omega_g_ss_rm: omega^2_G (Generalized Omega Squared) for Multi-Way and Mixed...

In MOTE: Effect Size and Confidence Interval Calculator

omega^2_G (Generalized Omega Squared) for Multi-Way and Mixed ANOVA from F

Description

This function displays \omega^2_G (generalized omega squared) from ANOVA analyses and its non-central confidence interval based on the F distribution. This formula is appropriate for multi-way repeated-measures designs and mixed-level designs.

Usage

omega_g_ss_rm(dfm, dfe, ssm, ssm2, sst, mss, j, f_value, a = 0.05, Fvalue)

omega.gen.SS.rm(dfm, dfe, ssm, ssm2, sst, mss, j, 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 MAIN model/IV/between
ssm2	sum of squares for the OTHER model/IV/between
sst	sum of squares total across the whole ANOVA
mss	mean square for the subject variance
j	number of levels in the OTHER IV
f_value	F statistic from the output for your IV
a	significance level
Fvalue	Backward-compatible argument for the F statistic (deprecated; use 'f_value' instead). This argument is only used by the wrapper function 'omega.gen.SS.rm()', which forwards 'Fvalue' to the 'f_value' argument of 'omega_g_ss_rm()'.

Details

Omega squared is calculated by subtracting the product of the degrees of freedom of the model and the mean square of the subject variance from the sum of squares for the model.

This is divided by the value obtained after combining the sum of squares total, sum of squares for the other independent variable, and the mean square of the subject variance multiplied by the number of levels in the other model/IV/between.

\omega^2_G = \frac{SS_M - (df_m \times MS_S)}{SS_T + SS_{M2} + j \times MS_S}

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_g_ss_rm()' to follow modern R style guidelines. The original dotted version 'omega.gen.SS.rm()' 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_g_ss_rm()' and the snake_case output names, but existing code using the older names will continue to work.

Value

omega

\omega^2_G effect size (legacy name; see also 'omega_value')

omegalow

lower-level confidence interval of \omega^2_G (legacy name; see also 'omega_lower_limit')

omegahigh

upper-level confidence interval of \omega^2_G (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_G statistic and confidence interval in APA style for markdown printing

statistic

the F-statistic in APA style for markdown printing

omega_value

\omega^2_G effect size (snake_case alias of 'omega')

omega_lower_limit

lower-level confidence interval of \omega^2_G (alias of 'omegalow')

omega_upper_limit

upper-level confidence interval of \omega^2_G (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 "mix2_data"
# dataset, included in the MOTE library.

# Given previous research, we know that backward strength in free
# association tends to increase the ratings participants give when
# you ask them how many people out of 100 would say a word in
# response to a target word (like Family Feud). This result is
# tied to people’s overestimation of how well they think they know
# something, which is bad for studying. So, we gave people instructions
# on how to ignore the BSG.  Did it help? Is there an interaction
# between BSG and instructions given?

# You would calculate one partial GOS value for each F-statistic.
# Here's an example for the main effect 1 with typing in numbers.
omega_g_ss_rm(dfm = 1, dfe = 156,
          ssm = 6842.46829,
          ssm2 = 14336.07886,
          sst = sum(c(30936.498, 6842.46829,
                      14336.07886, 8657.094, 71.07608)),
          mss = 30936.498 / 156,
          j = 2, f_value = 34.503746, a = .05)

# Backwards-compatible dotted name (deprecated)
omega.gen.SS.rm(dfm = 1, dfe = 156,
                ssm = 6842.46829,
                ssm2 = 14336.07886,
                sst = sum(c(30936.498, 6842.46829,
                            14336.07886, 8657.094, 71.07608)),
                mss = 30936.498 / 156,
                j = 2, Fvalue = 34.503746, a = .05)

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