 + df2 + 1' and 'p = df1'.

Value

A named list with the following elements:

lower_conf_limit_r2: The lower confidence limit for R^2.
prob_less_lower: Probability associated with values less than the lower limit.
upper_conf_limit_r2: The upper confidence limit for R^2.
prob_greater_upper: Probability associated with values greater than the upper limit.