omega_f: omega^2 for ANOVA from F
In MOTE: Effect Size and Confidence Interval Calculator

omega_f

R Documentation

`\omega^2` for ANOVA from `F`

Description

This function displays \omega^2 from ANOVA analyses and its non-central confidence interval based on the F distribution. These values are calculated directly from F statistics and can be used for between subjects and repeated measures designs. Remember if you have two or more IVs, these values are partial omega squared.

Usage

omega_f(dfm, dfe, f_value, n, a = 0.05, Fvalue)

omega.F(dfm, dfe, Fvalue, n, a = 0.05)

Arguments

`dfm`	degrees of freedom for the model/IV/between
`dfe`	degrees of freedom for the error/residual/within
`f_value`	F statistic
`n`	full sample size
`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 'omega.F()'.

Details

Omega squared or partial omega squared is calculated by subtracting one from the F-statistic and multiplying it by degrees of freedom of the model. This is divided by the same value after adding the number of valid responses. This value will be omega squared for one-way ANOVA designs, and will be partial omega squared for multi-way ANOVA designs (i.e. with more than one IV).

\omega^2 = \frac{df_m (F - 1)}{df_m (F - 1) + n}

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_f()' to follow modern R style guidelines. The original dotted version 'omega.F()' 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_f()' 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_f(dfm = 2, dfe = 8,
        f_value = 5.134, n = 11, a = .05)

# Backwards-compatible dotted name (deprecated)
omega.F(dfm = 2, dfe = 8,
        Fvalue = 5.134, n = 11, a = .05)

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