MOTE (version 1.2.2)

ges_partial_ss_rm: \(\eta^2_{G}\) (Partial Generalized Eta-Squared) for Repeated-Measures 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 multi-way repeated measures designs.

Usage

ges_partial_ss_rm(
  dfm,
  dfe,
  ssm,
  sss,
  sse1,
  sse2,
  sse3,
  f_value,
  a = 0.05,
  Fvalue
)
ges.partial.SS.rm(dfm, dfe, ssm, sss, sse1, sse2, sse3, 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

sse1

sum of squares for the error/residual/within for the first IV

sse2

sum of squares for the error/residual/within for the second IV

sse3

sum of squares for the error/residual/within for the interaction

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.rm()` 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 first and second independent variables, and the sum of squares for the interaction are added together. The sum of squares of the model is divided by this value.

$$\eta^2_{G} = \frac{SS_M}{SS_M + SS_S + SS_{E1} + SS_{E2} + SS_{E3}}$$

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_rm()` to follow modern R style guidelines. The original dotted version `ges.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., `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_rm()` 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 "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 GES value for each F-statistic.
# Here's an example for the interaction with typing in numbers.
ges_partial_ss_rm(dfm = 1, dfe = 157,
                  ssm = 2442.948, sss = 76988.13,
                  sse1 = 5402.567, sse2 = 8318.75, sse3 = 6074.417,
                  f_value = 70.9927, a = .05)

# Backwards-compatible dotted name (deprecated)
ges.partial.SS.rm(dfm = 1, dfe = 157,
                  ssm = 2442.948, sss = 76988.13,
                  sse1 = 5402.567, sse2 = 8318.75, sse3 = 6074.417,
                  Fvalue = 70.9927, a = .05)