MOTE (version 1.2.2)

omega_f: \(\omega^2\) 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)

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`)

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.

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)