epsilon_full_ss: epsilon^2 for ANOVA from F and Sum of Squares

In MOTE: Effect Size and Confidence Interval Calculator

\epsilon^2 for ANOVA from F and Sum of Squares

Description

**Note on function and output names:** This effect size is now implemented with the snake_case function name 'epsilon_full_ss()' to follow modern R style guidelines. The original dotted version 'epsilon.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., 'epsilon', 'epsilonlow', 'epsilonhigh', 'dfm', 'dfe', 'F', 'p', 'estimate', 'statistic') and newer snake_case aliases (e.g., 'epsilon_value', 'epsilon_lower_limit', 'epsilon_upper_limit', 'df_model', 'df_error', 'f_value', 'p_value'). New code should prefer 'epsilon_full_ss()' and the snake_case output names, but existing code using the older names will continue to work.

Usage

epsilon_full_ss(dfm, dfe, msm, mse, sst, a = 0.05)

epsilon.full.SS(dfm, dfe, msm, mse, sst, a = 0.05)

Arguments

dfm	degrees of freedom for the model/IV/between
dfe	degrees of freedom for the error/residual/within
msm	mean square for the model/IV/between
mse	mean square for the error/residual/within
sst	sum of squares total
a	significance level

Details

This function displays \epsilon^2 from ANOVA analyses and its non-central confidence interval based on the F distribution. This formula works for one way and multi way designs with careful focus on the sum of squares total calculation.

To calculate \epsilon^2, first, the mean square for the error is is multiplied by the degrees of freedom for the model. The product is divided by the sum of squares total.

\epsilon^2 = \frac{df_m (ms_m - ms_e)}{SS_T}

Learn more on our example page.

Value

Provides the effect size (\epsilon^2) with associated confidence intervals from the F-statistic.

epsilon

effect size

epsilonlow

lower level confidence interval of epsilon

epsilonhigh

upper level confidence interval of epsilon

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 \epsilon^2 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 "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)

epsilon_full_ss(dfm = 2, dfe = 8, msm = 12.621,
                mse = 2.458, sst = (25.24 + 19.67), a = .05)

# Backwards-compatible dotted name (deprecated)
epsilon.full.SS(dfm = 2, dfe = 8, msm = 12.621,
                mse = 2.458, sst = (25.24 + 19.67), a = .05)

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