# etasq {heplots}

### Description

Calculates partial eta-squared for linear models or multivariate analogs of eta-squared (or R^2), indicating the partial association for each term in a multivariate linear model. There is a different analog for each of the four standard multivariate test statistics: Pillai's trace, Hotelling-Lawley trace, Wilks' Lambda and Roy's maximum root test.

### Usage

etasq(x, ...) ## S3 method for class 'lm': etasq((x, anova = FALSE, partial = TRUE, ...)) ## S3 method for class 'mlm': etasq((x, ...)) ## S3 method for class 'Anova.mlm': etasq((x, anova = FALSE, ...))

### Arguments

- x
- A
`lm`

,`mlm`

or`Anova.mlm`

object - anova
- A logical, indicating whether the result should also contain the test statistics produced by
`Anova()`

. - partial
- A logical, indicating whether to calculate partial or classical eta^2.
- ...
- Other arguments passed down to
`Anova`

.

### Details

For univariate linear models, classical η^2 = SSH / SST and partial η^2 = SSH / (SSH + SSE). These are identical in one-way designs.

Partial eta-squared describes the proportion of total variation attributable to a given factor, partialling out (excluding) other factors from the total nonerror variation. These are commonly used as measures of effect size or measures of (non-linear) strength of association in ANOVA models.

All multivariate tests are based on the s=min(p, df_h) latent roots of H E^{-1}. The analogous multivariate partial η^2 measures are calculated as:

- Pillai's trace (V)
- η^2 = V/s
- Hotelling-Lawley trace (T)
- η^2 = T/(T+s)
- Wilks' Lambda (L)
- η^2 = L^{1/s}
- Roy's maximum root (R)
- η^2 = R/(R+1)

### Values

When `anova=FALSE`

, a one-column data frame containing the eta-squared values for each term in the model.

When `anova=TRUE`

, a 5-column (lm) or 7-column (mlm) data frame containing the eta-squared values and the test statistics produced by `print.Anova()`

for each term in the model.

### References

Muller, K. E. and Peterson, B. L. (1984). Practical methods for computing power in testing the Multivariate General Linear Hypothesis *Computational Statistics and Data Analysis*, 2, 143-158.

Muller, K. E. and LaVange, L. M. and Ramey, S. L. and Ramey, C. T. (1992). Power Claculations for General Linear Multivariate Models Including Repeated Measures Applications. *Journal of the American Statistical Association*, 87, 1209-1226.

### See Also

`Anova`

### Examples

Documentation reproduced from package heplots, version 1.1-0. License: GPL (>= 2)