https://openmetaanalysis.github.io/voting/

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113	  <h1>openMetaAnalysis: <span style="font-size:50%">collaborative and continuous</span></h1>
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123	<li><a href="https://openmetaanalysis.github.io/arrows_plot/" class="menuitem">Arrows plot</a></li>
124 	<li><a href="https://openmetaanalysis.github.io/votinb/" class="menuitem">Vote counting</a></li>
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132<div style="clear:both">&nbsp;</div>
133
134	<div><span style="font-weight:bold">Vote counting:</span></div> 
135	<div>&nbsp;</div>
136<h3>Vote Counting with the Binomial Test and Wilson Confidence Interval Calculator</h3>
137
138<label for="successes">Successes:</label>
139<input type="number" id="successes"s value="10" min="0"><br>
140
141<label for="trials">Trials:</label>
142<input type="number" id="trials" value="12" min="1"><br><br>
143	<div>Replace these values with yours. Per the Cochrane reference below, "For each study, the effect is categorized as beneficial or harmful based on the direction of effect" (eg, statistical significance is not required)</div>
144      <div>Suggested summary of the results as stated by the Cochrane (reference below): "‘There was evidence that midwife-led models of care had an effect on satisfaction, with 10 of 12 studies favouring the intervention (83% (95% CI 55% to 95%), P = 0.039)"</div>
145<button onclick="calculateCI()">Calculate</button>
146
147<p id="output"></p>
148

149<script>
150function calculateCI() {
151    const successes = parseInt(document.getElementById('successes').value);
152    const trials = parseInt(document.getElementById('trials').value);
153    const alpha = 0.05;
154
155    // Exact binomial (Clopper-Pearson)
156    const lowerExact = jStat.beta.inv(alpha / 2, successes, trials - successes + 1);
157    const upperExact = jStat.beta.inv(1 - alpha / 2, successes + 1, trials - successes);
158
159    // Wilson Score interval
160    const z = jStat.normal.inv(1 - alpha / 2, 0, 1);
161    const p = successes / trials;
162    const denominator = 1 + (z * z / trials);
163    const centreAdjustedProb = p + (z * z / (2 * trials));
164    const adjustedStdError = Math.sqrt((p * (1 - p) + z * z / (4 * trials)) / trials);
165
166    const lowerWilson = (centreAdjustedProb - z * adjustedStdError) / denominator;
167    const upperWilson = (centreAdjustedProb + z * adjustedStdError) / denominator;
168
169    // Binomial exact p-value (two-sided)
170    const pValue = 2 * Math.min(
171        jStat.binomial.cdf(successes, trials, 0.5),
172        1 - jStat.binomial.cdf(successes - 1, trials, 0.5)
173    );
174
175    // Output results
176    const result = `<strong>Exact Binomial (Clopper-Pearson) CI:</strong> ${(lowerExact * 100).toFixed(1)}% to ${(upperExact * 100).toFixed(1)}%<br>
177                    <strong>Wilson Score CI:</strong> ${(lowerWilson * 100).toFixed(1)}% to ${(upperWilson * 100).toFixed(1)}% (used by the Cochrane Collaboration in <a href=\"https://training.cochrane.org/handbook/current/chapter-12#_Ref524789667\">their example</a>)<br>
178                    <strong>Exact Binomial P-value:</strong> ${pValue.toFixed(3)}`;
179
180    document.getElementById('output').innerHTML = result;
181}
182
183// Initial calculation
184calculateCI();
185</script>

185
186	    
187<h3>References</h3>
188<div>
189<ol>
190<li>McKenzie JE, Brennan SE. <a href="https://training.cochrane.org/handbook/current/chapter-12#_Ref524789667">Chapter 12: Synthesizing and presenting findings using other methods</a> [last updated October 2019]. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.5. Cochrane, 2024.</li>
191<li>Boon. The effect directon plot revisited. Res Synth Methods. 2020. DOI: <a href="https://doi.org/10.1002/jrsm.1458">10.1002/jrsm.1458</a></li>
192</ol>
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