MOTE (version 1.2.2)

ges_partial_ss_mix: \(\eta^2_{G}\) (Partial Generalized Eta-Squared) for Mixed Design ANOVA from \(F\)

Description

This function displays partial generalized eta-squared (\(\eta^2_{G}\)) from ANOVA analyses and its non-central confidence interval based on the \(F\) distribution. This formula works for mixed designs.

Usage

ges_partial_ss_mix(dfm, dfe, ssm, sss, sse, f_value, a = 0.05, Fvalue)
ges.partial.SS.mix(dfm, dfe, ssm, sss, sse, Fvalue, a = 0.05)

Value

ges

\(\eta^2_{G}\) effect size

geslow

lower level confidence interval for \(\eta^2_{G}\)

geshigh

upper level confidence interval for \(\eta^2_{G}\)

dfm

degrees of freedom for the model/IV/between

dfe

degrees of freedom for the error/residual/within

F

\(F\)-statistic

p

p-value

estimate

the \(\eta^2_{G}\) statistic and confidence interval in APA style for markdown printing

statistic

the \(F\)-statistic in APA style for markdown printing

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 model/IV/between

sss

sum of squares subject variance

sse

sum of squares for the error/residual/within

f_value

F statistic

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 `ges.partial.SS.mix()` API.

Details

To calculate partial generalized eta squared, first, the sum of squares of the model, sum of squares of the subject variance, sum of squares for the subject variance, and the sum of squares for the error/residual/within are added together.

$$\eta^2_{G} = \frac{SS_M}{SS_M + SS_S + SS_E}$$

Learn more on our example page.

**Note on function and output names:** This effect size is now implemented with the snake_case function name `ges_partial_ss_mix()` to follow modern R style guidelines. The original dotted version `ges.partial.SS.mix()` 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., `ges`, `geslow`, `geshigh`, `dfm`, `dfe`, `F`, `p`, `estimate`, `statistic`) and newer snake_case aliases (e.g., `ges_value`, `ges_lower_limit`, `ges_upper_limit`, `df_model`, `df_error`, `f_value`, `p_value`). New code should prefer `ges_partial_ss_mix()` 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
# "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 GES value for each F-statistic.
# Here's an example for the interaction using reported ANOVA values.
ges_partial_ss_mix(dfm = 1, dfe = 156,
                   ssm = 71.07608,
                   sss = 30936.498,
                   sse = 8657.094,
                   f_value = 1.280784, a = .05)

# Backwards-compatible dotted name (deprecated)
ges.partial.SS.mix(dfm = 1, dfe = 156,
                   ssm = 71.07608,
                   sss = 30936.498,
                   sse = 8657.094,
                   Fvalue = 1.280784, a = .05)