MOTE (version 1.2.2)

eta_full_ss: \(\eta^2\) for ANOVA from \(F\) and Sum of Squares

Description

This function displays \(\eta^2\) from ANOVA analyses and its non-central confidence interval based on the \(F\) distribution. This formula works for one way and multi way designs with careful focus on the sum of squares total.

Usage

eta_full_ss(dfm, dfe, ssm, sst, f_value, a = 0.05, Fvalue)
eta.full.SS(dfm, dfe, ssm, sst, Fvalue, a = 0.05)

Value

Provides the effect size (\(\eta^2\)) with associated confidence intervals and relevant statistics.

eta

\(\eta^2\) effect size

etalow

lower level confidence interval of \(\eta^2\)

etahigh

upper level confidence interval of \(\eta^2\)

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 \(\eta^2\) 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

sst

sum of squares total

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 `eta.full.SS()`.

Details

Eta squared is calculated by dividing the sum of squares for the model by the sum of squares total.

$$\eta^2 = \frac{SS_M}{SS_T}$$

**Note on function and output names:** This effect size is now implemented with the snake_case function name `eta_full_ss()` to follow modern R style guidelines. The original dotted version `eta.full.SS()` 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., `eta`, `etalow`, `etahigh`, `dfm`, `dfe`, `F`, `p`, `estimate`, `statistic`) and newer snake_case aliases (e.g., `eta_value`, `eta_lower_limit`, `eta_upper_limit`, `df_model`, `df_error`, `f_value`, `p_value`). New code should prefer `eta_full_ss()` and the snake_case output names, but existing code using the older names will continue to work.

Learn more on our example page.

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)

eta_full_ss(dfm = 2, dfe = 8, ssm = 25.24,
            sst = (25.24 + 19.67), f_value = 5.134, a = .05)

# Backwards-compatible dotted name (deprecated)
eta.full.SS(dfm = 2, dfe = 8, ssm = 25.24,
            sst = (25.24 + 19.67), Fvalue = 5.134, a = .05)