Fix notched box autorange

src/traces/box/attributes.js

@@ -100,7 +100,12 @@ module.exports = {
         role: 'style',
         editType: 'calc',
         description: [
-            'Determines whether or not notches should be drawn.'
+            'Determines whether or not notches are drawn.',
+            'Notches displays a confidence interval around the median.',
+            'We compute the confidence interval as median +/- 1.57 / IQR * sqrt(N),',
+            'where IQR is the interquartile range and N is the sample size.',
+            'If two boxes\' notches do not overlap there is 95% confidence their medians differ.',
+            'See https://sites.google.com/site/davidsstatistics/home/notched-box-plots for more info.'
         ].join(' ')
     },
     notchwidth: {

src/traces/box/calc.js

@@ -69,6 +69,9 @@ module.exports = function calc(gd, trace) {
         Lib.identity :
         function(pt) { return (pt.v < cdi.lf || pt.v > cdi.uf); };
 
+    var minLowerNotch = Infinity;
+    var maxUpperNotch = -Infinity;
+
     // build calcdata trace items, one item per distinct position
     for(i = 0; i < pLen; i++) {
         if(ptsPerBin[i].length > 0) {
@@ -123,6 +126,8 @@ module.exports = function calc(gd, trace) {
             var mci = 1.57 * iqr / Math.sqrt(bvLen);
             cdi.ln = cdi.med - mci;
             cdi.un = cdi.med + mci;
+            minLowerNotch = Math.min(minLowerNotch, cdi.ln);
+            maxUpperNotch = Math.max(maxUpperNotch, cdi.un);
 
             cdi.pts2 = pts.filter(ptFilterFn);
 
@@ -131,8 +136,11 @@ module.exports = function calc(gd, trace) {
     }
 
     calcSelection(cd, trace);
-    var extremes = Axes.findExtremes(valAxis, val, {padded: true});
-    trace._extremes[valAxis._id] = extremes;
+
+    trace._extremes[valAxis._id] = Axes.findExtremes(valAxis,
+        trace.notched ? val.concat([minLowerNotch, maxUpperNotch]) : val,
+        {padded: true}
+    );
 
     if(cd.length > 0) {
         cd[0].t = {

test/image/mocks/box_notched-inverted-end.json

@@ -0,0 +1,36 @@
+{
+  "data": [
+    {
+      "x": [113.35, 29.54, 21.7, 113.35, 29.54, 21.7],
+      "name": "[113.35,29.54,21.7,113.35,29.54,21.7]",
+      "type": "box",
+      "notched": true
+    },
+    {
+      "x": [39.4, 88.63, 39.4, 88.63],
+      "name": "[39.4,88.63,39.4,88.63]",
+      "type": "box",
+      "notched": true
+    }
+  ],
+  "layout": {
+    "title": {
+      "text": "Samples where the confidence interval<br>median ± 1.57 / IQR * sqrt(N)<br>go beyond the fences",
+      "x": 0.02
+    },
+    "xaxis": {
+      "showline": true,
+      "mirror": true,
+      "zeroline": false
+    },
+    "yaxis": {
+      "showline": true,
+      "mirror": true,
+      "zeroline": false
+    },
+    "showlegend": false,
+    "margin": {"l": 220, "b": 20, "r": 20},
+    "width": 600,
+    "height": 300
+  }
+}