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

In MOTE: Effect Size and Confidence Interval Calculator

\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)

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.

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

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)
}

MOTE documentation built on Dec. 15, 2025, 9:06 a.m.