MOTE (version 1.2.2)

eta_partial_ss: \(\eta^2_p\) for ANOVA from \(F\) and Sum of Squares

Description

This function displays \(\eta^2_p\) from ANOVA analyses and its non-central confidence interval based on the \(F\) distribution. This formula works for one way and multi way designs.

Usage

eta_partial_ss(dfm, dfe, ssm, sse, f_value, a = 0.05, Fvalue)
eta.partial.SS(dfm, dfe, ssm, sse, Fvalue, a = 0.05)

Value

Provides the effect size (\(\eta^2_p\)) with associated confidence intervals and relevant statistics.

eta

\(\eta^2_p\) effect size

etalow

lower level confidence interval of \(\eta^2_p\)

etahigh

upper level confidence interval of \(\eta^2_p\)

dfm

degrees of freedom for the model/IV/between

dfe

degrees of freedom for the error/residual/within

F

\(F\)-statistic

p

p-value

estimate

the \(\eta^2_p\) statistic and confidence interval in APA style for markdown printing

statistic

the \(F\)-statistic in APA style for markdown printing

Arguments

dfm

degrees of freedom for the model/IV/between

dfe

degrees of freedom for the error/residual/within

ssm

sum of squares for the model/IV/between

sse

sum of squares for the error/residual/within

f_value

F statistic

a

significance level

Fvalue

Backward-compatible argument for the F statistic (deprecated; use `f_value` instead). If supplied, it overrides `f_value`. Included for users of the legacy `eta.partial.SS()`.

Details

\(\eta^2_p\) is calculated by dividing the sum of squares of the model by the sum of the sum of squares of the model and sum of squares of the error.

$$\eta^2_p = \frac{SS_M}{SS_M + SS_E}$$

Learn more on our example page.

**Note on function and output names:** This effect size is now implemented with the snake_case function name `eta_partial_ss()` to follow modern R style guidelines. The original dotted version `eta.partial.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., `eta`, `etalow`, `etahigh`, `dfm`, `dfe`, `F`, `p`, `estimate`, `statistic`) and newer snake_case aliases (e.g., `eta_value`, `eta_lower_limit`, `eta_upper_limit`, `df_model`, `df_error`, `f_value`, `p_value`). New code should prefer `eta_partial_ss()` and the snake_case output names, but existing code using the older names will continue to work.

Examples

# The following example is derived from the "bn2_data"
# dataset, included in the MOTE library.

# Is there a difference in athletic spending budget for different sports?
# Does that spending interact with the change in coaching staff?
# This data includes (fake) athletic 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.

# Example using reported ANOVA table values directly
eta_partial_ss(dfm = 4, dfe = 990,
               ssm = 338057.9, sse = 32833499,
               f_value = 2.548, a = .05)

# Example computing Type III SS with code (requires the "car" package)
if (requireNamespace("car", quietly = TRUE)) {

  # Fit the model using stats::lm
  mod <- stats::lm(money ~ coach * type, data = bn2_data)

  # Type III table for the effects
  aov_type3 <- car::Anova(mod, type = 3)

  # Extract DF, SS, and F for the interaction (coach:type)
  dfm_int <- aov_type3["coach:type", "Df"]
  ssm_int <- aov_type3["coach:type", "Sum Sq"]
  F_int   <- aov_type3["coach:type", "F value"]

  # Residual DF and SS from the standard ANOVA table
  aov_type1 <- stats::anova(mod)
  dfe <- aov_type1["Residuals", "Df"]
  sse <- aov_type1["Residuals", "Sum Sq"]

  # Calculate partial eta-squared for the interaction using Type III SS
  eta_partial_ss(dfm = dfm_int, dfe = dfe,
                 ssm = ssm_int, sse = sse,
                 f_value = F_int, a = .05)
#'
# Backwards-compatible dotted name (deprecated)
eta.partial.SS(dfm = 4, dfe = 990,
               ssm = 338057.9, sse = 32833499,
               Fvalue = 2.548, a = .05)
}