omega_full_ss: omega^2 for One-Way and Multi-Way ANOVA from F
In MOTE: Effect Size and Confidence Interval Calculator

omega_full_ss

R Documentation

omega^2 for One-Way and Multi-Way ANOVA from F

Description

This function displays \omega^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 which error term you are using for the calculation.

Usage

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

omega.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

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.

\omega^2 = \frac{df_m (ms_m - ms_e)}{SS_T + ms_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 '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.

Value

omega: \omega^2 effect size (legacy name; see also 'omega_value')
omegalow: lower-level confidence interval of \omega^2 (legacy name; see also 'omega_lower_limit')
omegahigh: upper-level confidence interval of \omega^2 (legacy name; see also 'omega_upper_limit')
dfm: degrees of freedom for the model/IV/between (legacy name; see also 'df_model')
dfe: degrees of freedom for the error/residual/within (legacy name; see also 'df_error')
F: F-statistic (legacy name; see also 'f_value')
p: p-value (legacy name; see also 'p_value')
estimate: the \omega^2 statistic and confidence interval in APA style for markdown printing
statistic: the F-statistic in APA style for markdown printing
omega_value: \omega^2 effect size (snake_case alias of 'omega')
omega_lower_limit: lower-level confidence interval of \omega^2 (alias of 'omegalow')
omega_upper_limit: upper-level confidence interval of \omega^2 (alias of 'omegahigh')
df_model: degrees of freedom for the model/IV/between (alias of 'dfm')
df_error: degrees of freedom for the error/residual/within (alias of 'dfe')
f_value: F-statistic (alias of 'F')
p_value: p-value (alias of 'p')

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)

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