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<table width="100%" summary="page for eta.F"><tr><td>eta.F</td><td style="text-align: right;">R Documentation</td></tr></table>

<h2>Eta and Coefficient of Determination (R2) for ANOVA from F</h2>

<h3>Description</h3>

<p>This function displays eta squared from ANOVA analyses
and their non-central confidence interval based on the F distribution.
These values are calculated directly from F statistics and can be used
for between subjects and repeated measures designs.
Remember if you have two or more IVs, these values are partial eta squared.
</p>


<h3>Usage</h3>

<pre>
eta.F(dfm, dfe, Fvalue, a = 0.05)
</pre>


<h3>Arguments</h3>

<table summary="R argblock">
<tr valign="top"><td><code>dfm</code></td>
<td>
<p>degrees of freedom for the model/IV/between</p>
</td></tr>
<tr valign="top"><td><code>dfe</code></td>
<td>
<p>degrees of freedom for the error/residual/within</p>
</td></tr>
<tr valign="top"><td><code>Fvalue</code></td>
<td>
<p>F statistic</p>
</td></tr>
<tr valign="top"><td><code>a</code></td>
<td>
<p>significance level</p>
</td></tr>
</table>


<h3>Details</h3>

<p>Eta is calculated by multiplying the degrees of freedom of
the model by the F-statistic. This is divided by the product
of degrees of freedom of the model, the F-statistic, and
the degrees of freedom for the error or residual.
</p>
<p>eta^2 = (dfm * Fvalue) / (dfm * Fvalue + dfe)
</p>
<p><a href="https://www.aggieerin.com/shiny-server/tests/etaf.html">Learn more on our example page.</a>
</p>


<h3>Value</h3>

<p>Provides eta with associated confidence intervals and relevant statistics.
</p>
<table summary="R valueblock">
<tr valign="top"><td><code>eta</code></td>
<td>
<p>effect size</p>
</td></tr>
<tr valign="top"><td><code>etalow</code></td>
<td>
<p>lower level confidence interval of eta</p>
</td></tr>
<tr valign="top"><td><code>etahigh</code></td>
<td>
<p>upper level confidence interval of eta</p>
</td></tr>
<tr valign="top"><td><code>dfm</code></td>
<td>
<p>degrees of freedom for the model/IV/between</p>
</td></tr>
<tr valign="top"><td><code>dfe</code></td>
<td>
<p>degrees of freedom for the error/resisual/within</p>
</td></tr>
<tr valign="top"><td><code>F</code></td>
<td>
<p>F-statistic</p>
</td></tr>
<tr valign="top"><td><code>p</code></td>
<td>
<p>p-value</p>
</td></tr>
<tr valign="top"><td><code>estimate</code></td>
<td>
<p>the eta squared statistic and confidence interval in
APA style for markdown printing</p>
</td></tr>
<tr valign="top"><td><code>statistic</code></td>
<td>
<p>the F-statistic in APA style for markdown printing</p>
</td></tr>
</table>


<h3>Examples</h3>

<pre>

#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.F(dfm = 2, dfe = 8,
      Fvalue = 5.134, a = .05)
</pre>


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