fixing the site
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<div id="updated">Updated: 2025-12-28 Sun 19:48</div>
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</div>
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<h1 class="title">ise<sub>week</sub><sub>7</sub></h1>
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<div class="title-metadata">
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<span class="metadata-item">
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<span class="metadata-label">planted:</span>
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<span class="metadata-value">2025-03-31</span>
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</span>
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<span class="metadata-item">
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<span class="metadata-label">last tended to:</span>
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<span class="metadata-value">2025-12-28</span>
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</span>
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</div>
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</div>
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<div id="outline-container-orgf4f7db0" class="outline-2">
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<h2 id="orgf4f7db0"><a href="#orgf4f7db0"><span class="done DONE">DONE</span> Statistical Test Selection and Use (pages 21-67)</a></h2>
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</div>
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<div id="outline-container-org1c8d9c0" class="outline-2">
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<h2 id="org1c8d9c0"><a href="#org1c8d9c0">7.1 Comparing Algorithms in Intelligent Software Engineering</a></h2>
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<div class="outline-text-2" id="text-org1c8d9c0">
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</div>
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||||
<div id="outline-container-org6f86e3e" class="outline-3">
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||||
<h3 id="org6f86e3e"><a href="#org6f86e3e">1. Motivation</a></h3>
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||||
<div class="outline-text-3" id="text-org6f86e3e">
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<ul class="org-ul">
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<li>Algorithms and configurations vary in performance.</li>
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<li>No universally best algorithm: performance depends on the specific problem (“No Free Lunch” theorem).</li>
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<li>To determine which algorithm/configuration is suitable, <b><b>comparison is essential</b></b>.</li>
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<li>However, comparison is challenging due to the <b><b>stochastic nature</b></b> of computational intelligence algorithms.</li>
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</ul>
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</div>
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</div>
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<div id="outline-container-org0072836" class="outline-3">
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<h3 id="org0072836"><a href="#org0072836">2. Stochastic Behaviour in Algorithms</a></h3>
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<div class="outline-text-3" id="text-org0072836">
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<ul class="org-ul">
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||||
<li>Sources of randomness:
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<ul class="org-ul">
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<li>In the algorithm (e.g., random initial population, stochastic gradient descent, mutation/crossover probabilities).</li>
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<li>In data sampling.</li>
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||||
</ul></li>
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||||
<li>Result: Running the same algorithm multiple times on the same problem yields <b><b>different results</b></b>.</li>
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<li>Therefore, comparisons must account for this randomness.</li>
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</ul>
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</div>
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</div>
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<div id="outline-container-org2578b69" class="outline-3">
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<h3 id="org2578b69"><a href="#org2578b69">3. Handling Stochastic Behaviour</a></h3>
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<div class="outline-text-3" id="text-org2578b69">
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||||
<ul class="org-ul">
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||||
<li>To compare algorithms meaningfully:
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||||
<ul class="org-ul">
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||||
<li>Run each algorithm <b><b>multiple times</b></b> (e.g., 30+ runs) using <b><b>different random seeds</b></b>.</li>
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||||
<li>This helps capture typical performance and reduce reliance on single-run outliers.</li>
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</ul></li>
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||||
</ul>
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||||
</div>
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||||
</div>
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||||
<div id="outline-container-orge1c8339" class="outline-3">
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||||
<h3 id="orge1c8339"><a href="#orge1c8339">4. Methods for Comparison</a></h3>
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||||
<div class="outline-text-3" id="text-orge1c8339">
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||||
</div>
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||||
<div id="outline-container-org72d5d0f" class="outline-4">
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||||
<h4 id="org72d5d0f"><a href="#org72d5d0f">a. Mean (Average)</a></h4>
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||||
<div class="outline-text-4" id="text-org72d5d0f">
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||||
<ul class="org-ul">
|
||||
<li>Simple and common.</li>
|
||||
<li>Problems:
|
||||
<ul class="org-ul">
|
||||
<li>Sensitive to <b><b>outliers</b></b>.</li>
|
||||
<li>Does not represent <b><b>variability</b></b> in results.</li>
|
||||
</ul></li>
|
||||
</ul>
|
||||
</div>
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||||
</div>
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||||
<div id="outline-container-orgdf083a9" class="outline-4">
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||||
<h4 id="orgdf083a9"><a href="#orgdf083a9">b. Mean + Standard Deviation</a></h4>
|
||||
<div class="outline-text-4" id="text-orgdf083a9">
|
||||
<ul class="org-ul">
|
||||
<li>Adds information about variation.</li>
|
||||
<li>Still affected by outliers.</li>
|
||||
<li>Hard to tell whether differences are statistically significant.</li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
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||||
<div id="outline-container-org0abd1f5" class="outline-4">
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||||
<h4 id="org0abd1f5"><a href="#org0abd1f5">c. Median</a></h4>
|
||||
<div class="outline-text-4" id="text-org0abd1f5">
|
||||
<ul class="org-ul">
|
||||
<li>More robust to outliers.</li>
|
||||
<li>Example:
|
||||
<ul class="org-ul">
|
||||
<li>Sorted list: 0.000001, 0.6, 0.62, 0.65, 0.7, 0.75, 0.8, 0.8, 0.81</li>
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||||
<li>Median = 0.7</li>
|
||||
</ul></li>
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||||
<li>Problem: Ignores <b><b>variation</b></b> in data.</li>
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||||
</ul>
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||||
</div>
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||||
</div>
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||||
<div id="outline-container-orgbad24f4" class="outline-4">
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||||
<h4 id="orgbad24f4"><a href="#orgbad24f4">d. Median + Quartiles</a></h4>
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||||
<div class="outline-text-4" id="text-orgbad24f4">
|
||||
<ul class="org-ul">
|
||||
<li>1st and 3rd quartiles provide information about data spread.</li>
|
||||
<li>Still doesn’t guarantee ability to distinguish between groups.</li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
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||||
<div id="outline-container-orgacd9171" class="outline-4">
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||||
<h4 id="orgacd9171"><a href="#orgacd9171">e. Statistical Hypothesis Testing</a></h4>
|
||||
<div class="outline-text-4" id="text-orgacd9171">
|
||||
<ul class="org-ul">
|
||||
<li>Scientific method to determine if observed differences are <b><b>statistically significant</b></b>.</li>
|
||||
<li>Necessary for robust and credible comparison of algorithms.</li>
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||||
</ul>
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||||
</div>
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||||
</div>
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||||
</div>
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||||
<div id="outline-container-orgc4650f0" class="outline-3">
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||||
<h3 id="orgc4650f0"><a href="#orgc4650f0">5. Statistical Hypothesis Testing: Process</a></h3>
|
||||
<div class="outline-text-3" id="text-orgc4650f0">
|
||||
<ol class="org-ol">
|
||||
<li>Define what to compare (e.g., accuracy or fitness).</li>
|
||||
<li>Ensure fair comparison:
|
||||
<ul class="org-ul">
|
||||
<li>Equal number of evaluations or explain why not.</li>
|
||||
<li>Example: Adjust generations to equate computational budget across algorithms.</li>
|
||||
</ul></li>
|
||||
<li>Formulate hypotheses:
|
||||
<ul class="org-ul">
|
||||
<li><b><b>Null hypothesis (H₀)</b></b>: No difference between the two groups.</li>
|
||||
<li><b><b>Alternative hypothesis (H₁)</b></b>: A statistically significant difference exists.</li>
|
||||
</ul></li>
|
||||
<li>Select an appropriate test based on data distribution.</li>
|
||||
</ol>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-org4eb637a" class="outline-3">
|
||||
<h3 id="org4eb637a"><a href="#org4eb637a">6. Choosing the Test</a></h3>
|
||||
<div class="outline-text-3" id="text-org4eb637a">
|
||||
</div>
|
||||
<div id="outline-container-org80e038a" class="outline-4">
|
||||
<h4 id="org80e038a"><a href="#org80e038a">a. Normality Assumption</a></h4>
|
||||
<div class="outline-text-4" id="text-org80e038a">
|
||||
<ul class="org-ul">
|
||||
<li>Many statistical tests assume a <b><b>normal distribution</b></b> of values.</li>
|
||||
<li>Visual inspection or tests (e.g., Shapiro-Wilk) can check this.</li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-org9158ad5" class="outline-4">
|
||||
<h4 id="org9158ad5"><a href="#org9158ad5">b. Parametric vs Non-parametric Tests</a></h4>
|
||||
<div class="outline-text-4" id="text-org9158ad5">
|
||||
<ul class="org-ul">
|
||||
<li>Parametric tests (e.g., t-test):
|
||||
<ul class="org-ul">
|
||||
<li>More powerful.</li>
|
||||
<li>Require assumptions (e.g., normality, homogeneity of variance).</li>
|
||||
</ul></li>
|
||||
<li>Non-parametric tests (e.g., Wilcoxon, Mann-Whitney):
|
||||
<ul class="org-ul">
|
||||
<li>Safer for non-normal data.</li>
|
||||
<li>Widely used in stochastic algorithm comparisons.</li>
|
||||
</ul></li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-org17604cb" class="outline-4">
|
||||
<h4 id="org17604cb"><a href="#org17604cb">c. Paired vs Unpaired Tests</a></h4>
|
||||
<div class="outline-text-4" id="text-org17604cb">
|
||||
<ul class="org-ul">
|
||||
<li><b><b>Paired</b></b>: Use when comparing results from same initial conditions.</li>
|
||||
<li><b><b>Unpaired</b></b>: Use when runs are completely independent.</li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-org97b2589" class="outline-3">
|
||||
<h3 id="org97b2589"><a href="#org97b2589">7. Test Outputs</a></h3>
|
||||
<div class="outline-text-3" id="text-org97b2589">
|
||||
<ul class="org-ul">
|
||||
<li>Test produces a <b><b>statistic</b></b> and a <b><b>p-value</b></b>.
|
||||
<ul class="org-ul">
|
||||
<li>If <b><b>p ≤ 0.05</b></b>, reject H₀: significant difference exists.</li>
|
||||
<li>If <b><b>p > 0.05</b></b>, do not reject H₀: no significant difference found.</li>
|
||||
</ul></li>
|
||||
<li>Significance level is usually set to <b><b>0.05</b></b>, corresponding to 95% confidence.</li>
|
||||
<li>Lower significance (e.g., 0.01) may be used in critical applications.</li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-org9186d09" class="outline-3">
|
||||
<h3 id="org9186d09"><a href="#org9186d09">8. Interpreting P-Values</a></h3>
|
||||
<div class="outline-text-3" id="text-org9186d09">
|
||||
<ul class="org-ul">
|
||||
<li>High p-value → Observed difference likely due to chance → <b><b>Do not reject H₀</b></b>.</li>
|
||||
<li>Low p-value → Observed difference unlikely due to chance → <b><b>Reject H₀</b></b>.</li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-org2a33cb7" class="outline-3">
|
||||
<h3 id="org2a33cb7"><a href="#org2a33cb7">9. Test Examples (in R)</a></h3>
|
||||
<div class="outline-text-3" id="text-org2a33cb7">
|
||||
<ul class="org-ul">
|
||||
<li>Two-tailed Wilcoxon Rank-Sum Test (unpaired).</li>
|
||||
<li>Two-tailed Wilcoxon Signed-Rank Test (paired).</li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-org8176556" class="outline-3">
|
||||
<h3 id="org8176556"><a href="#org8176556">10. Multiple Comparisons Problem</a></h3>
|
||||
<div class="outline-text-3" id="text-org8176556">
|
||||
<ul class="org-ul">
|
||||
<li>Comparing many algorithms or configurations increases the risk of <b><b>Type I errors</b></b> (false positives).</li>
|
||||
<li>Correction methods:
|
||||
<ul class="org-ul">
|
||||
<li>Adjust the significance threshold (e.g., Bonferroni correction).</li>
|
||||
<li>Downside: Conservative → <b><b>reduced power</b></b> (risk of missing real differences).</li>
|
||||
</ul></li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-orgb3365b9" class="outline-3">
|
||||
<h3 id="orgb3365b9"><a href="#orgb3365b9">11. Tests for N Groups</a></h3>
|
||||
<div class="outline-text-3" id="text-orgb3365b9">
|
||||
<ul class="org-ul">
|
||||
<li>Stronger than multiple pairwise tests with correction.</li>
|
||||
<li>Common tests:
|
||||
<ul class="org-ul">
|
||||
<li><b><b>Kruskal-Wallis Test</b></b>: for unpaired comparisons across groups.</li>
|
||||
<li><b><b>Friedman Test</b></b>: for paired comparisons across groups.</li>
|
||||
</ul></li>
|
||||
</ul>
|
||||
</div>
|
||||
<div id="outline-container-org09587aa" class="outline-4">
|
||||
<h4 id="org09587aa"><a href="#org09587aa">Post-hoc Analysis</a></h4>
|
||||
<div class="outline-text-4" id="text-org09587aa">
|
||||
<ul class="org-ul">
|
||||
<li>Needed when the global test finds significant differences but doesn’t specify <b><b>which pairs</b></b> differ.
|
||||
<ul class="org-ul">
|
||||
<li>Kruskal-Wallis → Dunn post-hoc test.</li>
|
||||
<li>Friedman → Nemenyi post-hoc test.</li>
|
||||
</ul></li>
|
||||
</ul>
|
||||
|
||||
|
||||
<p class="backlinks-section" id="backlinks">
|
||||
Backlinks
|
||||
</p>
|
||||
<ul class="org-ul backlinks-list">
|
||||
<li><a href="20250329114733-ise.html#ID-c69e4c4d-2fb4-4cf1-a835-a235cf6db8e9">ise</a></li>
|
||||
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|
||||
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|
||||
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|
||||
</div>
|
||||
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|
||||
</div>
|
||||
</div></article></div></div>
|
||||
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|
||||
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|
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Reference in New Issue
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