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40 changes: 20 additions & 20 deletions docs/semuahalaman/modulprak/2024/ganjil/psd/modul9.html
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<meta name="dcterms.date" content="2024-11-25">
<meta name="description" content="Offline di Departemen Matematika">

<title>(Pertemuan 09) ANOVA dan Chi-Squared – Lab Praktikum Departemen Matematika FMIPA UI</title>
<title>(Pertemuan 09) ANOVA dan Uji Chi-Squared – Lab Praktikum Departemen Matematika FMIPA UI</title>
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<header id="title-block-header" class="quarto-title-block default">
<div class="quarto-title">
<h1 class="title">(Pertemuan 09) ANOVA dan Chi-Squared</h1>
<p class="subtitle lead">ANOVA and Chi-Squared</p>
<h1 class="title">(Pertemuan 09) ANOVA dan Uji Chi-Squared</h1>
<p class="subtitle lead">ANOVA and Chi-Squared Test</p>
</div>

<div>
Expand Down Expand Up @@ -274,9 +274,9 @@ <h2 class="anchored" data-anchor-id="ukuran-sampel-seragam">Ukuran Sampel Seraga
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a> <span class="cf">function</span>(x) <span class="fu">c</span>(<span class="at">mean =</span> <span class="fu">mean</span>(x),<span class="at">sd =</span> <span class="fu">sd</span>(x)))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code> pop.source pops.value.mean pops.value.sd
1 pops.1 1.0025509 1.1154917
2 pops.2 1.3577494 0.9804963
3 pops.3 0.8434632 0.8088781</code></pre>
1 pops.1 0.7641406 0.9870588
2 pops.2 0.9432723 1.2528974
3 pops.3 0.8596178 0.6817645</code></pre>
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<div class="cell">
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One-way analysis of means

data: pops.value and pop.source
F = 0.72722, num df = 2, denom df = 27, p-value = 0.4925</code></pre>
F = 0.080101, num df = 2, denom df = 27, p-value = 0.9232</code></pre>
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</div>
<p>Fungsi lain yang dapat digunakan adalah aov()</p>
Expand All @@ -314,8 +314,8 @@ <h2 class="anchored" data-anchor-id="ukuran-sampel-seragam">Ukuran Sampel Seraga
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(av)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<pre><code> Df Sum Sq Mean Sq F value Pr(&gt;F)
pop.source 2 1.387 0.6933 0.727 0.492
Residuals 27 25.740 0.9533 </code></pre>
pop.source 2 0.161 0.0803 0.08 0.923
Residuals 27 27.080 1.0029 </code></pre>
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</div>
<p>Ingat lagi bahwa daerah kritis uji ANOVA adalah:</p>
Expand Down Expand Up @@ -366,16 +366,16 @@ <h2 class="anchored" data-anchor-id="ukuran-sampel-tidak-seragam">Ukuran Sampel
One-way analysis of means

data: pops.value and pop.source
F = 0.98669, num df = 2, denom df = 31, p-value = 0.3842</code></pre>
F = 0.4461, num df = 2, denom df = 31, p-value = 0.6442</code></pre>
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</div>
<div class="cell">
<div class="sourceCode cell-code" id="cb15"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a>av <span class="ot">&lt;-</span> <span class="fu">aov</span>(pops.value <span class="sc">~</span> pop.source, <span class="at">data =</span> data)</span>
<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(av)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<pre><code> Df Sum Sq Mean Sq F value Pr(&gt;F)
pop.source 2 2.17 1.085 0.987 0.384
Residuals 31 34.09 1.100 </code></pre>
pop.source 2 0.511 0.2556 0.446 0.644
Residuals 31 17.764 0.5730 </code></pre>
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</div>
<p>Ingat lagi bahwa daerah kritis uji ANOVA adalah:</p>
Expand Down Expand Up @@ -444,10 +444,10 @@ <h3 class="anchored" data-anchor-id="menggunakan-statistik-uji">Menggunakan stat
<span id="cb24-2"><a href="#cb24-2" aria-hidden="true" tabindex="-1"></a>dadu <span class="ot">&lt;-</span> <span class="fu">ceiling</span>(<span class="fu">runif</span>(<span class="at">n=</span>n_dadu, <span class="at">min =</span> <span class="dv">0</span>, <span class="at">max=</span><span class="dv">6</span>))</span>
<span id="cb24-3"><a href="#cb24-3" aria-hidden="true" tabindex="-1"></a>dadu</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code> [1] 2 2 5 6 3 2 3 4 3 4 5 3 4 4 4 1 4 4 1 5 1 6 3 1 4 4 1 2 3 5 5 5 2 6 3 4 1
[38] 1 2 3 5 6 1 5 3 2 6 5 3 2 5 5 2 6 5 2 6 1 5 6 2 6 5 6 4 6 3 4 4 4 3 5 1 3
[75] 2 2 3 5 2 6 3 3 5 5 4 2 4 2 1 6 1 4 3 1 3 1 2 6 4 6 1 6 2 1 1 2 3 3 4 5 1
[112] 1 6 6 5 4 4 4 2 5</code></pre>
<pre><code> [1] 2 6 5 4 6 6 1 2 3 4 3 5 5 6 6 5 1 5 3 5 5 5 5 6 5 2 4 5 1 5 2 3 6 3 3 5 6
[38] 3 6 6 2 4 1 4 6 3 2 3 1 6 2 6 5 4 3 4 2 5 6 6 5 4 3 1 5 3 6 1 6 4 2 4 1 4
[75] 4 6 1 4 2 5 2 5 6 1 2 4 4 6 3 1 4 3 4 6 5 6 6 2 2 6 2 1 2 4 2 6 4 6 3 2 3
[112] 1 6 4 1 4 3 1 4 3</code></pre>
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<p>Dengan cara yang sama, kita dapat melakukan uji chi-squared</p>
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Chi-squared test for given probabilities

data: dadu
X-squared = 95.429, df = 119, p-value = 0.945</code></pre>
X-squared = 91.725, df = 119, p-value = 0.97</code></pre>
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<p>Terdapat pesan “Warning: Chi-squared approximation may be incorrect”. Hal ini terjadi karena terdapat beberapa pengulangan nilai pada ruang sampel, di mana masing-masing nilai tersebut dianggap sebagai observasi independen yang memiliki probabilitas <span class="math inline">\(\frac{1}{120}\)</span>. Sedangkan, kita ingin menguji apakah peluang masing-masing mata dadu muncul bernilai <span class="math inline">\(\frac{1}{6}\)</span>.</p>
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<div class="cell-output cell-output-stdout">
<pre><code>dadu
1 2 3 4 5 6
19 20 20 22 21 18 </code></pre>
15 18 18 22 20 27 </code></pre>
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</div>
<p>Maka, kita dapat melakukan uji chi-squared tanpa menggunakan fungsi chisq.test()</p>
Expand All @@ -488,7 +488,7 @@ <h3 class="anchored" data-anchor-id="menggunakan-statistik-uji">Menggunakan stat
<div class="cell-output cell-output-stdout">
<pre><code> [,1] [,2] [,3] [,4] [,5] [,6]
val.dadu "1" "2" "3" "4" "5" "6"
obs.dadu "19" "20" "20" "22" "21" "18"
obs.dadu "15" "18" "18" "22" "20" "27"
ex.dadu "20" "20" "20" "20" "20" "20"</code></pre>
</div>
</div>
Expand All @@ -503,7 +503,7 @@ <h3 class="anchored" data-anchor-id="menggunakan-statistik-uji">Menggunakan stat
<div class="sourceCode cell-code" id="cb33"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb33-1"><a href="#cb33-1" aria-hidden="true" tabindex="-1"></a>chi.hitung <span class="ot">&lt;-</span> <span class="fu">sum</span>((obs.dadu<span class="sc">-</span>ex.dadu)<span class="sc">**</span><span class="dv">2</span><span class="sc">/</span>ex.dadu)</span>
<span id="cb33-2"><a href="#cb33-2" aria-hidden="true" tabindex="-1"></a>chi.hitung</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code>[1] 0.5</code></pre>
<pre><code>[1] 4.3</code></pre>
</div>
</div>
<p>dan <span class="math inline">\(\chi^2_{\alpha, k-1}\)</span></p>
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4 changes: 2 additions & 2 deletions docs/semuahalaman/modulprak/2024/ganjil/psd/psd2024.html
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<a href="../../../../../semuahalaman/modulprak/2024/ganjil/psd/modul9.html" class="quarto-grid-link">
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<h5 class="no-anchor card-title listing-title">
(Pertemuan 09) ANOVA dan Chi-Squared
(Pertemuan 09) ANOVA dan Uji Chi-Squared
</h5>
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2 changes: 1 addition & 1 deletion semuahalaman/modulprak/2024/ganjil/psd/modul8.qmd
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---
title: "(Pertemuan 8) Pengujian Hipotesis Menggunakan R"
title: "(Pertemuan 08) Pengujian Hipotesis Menggunakan R"
subtitle: "Hypothesis Testing in R"
description: "Offline di Departemen Matematika"
date: 11/18/2024
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