Description Usage Arguments Details Value Author(s) References See Also Examples

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.

1 2 3 4 5 6 7 8 9 10 |

`x` |
A |

`anova` |
A logical, indicating whether the result should also contain the
test statistics produced by |

`partial` |
A logical, indicating whether to calculate partial or classical eta^2. |

`...` |
Other arguments passed down to |

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, partialing 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)*

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.

Michael Friendly

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 Calculations for General Linear Multivariate Models Including Repeated Measures Applications.
*Journal of the American Statistical Association*, 87, 1209-1226.

1 2 3 4 5 6 7 8 9 |

```
Loading required package: car
eta^2
Block 0.5585973
Contour 0.6692989
Depth 0.5983772
Contour:Depth 0.2058495
eta^2
Block 0.5585973
Contour 0.6692989
Depth 0.5983772
Contour:Depth 0.2058495
Type II MANOVA Tests: Pillai test statistic
eta^2 Df test stat approx F num Df den Df Pr(>F)
Block 0.55860 3 1.6758 3.7965 27 81 1.777e-06 ***
Contour 0.66930 2 1.3386 5.8468 18 52 2.730e-07 ***
Depth 0.59838 3 1.7951 4.4697 27 81 8.777e-08 ***
Contour:Depth 0.20585 6 1.2351 0.8640 54 180 0.7311
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
eta^2
Block 0.5701385
Contour 0.7434504
Depth 0.8294239
Contour:Depth 0.2250388
eta^2
Block 0.5823516
Contour 0.8009753
Depth 0.9421533
Contour:Depth 0.2456774
```

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.