statistical_inferences/sequential_testing_app_book.html at master · Lakens/statistical_inferences · GitHub

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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Sequential Testing Simulation</title>
<link rel="preconnect" href="https://fonts.googleapis.com">
<link href="https://fonts.googleapis.com/css2?family=Montserrat:wght@600&family=Open+Sans:ital,wght@0,400;0,600;1,400&family=Fira+Code&display=swap" rel="stylesheet">
<script src="https://cdnjs.cloudflare.com/ajax/libs/jstat/1.9.6/jstat.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/plotly.js/2.26.0/plotly.min.js"></script>
<style>
:root {
  --bg:     #fffafa;
  --bg2:    #f7f7f7;
  --ink:    #1c1717;
  --ink2:   #3d3535;
  --ink3:   #666060;
  --rule:   #d6dadc;
  --red:    #a60a0a;
  --red-l:  #c41010;
  --red-bg: #fff5f5;
}

*, *::before, *::after { box-sizing: border-box; margin: 0; padding: 0; }

body {
  background: var(--bg);
  color: var(--ink);
  font-family: 'Open Sans', sans-serif;
  font-size: 15px;
  line-height: 1.65;
  padding: 20px 20px 0;
  overflow: hidden;
}

.calc-label {
  font-family: 'Open Sans', sans-serif;
  font-size: 10px;
  font-weight: 600;
  letter-spacing: 0.18em;
  text-transform: uppercase;
  color: var(--ink3);
  margin-bottom: 5px;
}

.calc-heading {
  font-family: 'Montserrat', sans-serif;
  font-weight: 600;
  font-size: 1.1rem;
  color: var(--ink);
  margin-bottom: 16px;
  padding-bottom: 9px;
  border-bottom: 2px solid var(--red);
}

.input-panel {
  background: var(--bg2);
  border: 1px solid var(--rule);
  border-left: 3px solid var(--red);
  padding: 16px 18px;
  margin-bottom: 20px;
}

.input-grid {
  display: grid;
  grid-template-columns: 1fr 1fr 1fr;
  gap: 16px;
  align-items: end;
}

.input-group { display: flex; flex-direction: column; gap: 5px; }

.input-label {
  font-family: 'Open Sans', sans-serif;
  font-size: 10px;
  font-weight: 600;
  letter-spacing: 0.08em;
  text-transform: uppercase;
  color: var(--ink3);
}

.input-label .sym {
  font-style: italic;
  font-size: 0.88rem;
  text-transform: none;
  letter-spacing: 0;
  font-weight: 400;
  color: var(--red);
}

input[type="number"] {
  font-family: 'Fira Code', monospace;
  font-size: 13px;
  background: var(--bg);
  border: 1px solid var(--rule);
  border-bottom: 2px solid var(--red);
  padding: 6px 8px;
  color: var(--ink);
  outline: none;
  width: 100%;
  transition: border-color .2s;
}
input[type="number"]:focus { border-bottom-color: var(--red-l); }

input[type="range"] {
  -webkit-appearance: none;
  width: 100%;
  height: 2px;
  background: var(--rule);
  outline: none;
  cursor: pointer;
  border-radius: 1px;
  margin-top: 5px;
}
input[type="range"]::-webkit-slider-thumb {
  -webkit-appearance: none;
  width: 14px;
  height: 14px;
  border-radius: 50%;
  background: var(--bg);
  border: 2px solid var(--red);
  cursor: pointer;
  transition: transform .15s;
}
input[type="range"]::-webkit-slider-thumb:hover { transform: scale(1.25); }
input[type="range"]::-moz-range-thumb {
  width: 14px;
  height: 14px;
  border-radius: 50%;
  background: var(--bg);
  border: 2px solid var(--red);
  cursor: pointer;
}

.slider-value {
  font-family: 'Fira Code', monospace;
  font-size: 12px;
  color: var(--red);
  font-weight: 500;
}

.sim-btn {
  font-family: 'Montserrat', sans-serif;
  font-weight: 600;
  font-size: 0.85rem;
  letter-spacing: 0.06em;
  background: var(--red);
  color: #fff;
  border: none;
  padding: 10px 0;
  cursor: pointer;
  width: 100%;
  transition: background .15s;
}
.sim-btn:hover  { background: var(--red-l); }
.sim-btn:active { opacity: 0.82; }

.plot-wrap {
  margin-bottom: 18px;
  border: 1px solid var(--rule);
  background: var(--bg);
}
#seqPlot { width: 100%; height: 380px; }

.text-block {
  font-size: 0.9rem;
  line-height: 1.6;
  padding: 11px 14px;
  margin-bottom: 10px;
  background: var(--bg2);
  border-left: 3px solid var(--rule);
  color: var(--ink2);
}
.text-block strong { color: var(--ink); }
.text-block.result { border-left-color: var(--red); }
.text-block.sig    { border-left-color: var(--red); background: var(--red-bg); }

@media (max-width: 500px) {
  .input-grid { grid-template-columns: 1fr 1fr; }
  .sim-btn    { grid-column: span 2; }
  #seqPlot    { height: 280px; }
}
</style>
</head>
<body>

<p class="calc-label">Interactive simulation</p>
<h2 class="calc-heading">Sequential Testing and <em>p</em>-value Trajectories</h2>

<div class="input-panel">
  <div class="input-grid">

    <div class="input-group">
      <label class="input-label" for="maxN">Sample size per group <span class="sym">n</span></label>
      <input type="number" id="maxN" min="20" max="5000" value="200">
    </div>

    <div class="input-group">
      <label class="input-label" for="d">Cohen's <span class="sym">d</span> (true effect)</label>
      <input type="range" id="d" min="0" max="2" step="0.01" value="0">
      <div class="slider-value" id="dVal">0.00</div>
    </div>

    <button class="sim-btn" id="simBtn" onclick="runSimulation()">Simulate</button>

  </div>
</div>

<div class="plot-wrap">
  <div id="seqPlot"></div>
</div>

<div id="textResult" class="text-block result"></div>

<script>
// ── Normal random variate (Box-Muller) ────────────────────────────────
function rnorm(mean, sd) {
  var u1, u2;
  do { u1 = Math.random(); } while (u1 === 0);
  u2 = Math.random();
  return mean + sd * Math.sqrt(-2 * Math.log(u1)) * Math.cos(2 * Math.PI * u2);
}

// ── Two-sample t-test p-value (equal variance / pooled) ──────────────
// Accepts running sums to keep the simulation O(n).
// Both groups have exactly n observations each.
function pooledPValue(sumX, sumX2, sumY, sumY2, n) {
  if (n < 2) return 1;
  var meanX = sumX / n;
  var meanY = sumY / n;
  var ssX   = sumX2 - n * meanX * meanX;  // sum of squared deviations
  var ssY   = sumY2 - n * meanY * meanY;
  var sp2   = (ssX + ssY) / (2 * n - 2); // pooled variance
  if (sp2 <= 0) return 1;
  var se    = Math.sqrt(sp2 * 2 / n);    // SE of difference in means
  var t     = (meanX - meanY) / se;
  var df    = 2 * n - 2;
  return 2 * (1 - jStat.studentt.cdf(Math.abs(t), df));
}

// ── postHeight for iframe auto-resize (debounced to prevent push-down) ───
var _phTimer = null;
function postHeight() {
  clearTimeout(_phTimer);
  _phTimer = setTimeout(function() {
    var h = Math.max(document.body.scrollHeight, document.documentElement.scrollHeight);
    window.parent.postMessage({ iframeHeight: h }, '*');
  }, 150);
}

// ── Main simulation ───────────────────────────────────────────────────
function runSimulation() {
  var maxN  = Math.max(20, Math.min(5000, parseInt(document.getElementById('maxN').value) || 200));
  var trueD = parseFloat(document.getElementById('d').value) || 0;

  document.getElementById('dVal').textContent = trueD.toFixed(2);

  var sampleSizes = [];
  var pValues     = [];

  var sumX = 0, sumX2 = 0;
  var sumY = 0, sumY2 = 0;

  for (var i = 0; i < maxN; i++) {
    var xi = rnorm(0,     1);
    var yi = rnorm(trueD, 1);
    sumX  += xi;   sumX2 += xi * xi;
    sumY  += yi;   sumY2 += yi * yi;

    var n = i + 1;
    if (n >= 10) {
      sampleSizes.push(n);
      pValues.push(pooledPValue(sumX, sumX2, sumY, sumY2, n));
    }
  }

  // ── Statistics ───────────────────────────────────────────────────────
  var minP    = Math.min.apply(null, pValues);
  var minIdx  = pValues.indexOf(minP);
  var minN    = sampleSizes[minIdx];

  var firstSigN = null;
  for (var k = 0; k < pValues.length; k++) {
    if (pValues[k] < 0.05) { firstSigN = sampleSizes[k]; break; }
  }

  // ── Plot ─────────────────────────────────────────────────────────────
  Plotly.react('seqPlot', [
    {
      x: sampleSizes, y: pValues,
      type: 'scatter', mode: 'lines',
      name: 'p-value',
      line: { color: '#a60a0a', width: 2 },
      hovertemplate: 'n = %{x}<br>p = %{y:.4f}<extra></extra>'
    }
  ], {
    xaxis: {
      title: { text: 'Sample size per group', font: { size: 13 } },
      range: [10, maxN],
      zeroline: false, gridcolor: '#ede8e8', linecolor: '#d6dadc'
    },
    yaxis: {
      title: { text: 'p-value', font: { size: 13 } },
      range: [0, 1],
      zeroline: false, gridcolor: '#ede8e8', linecolor: '#d6dadc'
    },
    shapes: [
      {
        type: 'line', x0: 0, x1: 1, xref: 'paper',
        y0: 0.05, y1: 0.05, yref: 'y',
        line: { color: '#666060', dash: 'dash', width: 1.5 }
      }
    ],
    annotations: [
      {
        x: 1, y: 0.05, xref: 'paper', yref: 'y',
        text: 'α = 0.05', showarrow: false,
        xanchor: 'right', yanchor: 'bottom',
        font: { family: "'Open Sans', sans-serif", size: 11, color: '#666060' }
      }
    ],
    plot_bgcolor:  '#fffafa',
    paper_bgcolor: '#fffafa',
    font: { family: "'Open Sans', sans-serif", color: '#1c1717', size: 12 },
    margin: { l: 55, r: 24, t: 16, b: 48 },
    showlegend: false,
    hovermode: 'x unified'
  }, { responsive: true }).then(postHeight);

  // ── Text output ───────────────────────────────────────────────────────
  var sigText = firstSigN !== null
    ? 'The <em>p</em>-value first dropped below 0.05 at sample size <strong>' + firstSigN + '</strong>.'
    : 'The <em>p</em>-value <strong>never</strong> dropped below 0.05.';

  var el = document.getElementById('textResult');
  el.className = 'text-block ' + (firstSigN !== null ? 'sig' : 'result');
  el.innerHTML =
    'Lowest <em>p</em>-value: <strong>' + minP.toFixed(4) + '</strong> ' +
    'at sample size <strong>' + minN + '</strong>. ' + sigText;

  postHeight();
}

// ── Slider live update ───────────────────────────────────────────────
document.getElementById('d').addEventListener('input', function() {
  document.getElementById('dVal').textContent =
    parseFloat(this.value).toFixed(2);
});

window.addEventListener('load', function() { setTimeout(postHeight, 400); });
if (typeof ResizeObserver !== 'undefined') {
  new ResizeObserver(postHeight).observe(document.body);
}

// Run one simulation on load
runSimulation();
</script>
</body>
</html>