Meta-analysis
<span class="n">library</span><span class="p">(</span><span class="n">dplyr</span><span class="p">)</span><span class="w"> </span><span class="c1"># data manipulation</span><span class="w">
</span><span class="n">library</span><span class="p">(</span><span class="n">ggplot2</span><span class="p">)</span><span class="w"> </span><span class="c1"># visualizations</span><span class="w">
</span><span class="n">library</span><span class="p">(</span><span class="n">metafor</span><span class="p">)</span><span class="w"> </span><span class="c1"># ready-made meta-analysis code</span><span class="w">
</span><span class="n">library</span><span class="p">(</span><span class="n">gt</span><span class="p">)</span><span class="w"> </span><span class="c1"># nice tables</span><span class="w">
</span>
Basic principle
Scientific question
Does playing Mozart to newborns improves their IQ?
You look a bit around and find 3 studies :
<span class="n">etudes</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">data.frame</span><span class="p">(</span><span class="w">
</span><span class="n">article</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nf">c</span><span class="p">(</span><span class="s2">"A"</span><span class="p">,</span><span class="s2">"B"</span><span class="p">,</span><span class="s2">"C"</span><span class="p">),</span><span class="w">
</span><span class="n">y</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nf">c</span><span class="p">(</span><span class="m">0.5</span><span class="p">,</span><span class="w"> </span><span class="m">0.01</span><span class="p">,</span><span class="w"> </span><span class="m">-0.1</span><span class="p">),</span><span class="w"> </span><span class="c1"># 0 no effect, <0 negative effect, >0 positive effect</span><span class="w">
</span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nf">c</span><span class="p">(</span><span class="m">10</span><span class="p">,</span><span class="m">150</span><span class="p">,</span><span class="m">12</span><span class="p">),</span><span class="w">
</span><span class="n">v</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nf">c</span><span class="p">(</span><span class="m">0.04</span><span class="p">,</span><span class="m">0.01</span><span class="p">,</span><span class="w"> </span><span class="m">0.03</span><span class="p">)</span><span class="w"> </span><span class="c1"># variance</span><span class="w">
</span><span class="p">)</span><span class="w">
</span><span class="n">etudes</span><span class="w"> </span><span class="o">%>%</span><span class="w"> </span><span class="n">gt</span><span class="w">
</span>
article
y
n
v
A
0.50
10
0.04
B
0.01
150
0.01
C
-0.10
12
0.03
A simplistic way
<span class="n">etudes</span><span class="w"> </span><span class="o">%>%</span><span class="w">
</span><span class="n">summarise</span><span class="p">(</span><span class="w">
</span><span class="n">effet_resume</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mean</span><span class="p">(</span><span class="n">y</span><span class="p">)</span><span class="w">
</span><span class="p">)</span><span class="w">
</span>
effet_resume
1 0.1366667
Weighted mean
When we talk about mean, we usually refer to the arithmetic mean :
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