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```
#' Partial Omega Squared for Between Subjects ANOVA from F
#'
#' This function displays omega squared from ANOVA analyses
#' and its non-central confidence interval based on the F distribution.
#' This formula is appropriate for multi-way between subjects designs.
#'
#' Partial omega squared is calculated by subtracting the mean square for the error
#' from the mean square of the model, which is multiplied by degrees of freedom of
#' the model. This is divided by the product of the degrees of freedom
#' for the model are deducted from the sample size, multiplied by the
#' mean square of the error, plus the sum of squares for the model.
#'
#' omega^2 <- (dfm * (msm - mse)) / (ssm + (n-dfm)*mse)
#'
#' \href{https://www.aggieerin.com/shiny-server/tests/omegapbnss.html}{Learn more on our example page.}
#'
#' @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 ssm sum of squares for the model/IV/between
#' @param n total sample size
#' @param a significance level
#'
#' @return Provides omega squared with associated confidence intervals
#' and relevant statistics.
#'
#' \item{omega}{omega squared}
#' \item{omegalow}{lower level confidence interval of omega}
#' \item{omegahigh}{upper level confidence interval of omega}
#' \item{dfm}{degrees of freedom for the model/IV/between}
#' \item{dfe}{degrees of freedom for the error/resisual/within}
#' \item{F}{F-statistic}
#' \item{p}{p-value}
#' \item{estimate}{the omega squared statistic and confidence interval in
#' APA style for markdown printing}
#' \item{statistic}{the F-statistic in APA style for markdown printing}
#'
#' @keywords effect size, omega, ANOVA
#' @import MBESS
#' @import stats
#' @export
#' @examples
#'
#' #The following example is derived from the "bn2_data" dataset, included
#' #in the MOTE library.
#'
#' #Is there a difference in atheletic spending budget for different sports?
#' #Does that spending interact with the change in coaching staff? This data includes
#' #(fake) atheletic budgets for baseball, basketball, football, soccer, and volleyball teams
#' #with new and old coaches to determine if there are differences in
#' #spending across coaches and sports.
#'
#' library(ez)
#' bn2_data$partno = 1:nrow(bn2_data)
#' anova_model = ezANOVA(data = bn2_data,
#' dv = money,
#' wid = partno,
#' between = .(coach, type),
#' detailed = TRUE,
#' type = 3)
#'
#' #You would calculate one eta for each F-statistic.
#' #Here's an example for the interaction with typing in numbers.
#' omega.partial.SS.bn(dfm = 4, dfe = 990,
#' msm = 338057.9 / 4,
#' mse = 32833499 / 990,
#' ssm = 338057.9,
#' n = 1000, a = .05)
#'
#' #Here's an example for the interaction with code.
#' omega.partial.SS.bn(dfm = anova_model$ANOVA$DFn[4],
#' dfe = anova_model$ANOVA$DFd[4],
#' msm = anova_model$ANOVA$SSn[4] / anova_model$ANOVA$DFn[4],
#' mse = anova_model$ANOVA$SSd[4] / anova_model$ANOVA$DFd[4],
#' ssm = anova_model$ANOVA$SSn[4],
#' n = nrow(bn2_data),
#' a = .05)
omega.partial.SS.bn <- function (dfm, dfe, msm, mse, ssm, n, a = .05) {
if (missing(dfm)){
stop("Be sure to include the degrees of freedom for the model (IV).")
}
if (missing(dfe)){
stop("Be sure to include the degrees of freedom for the error.")
}
if (missing(msm)){
stop("Be sure to include the mean squared model for your model (IV).")
}
if (missing(mse)){
stop("Be sure to include the mean squared error for your model.")
}
if (missing(ssm)){
stop("Be sure to include the sum of squares for your model (IV).")
}
if (missing(n)){
stop("Be sure to include total sample size.")
}
if (a < 0 || a > 1) {
stop("Alpha should be between 0 and 1.")
}
omega <- (dfm * (msm - mse)) / (ssm + (n-dfm)*mse)
Fvalue <- msm / mse
limits <- ci.R2(R2 = omega, df.1 = dfm, df.2 = dfe, conf.level = (1-a))
p <- pf(Fvalue, dfm, dfe, lower.tail = F)
if (p < .001) {reportp = "< .001"} else {reportp = paste("= ", apa(p,3,F), sep = "")}
output <- list("omega" = omega, #omega stats
"omegalow" = limits$Lower.Conf.Limit.R2,
"omegahigh" = limits$Upper.Conf.Limit.R2,
"dfm" = dfm, #sig stats
"dfe" = dfe,
"F" = Fvalue,
"p" = p,
"estimate" = paste("$\\omega^2_{p}$ = ", apa(omega,2,T), ", ", (1-a)*100, "\\% CI [",
apa(limits$Lower.Conf.Limit.R2,2,T), ", ",
apa(limits$Upper.Conf.Limit.R2,2,T), "]", sep = ""),
"statistic" = paste("$F$(", dfm, ", ", dfe, ") = ",
apa(Fvalue,2,T), ", $p$ ",
reportp, sep = ""))
return(output)
}
#' @rdname omega.partial.SS.bn
#' @export
```

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