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kcormi committed Mar 21, 2024
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2 changes: 1 addition & 1 deletion part3/commonstatsmethods/index.html
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Expand Up @@ -2479,7 +2479,7 @@ <h2 id="goodness-of-fit-tests">Goodness of fit tests</h2>
<p><strong><code>AD</code></strong>: Compute a goodness-of-fit measure for binned fits using the <em>Anderson-Darling</em> test. It is based on the integral of the difference between the cumulative distribution function and the empirical distribution function over all bins. It also gives the tail ends of the distribution a higher weighting.</p>
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<p>The output tree will contain a branch called <strong><code>limit</code></strong>, which contains the value of the test statistic in each toy. You can make a histogram of this test statistic <span class="arithmatex">\(t\)</span>. From the distribution that is obtained in this way (<span class="arithmatex">\(f(t)\)</span>) and the single value obtained by running on the observed data (<span class="arithmatex">\(t_{0}\)</span>) you can calculate the p-value $$p = \int_{t=t_{0}}^{\mathrm{+inf}} f(t) dt $$. Note: in rare cases the test statistic value for the toys can be undefined (for AS and KD). In this case we set the test statistic value to -1. When plotting the test statistic distribution, those toys should be excluded. This is automatically taken care of if you use the GoF collection script in CombineHarvester, which is described below.</p>
<p>The output tree will contain a branch called <strong><code>limit</code></strong>, which contains the value of the test statistic in each toy. You can make a histogram of this test statistic <span class="arithmatex">\(t\)</span>. From the distribution that is obtained in this way (<span class="arithmatex">\(f(t)\)</span>) and the single value obtained by running on the observed data (<span class="arithmatex">\(t_{0}\)</span>) you can calculate the p-value <span class="arithmatex">\(p = \int_{t=t_{0}}^{\mathrm{+inf}} f(t) dt\)</span>. Note: in rare cases the test statistic value for the toys can be undefined (for AS and KD). In this case we set the test statistic value to -1. When plotting the test statistic distribution, those toys should be excluded. This is automatically taken care of if you use the GoF collection script in CombineHarvester, which is described below.</p>
<p>When generating toys, the default behavior will be used. See the section on <a href="http://cms-analysis.github.io/HiggsAnalysis-CombinedLimit/part3/runningthetool/#toy-data-generation">toy generation</a> for options that control how nuisance parameters are generated and fitted in these tests. It is recommended to use <em>frequentist toys</em> (<code>--toysFreq</code>) when running the <strong><code>saturated</code></strong> model, and the default toys for the other two tests.</p>
<p>Further goodness-of-fit methods could be added on request, especially if volunteers are available to code them.
The output limit tree will contain the value of the test statistic in each toy (or the data)</p>
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