R/omega_full_ss.R

In MOTE: Effect Size and Confidence Interval Calculator

#' omega^2 for One-Way and Multi-Way ANOVA from F
#'
#' This function displays \eqn{\omega^2} from ANOVA analyses
#' and its non-central confidence interval based on the \eqn{F} distribution.
#' This formula works for one way and multi way designs with careful
#' focus on which error term you are using for the calculation.
#'
#' Omega squared is calculated by deducting the mean square of the error
#' from the mean square of the model and multiplying by the degrees
#' of freedom for the model. This is divided by the sum of the sum of
#' squares total and the mean square of the error.
#'
#' \deqn{\omega^2 = \frac{df_m (ms_m - ms_e)}{SS_T + ms_e}}
#'
#' \href{https://www.aggieerin.com/shiny-server/tests/omegass.html}{Learn more on our example page.}
#'
#' **Note on function and output names:** This effect size is now implemented
#' with the snake_case function name `omega_full_ss()` to follow modern R style
#' guidelines. The original dotted version `omega.full.SS()` is still available
#' as a wrapper for backward compatibility, and both functions return the same
#' list. The returned object includes both the original element names (e.g.,
#' `omega`, `omegalow`, `omegahigh`, `dfm`, `dfe`, `F`, `p`, `estimate`,
#' `statistic`) and newer snake_case aliases (e.g., `omega_value`,
#' `omega_lower_limit`, `omega_upper_limit`, `df_model`, `df_error`, `f_value`,
#' `p_value`). New code should prefer `omega_full_ss()` and the snake_case
#' output names, but existing code using the older names will continue to work.
#'
#' @param dfm degrees of freedom for the model/IV/between
#' @param dfe degrees of freedom for the error/residual/within
#' @param msm mean square for the model/IV/between
#' @param mse mean square for the error/residual/within
#' @param sst sum of squares total
#' @param a significance level
#' @return \describe{
#'   \item{omega}{\eqn{\omega^2} effect size (legacy name; see
#' also `omega_value`)}
#'   \item{omegalow}{lower-level confidence interval of \eqn{\omega^2}
#'         (legacy name; see also `omega_lower_limit`)}
#'   \item{omegahigh}{upper-level confidence interval of \eqn{\omega^2}
#'         (legacy name; see also `omega_upper_limit`)}
#'   \item{dfm}{degrees of freedom for the model/IV/between
#'         (legacy name; see also `df_model`)}
#'   \item{dfe}{degrees of freedom for the error/residual/within
#'         (legacy name; see also `df_error`)}
#'   \item{F}{\eqn{F}-statistic (legacy name; see also `f_value`)}
#'   \item{p}{p-value (legacy name; see also `p_value`)}
#'   \item{estimate}{the \eqn{\omega^2} statistic and confidence
#' interval in APA style for markdown printing}
#'   \item{statistic}{the \eqn{F}-statistic in APA style for markdown printing}
#'   \item{omega_value}{\eqn{\omega^2} effect size (snake_case
#' alias of `omega`)}
#'   \item{omega_lower_limit}{lower-level confidence interval of
#' \eqn{\omega^2} (alias of `omegalow`)}
#'   \item{omega_upper_limit}{upper-level confidence interval of
#' \eqn{\omega^2} (alias of `omegahigh`)}
#'   \item{df_model}{degrees of freedom for the model/IV/between
#' (alias of `dfm`)}
#'   \item{df_error}{degrees of freedom for the error/residual/within
#' (alias of `dfe`)}
#'   \item{f_value}{\eqn{F}-statistic (alias of `F`)}
#'   \item{p_value}{p-value (alias of `p`)}
#' }
#'
#' @keywords effect size omega ANOVA
#' @import stats
#' @export
#' @examples
#'
#' # The following example is derived from the "bn1_data"
#' # dataset, included in the MOTE library.
#'
#' # A health psychologist recorded the number of close inter-personal
#' # attachments of 45-year-olds who were in excellent, fair, or poor
#' # health. People in the Excellent Health group had 4, 3, 2, and 3
#' # close attachments; people in the Fair Health group had 3, 5,
#' # and 8 close attachments; and people in the Poor Health group
#' # had 3, 1, 0, and 2 close attachments.
#'
#' anova_model <- lm(formula = friends ~ group, data = bn1_data)
#' summary.aov(anova_model)
#'
#' omega_full_ss(dfm = 2, dfe = 8,
#'               msm = 12.621, mse = 2.548,
#'               sst = (25.54 + 19.67), a = .05)
#'
#' # Backwards-compatible dotted name (deprecated)
#' omega.full.SS(dfm = 2, dfe = 8,
#'               msm = 12.621, mse = 2.548,
#'               sst = (25.54 + 19.67), a = .05)
omega_full_ss <- function(dfm, dfe, msm, mse, sst, a = .05) {

  if (missing(dfm)) {
    stop("Be sure to include the degrees of freedom for the model (IV).")
  }

  if (missing(dfe)) {
    stop("Be sure to include the degrees of freedom for the error.")
  }

  if (missing(msm)) {
    stop("Be sure to include the mean squared model for your model (IV).")
  }

  if (missing(mse)) {
    stop("Be sure to include the mean squared error for your model.")
  }

  if (missing(sst)) {
    stop("Be sure to include the sum of squares total for your model.")
  }

  if (a < 0 || a > 1) {
    stop("Alpha should be between 0 and 1.")
  }

  omega_value <- (dfm * (msm - mse)) / (sst + mse)

  f_value <- msm / mse

  limits <- ci_r2(
    r2         = omega_value,
    df1       = dfm,
    df2       = dfe,
    conf_level = (1 - a)
  )

  p_value <- pf(f_value, dfm, dfe, lower.tail = FALSE)

  if (p_value < .001) {
    report_p <- "< .001"
  } else {
    report_p <- paste("= ", apa(p_value, 3, FALSE), sep = "")
  }

  estimate <- paste(
    "$\\omega^2$ = ", apa(omega_value, 2, TRUE), ", ",
    (1 - a) * 100, "\\% CI [",
    apa(limits$lower_conf_limit_r2, 2, TRUE), ", ",
    apa(limits$upper_conf_limit_r2, 2, TRUE), "]",
    sep = ""
  )

  statistic <- paste(
    "$F$(", dfm, ", ", dfe, ") = ",
    apa(f_value, 2, TRUE), ", $p$ ",
    report_p,
    sep = ""
  )

  output <- list(
    # Legacy names
    omega     = omega_value,
    omegalow  = limits$lower_conf_limit_r2,
    omegahigh = limits$upper_conf_limit_r2,
    dfm       = dfm,
    dfe       = dfe,
    F         = f_value,
    p         = p_value,
    estimate  = estimate,
    statistic = statistic,

    # Snake_case aliases
    omega_value        = omega_value,
    omega_lower_limit  = limits$lower_conf_limit_r2,
    omega_upper_limit  = limits$upper_conf_limit_r2,
    df_model           = dfm,
    df_error           = dfe,
    f_value            = f_value,
    p_value            = p_value
  )

  return(output)
}

# Backward compatibility wrapper
#' @rdname omega_full_ss
#' @export
omega.full.SS <- function(dfm, dfe, msm, mse, sst, a = .05) { # nolint
  omega_full_ss(
    dfm = dfm,
    dfe = dfe,
    msm = msm,
    mse = mse,
    sst = sst,
    a   = a
  )
}