omega_partial_ss_rm: omega^2_p (Partial Omega Squared) for Repeated Measures ANOVA...

In MOTE: Effect Size and Confidence Interval Calculator

omega^2_p (Partial Omega Squared) for Repeated Measures ANOVA from F

Description

This function displays \omega^2_p 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_partial_ss_rm(dfm, dfe, msm, mse, mss, ssm, sse, sss, a = 0.05)

omega.partial.SS.rm(dfm, dfe, msm, mse, mss, ssm, sse, sss, 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
mss	mean square for the subject variance
ssm	sum of squares for the model/IV/between
sse	sum of squares for the error/residual/within
sss	sum of squares for the subject variance
a	significance level

Details

Partial omega squared is calculated by subtracting the mean square for the error from the mean square of the model, which is multiplied by degrees of freedom of the model. This is divided by the sum of the sum of squares for the model, sum of squares for the error, sum of squares for the subject, and the mean square of the subject.

\omega^2_p = \frac{df_m (MS_M - MS_E)}{SS_M + SS_E + SS_S + MS_S}

The F-statistic is calculated by dividing the mean square of the model by the mean square of the error.

F = msm / mse

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

Value

omega

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

omegalow

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

omegahigh

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

statistic

the F-statistic in APA style for markdown printing

omega_value

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

omega_lower_limit

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

omega_upper_limit

upper-level confidence interval of \omega^2_p (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 "rm2_data" dataset,
# included in the MOTE library.

# In this experiment people were given word pairs to rate based on
# their "relatedness". How many people out of a 100 would put LOST-FOUND
# together? Participants were given pairs of words and asked to rate them
# on how often they thought 100 people would give the second word if shown
# the first word.  The strength of the word pairs was manipulated through
# the actual rating (forward strength: FSG) and the strength of the reverse
# rating (backward strength: BSG). Is there an interaction between FSG and
# BSG when participants are estimating the relation between word pairs?

# You would calculate one partial GOS value for each F-statistic.
# You can leave out the MS options if you include all the SS options.
# Here's an example for the interaction with typing in numbers.
omega_partial_ss_rm(dfm = 1, dfe = 157,
                    msm = 2442.948 / 1,
                    mse = 5402.567 / 157,
                    mss = 76988.130 / 157,
                    ssm = 2442.948, sss = 76988.13,
                    sse = 5402.567, a = .05)

# Backwards-compatible dotted name (deprecated)
omega.partial.SS.rm(dfm = 1, dfe = 157,
                    msm = 2442.948 / 1,
                    mse = 5402.567 / 157,
                    mss = 76988.130 / 157,
                    ssm = 2442.948, sss = 76988.13,
                    sse = 5402.567, a = .05)

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