# Description

This function displays omega squared from ANOVA analyses and its non-central confidence interval based on the F distribution. This formula is appropriate for multi-way between subjects designs.

The formula for $\omega_p^2$ is: $$\frac{df_{model} \times (MS_{model} - MS_{error})}{SS_{model} + (N - df_{model}) \times MS_{error}}$$

The formula for F is: $$\frac{MS_{model}}{MS_{error}}$$

# R Function

omega.partial.SS.bn(dfm, dfe, msm, mse, ssm, n, a)

# 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
• ssm = sum of squares for the model/IV/between
• n = total sample size
• a = significance level

# Example

We looked at two year’s worth of athletic spending data (treating each receipt and years as separate between subjectsâ€™ events) for four different sports. Are there differences across sports and years in spending?

JASP

SPSS

SAS

# Function in R:

omega.partial.SS.bn(dfm = 1, dfe = 18250, msm = 1675682.823, mse = 33996.837, ssm = 1675682.823, n = 18260, a = 0.05)

# MOTE

## Effect Size:

$\omega_p^2$ = .00, 95% CI [.00, .00]

## Interpretation:

Your confidence interval does not include zero, and therefore, you might conclude that this effect size is different from zero.

Not applicable.

## Test Statistic:

F(1, 18250) = 49.29, p < .001

## Interpretation:

Your p-value is less than the alpha value, and therefore, this test would be considered statistically significant.