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<h1>Studies on the Effects of Modified School Calendars on Student Achievement</h1>
<div class="hidden name"><code>dat.konstantopoulos2011.Rd</code></div>
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<div class="ref-description">
<p>Results from 56 studies on the effects of modified school calendars on student achievement.</p>
</div>
<pre class="usage"><span class='no'>dat.konstantopoulos2011</span></pre>
<h2 class="hasAnchor" id="format"><a class="anchor" href="#format"></a>Format</h2>
<p>The data frame contains the following columns:</p><table class='table'>
<tr><td><b>district</b></td><td><code>numeric</code></td><td>district id number</td></tr>
<tr><td><b>school</b></td><td><code>numeric</code></td><td>school id number (within district)</td></tr>
<tr><td><b>study</b></td><td><code>numeric</code></td><td>study id number</td></tr>
<tr><td><b>yi</b></td><td><code>numeric</code></td><td>standardized mean difference</td></tr>
<tr><td><b>vi</b></td><td><code>numeric</code></td><td>corresponding sampling variance</td></tr>
<tr><td><b>year</b></td><td><code>numeric</code></td><td>year of the study</td></tr>
</table>
<h2 class="hasAnchor" id="details"><a class="anchor" href="#details"></a>Details</h2>
<p>Instead of following the more traditional school calendar with a long summer break (in addition to a short winter and spring break), some schools have switched to a modified school calendar comprising more frequent but shorter intermittent breaks (e.g., 9 weeks of school followed by 3 weeks off), while keeping the total number of days at school approximately the same. The effects of using such a modified calendar on student achievement have been examined in a number of studies and were meta-analyzed by Cooper et al. (2003).</p>
<p>The dataset (taken from Konstantopoulos, 2011) contains the results from 56 studies, each comparing the level of academic achievement in a group of students following a modified school calendar with that of a group of students following a more traditional school calendar. The difference between the two groups was quantified in terms of a standardized mean difference (with positive values indicating a higher mean level of achievement in the group following the modified school calendar).</p>
<p>The studies were conducted at various schools that were clustered within districts. The data therefore have a multilevel structure, with schools nested within districts. A multilevel meta-analysis of these data can be used to estimate and account for the amount of heterogeneity between districts and between schools within districts.</p>
<h2 class="hasAnchor" id="source"><a class="anchor" href="#source"></a>Source</h2>
<p>Konstantopoulos, S. (2011). Fixed effects and variance components estimation in three-level meta-analysis. <em>Research Synthesis Methods</em>, <b>2</b>, 61--76.</p>
<h2 class="hasAnchor" id="references"><a class="anchor" href="#references"></a>References</h2>
<p>Cooper, H., Valentine, J. C., Charlton, K., & Melson, A. (2003). The effects of modified school calendars on student achievement and on school and community attitudes. <em>Review of Educational Research</em>, <b>73</b>, 1--52.</p>
<h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
<pre class="examples"><div class='input'><span class='co'>### load data</span>
<span class='no'>dat</span> <span class='kw'><-</span> <span class='fu'>get</span>(<span class='fu'>data</span>(<span class='no'>dat.konstantopoulos2011</span>))
<span class='co'>### regular random-effects model</span>
<span class='no'>res</span> <span class='kw'><-</span> <span class='fu'><a href='rma.uni.html'>rma</a></span>(<span class='no'>yi</span>, <span class='no'>vi</span>, <span class='kw'>data</span><span class='kw'>=</span><span class='no'>dat</span>)
<span class='fu'>print</span>(<span class='no'>res</span>, <span class='kw'>digits</span><span class='kw'>=</span><span class='fl'>3</span>)</div><div class='output co'>#>
#> Random-Effects Model (k = 56; tau^2 estimator: REML)
#>
#> tau^2 (estimated amount of total heterogeneity): 0.088 (SE = 0.020)
#> tau (square root of estimated tau^2 value): 0.297
#> I^2 (total heterogeneity / total variability): 94.70%
#> H^2 (total variability / sampling variability): 18.89
#>
#> Test for Heterogeneity:
#> Q(df = 55) = 578.864, p-val < .001
#>
#> Model Results:
#>
#> estimate se zval pval ci.lb ci.ub
#> 0.128 0.044 2.916 0.004 0.042 0.214 **
#>
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> </div><div class='input'>
<span class='co'>### regular random-effects model using rma.mv()</span>
<span class='no'>res</span> <span class='kw'><-</span> <span class='fu'><a href='rma.mv.html'>rma.mv</a></span>(<span class='no'>yi</span>, <span class='no'>vi</span>, <span class='kw'>random</span> <span class='kw'>=</span> ~ <span class='fl'>1</span> <span class='kw'>|</span> <span class='no'>study</span>, <span class='kw'>data</span><span class='kw'>=</span><span class='no'>dat</span>)
<span class='fu'>print</span>(<span class='no'>res</span>, <span class='kw'>digits</span><span class='kw'>=</span><span class='fl'>3</span>)</div><div class='output co'>#>
#> Multivariate Meta-Analysis Model (k = 56; method: REML)
#>
#> Variance Components:
#>
#> estim sqrt nlvls fixed factor
#> sigma^2 0.088 0.297 56 no study
#>
#> Test for Heterogeneity:
#> Q(df = 55) = 578.864, p-val < .001
#>
#> Model Results:
#>
#> estimate se zval pval ci.lb ci.ub
#> 0.128 0.044 2.916 0.004 0.042 0.214 **
#>
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> </div><div class='input'>
<span class='co'>### multilevel random-effects model</span>
<span class='no'>res.ml</span> <span class='kw'><-</span> <span class='fu'><a href='rma.mv.html'>rma.mv</a></span>(<span class='no'>yi</span>, <span class='no'>vi</span>, <span class='kw'>random</span> <span class='kw'>=</span> ~ <span class='fl'>1</span> <span class='kw'>|</span> <span class='no'>district</span>/<span class='no'>school</span>, <span class='kw'>data</span><span class='kw'>=</span><span class='no'>dat</span>)
<span class='fu'>print</span>(<span class='no'>res.ml</span>, <span class='kw'>digits</span><span class='kw'>=</span><span class='fl'>3</span>)</div><div class='output co'>#>
#> Multivariate Meta-Analysis Model (k = 56; method: REML)
#>
#> Variance Components:
#>
#> estim sqrt nlvls fixed factor
#> sigma^2.1 0.065 0.255 11 no district
#> sigma^2.2 0.033 0.181 56 no district/school
#>
#> Test for Heterogeneity:
#> Q(df = 55) = 578.864, p-val < .001
#>
#> Model Results:
#>
#> estimate se zval pval ci.lb ci.ub
#> 0.185 0.085 2.185 0.029 0.019 0.350 *
#>
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> </div><div class='input'>
<span class='co'>### profile variance components</span>
<span class='fu'>profile</span>(<span class='no'>res.ml</span>, <span class='kw'>progbar</span><span class='kw'>=</span><span class='fl'>FALSE</span>)</div><div class='img'><img src='dat.konstantopoulos2011-1.png' alt='' width='768' height='614' /></div><div class='img'><img src='dat.konstantopoulos2011-2.png' alt='' width='768' height='614' /></div><div class='input'>
<span class='co'>### multivariate parameterization of the model</span>
<span class='no'>res.mv</span> <span class='kw'><-</span> <span class='fu'><a href='rma.mv.html'>rma.mv</a></span>(<span class='no'>yi</span>, <span class='no'>vi</span>, <span class='kw'>random</span> <span class='kw'>=</span> ~ <span class='fu'>factor</span>(<span class='no'>school</span>) <span class='kw'>|</span> <span class='no'>district</span>, <span class='kw'>data</span><span class='kw'>=</span><span class='no'>dat</span>)
<span class='fu'>print</span>(<span class='no'>res.mv</span>, <span class='kw'>digits</span><span class='kw'>=</span><span class='fl'>3</span>)</div><div class='output co'>#>
#> Multivariate Meta-Analysis Model (k = 56; method: REML)
#>
#> Variance Components:
#>
#> outer factor: district (nlvls = 11)
#> inner factor: factor(school) (nlvls = 11)
#>
#> estim sqrt fixed
#> tau^2 0.098 0.313 no
#> rho 0.665 no
#>
#> Test for Heterogeneity:
#> Q(df = 55) = 578.864, p-val < .001
#>
#> Model Results:
#>
#> estimate se zval pval ci.lb ci.ub
#> 0.185 0.085 2.185 0.029 0.019 0.350 *
#>
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> </div><div class='input'>
<span class='co'>### tau^2 from multivariate model = sum of the two variance components from the multilevel model</span>
<span class='fu'>round</span>(<span class='fu'>sum</span>(<span class='no'>res.ml</span>$<span class='no'>sigma2</span>), <span class='fl'>3</span>)</div><div class='output co'>#> [1] 0.098</div><div class='input'>
<span class='co'>### rho from multivariate model = intraclass correlation coefficient based on the multilevel model</span>
<span class='fu'>round</span>(<span class='no'>res.ml</span>$<span class='no'>sigma2</span>[<span class='fl'>1</span>] / <span class='fu'>sum</span>(<span class='no'>res.ml</span>$<span class='no'>sigma2</span>), <span class='fl'>3</span>)</div><div class='output co'>#> [1] 0.665</div></pre>
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<h2>Contents</h2>
<ul class="nav nav-pills nav-stacked">
<li><a href="#format">Format</a></li>
<li><a href="#details">Details</a></li>
<li><a href="#source">Source</a></li>
<li><a href="#references">References</a></li>
<li><a href="#examples">Examples</a></li>
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