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table_beta.html
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table_beta.html
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<html>
<head>
<title>Sensei</title>
<link rel="stylesheet" href="https://www.w3schools.com/w3css/4/w3.css">
<style>
* {
box-sizing: border-box;
}
body, html {
height: 100%;
margin: 0;
font-family: Arial;
}
/* Style tab links */
.tablink {
border-radius: 10px 10px 0px 0px;
background-color: #555;
color: white;
float: left;
border: none;
outline: none;
cursor: pointer;
padding: 8px 16px;
font-size: 17px;
width: 250px;
height: 40px;
}
.tablink:hover {
background-color: #777;
}
/* Style the tab content (and add height:100% for full page content) */
.tabcontent {
/*color: white;*/
display: none;
padding: 40px 0px;
height: 100%;
}
.row {
display: flex;
}
.column1 {
flex: 100%;
border-radius: 10px;
border: 2px solid #73AD21;
padding: 10px;
margin: 3px;
}
.column {
flex: 50%;
border-radius: 10px;
border: 2px solid #73AD21;
padding: 10px;
margin: 3px;
}
.column30 {
flex: 30%;
border-radius: 10px;
border: 2px solid #73AD21;
padding: 10px;
margin: 3px;
min-width: 300px;
}
.column40 {
flex: 40%;
border-radius: 10px;
border: 2px solid #73AD21;
padding: 10px;
margin: 3px;
}
.column60dummy {
flex: 60%;
padding: 0px;
margin: 0px;
}
.column60 {
flex: 60%;
border-radius: 10px;
border: 2px solid #73AD21;
padding: 10px;
margin: 3px;
}
.column70 {
flex: 70%;
border-radius: 10px;
border: 2px solid #73AD21;
padding: 10px;
margin: 3px;
}
label {
display: inline-block;
width: 150px;
text-align: left;
}
label.radio {
display: inline-block;
width: 250px;
text-align: left;
}
.block2 {
width: 50%;
float: left;
}
input[type=number] {
width:100px;
margin: 2px;
padding-left: 3px;
border: none; /* <-- This thing here */
border:solid 1px #ccc;
border-radius: 3px;
}
a.glossaryLink {
cursor: help;
border-bottom: 1px dashed #73AD21;
}
/* collapsible */
.collapsible {
background-color: #eee;
border: 1px dashed #aaa;
border-bottom-style: none;
color: black;
cursor: pointer;
padding: 12px 10px 12px 3px;
width: 100%;
text-align: left;
outline: none;
}
.active, .collapsible:hover {
border-color: #aaa;
}
.collapsible:after {
font-size: 15px;
content: '\002B';
color: black;
font-weight: bold;
float: right;
margin-left: 5px;
}
.active:after {
content: "\2212";
}
.content {
padding: 0px 10px 0px 3px;
max-height: 0;
overflow: hidden;
transition: max-height 0.2s ease-out;
background-color: #fafafa;
border: 1px dashed #aaa;
border-top: none;
}
</style>
<script src="https://cdn.jsdelivr.net/npm/jstat@latest/dist/jstat.min.js"></script>
<script src='https://cdn.plot.ly/plotly-latest.min.js'></script>
<script type="text/javascript">
function betaStatParam(m, std)
{
m = parseFloat(m);
var v = parseFloat(std);
v = v * v;
var a = ((1 - m) / v - 1 / m) * m * m;
var b = a * (1 / m - 1)
return [a, b]
}
function betaParamStat(a, b)
{
a = parseFloat(a);
b = parseFloat(b);
var m = a / (a + b);
var v = a * b / Math.pow(a + b, 2) / (a + b + 1);
return [m, Math.sqrt(v)];
}
function execBetaParamStat(suffix)
{
var temp = betaParamStat(document.getElementById("a".concat(suffix)).value, document.getElementById("b".concat(suffix)).value);
document.getElementById("mean".concat(suffix)).value = round(temp[0], 4);
document.getElementById("std".concat(suffix)).value = round(temp[1], 4);
}
function execBetaStatParam(suffix)
{
var temp = betaStatParam(document.getElementById("mean".concat(suffix)).value, document.getElementById("std".concat(suffix)).value);
document.getElementById("a".concat(suffix)).value = round(temp[0], 3);
document.getElementById("b".concat(suffix)).value = round(temp[1], 3);
}
function calcBetaRaw(M0, M1, N0, N1, a0, a1, b0, b1, alpha, test_type, offset, sign)
{
Ep0 = a0 / (a0 + b0);
Ep1 = a1 / (a1 + b1);
Vp0 = a0 * b0 * (a0 + b0 + N0) / ((N0 * (a0 + b0) * (a0 + b0)) * (a0 + b0 + 1));
Vp1 = a1 * b1 * (a1 + b1 + N1) / ((N1 * (a1 + b1) * (a1 + b1)) * (a1 + b1 + 1));
Et = (Ep1 - (Ep0 + offset)) / Math.sqrt(Vp0 / M0 + Vp1 / M1);
if (sign == 0) {
Et = Math.abs(Et);
} else {
Et = sign * Et;
}
nu = (Vp0 / M0 + Vp1 / M1) ** 2 / ((Vp0 / M0) ** 2 / (M0 - 1) + (Vp1 / M1) ** 2 / (M1 - 1));
if (test_type === "one_sided") t_star = jStat.studentt.inv(1 - alpha, nu);
else t_star = jStat.studentt.inv(1 - alpha / 2, nu);
console.log("unpaired", M0, M1, Et);
// return jStat.normal.cdf(t_star - Et, 0, 1)
return jStat.studentt.cdf(t_star - Et, nu)
}
function round(x, p) {return Math.round(x * Math.pow(10, p)) / Math.pow(10, p)}
function execCalcBeta()
{
var M0_min = parseFloat(document.getElementById("M0_min").value);
var M0_max = parseFloat(document.getElementById("M0_max").value);
var M1_min = parseFloat(document.getElementById("M1_min").value);
var M1_max = parseFloat(document.getElementById("M1_max").value);
var N0 = parseFloat(document.getElementById("N0").value);
var N1 = parseFloat(document.getElementById("N1").value);
var a0 = parseFloat(document.getElementById("a0").value);
var a1 = parseFloat(document.getElementById("a1").value);
var b0 = parseFloat(document.getElementById("b0").value);
var b1 = parseFloat(document.getElementById("b1").value);
var alpha = parseFloat(document.getElementById("alpha").value);
var beta = parseFloat(document.getElementById("beta").value);
var test_type = "";
var sign = 0;
var offset = 0.0;
var lower_bound = 0.0;
var upper_bound = 0.0;
if (document.getElementById('one_sided').checked) {
test_type = "one_sided";
sign = 0;
offset = 0.0;
} else if (document.getElementById('two_sided').checked) {
test_type = "two_sided";
sign = 0;
offset = 0.0;
} else if (document.getElementById('sesoi_test').checked) {
test_type = "one_sided";
offset = parseFloat(document.getElementById("sesoi_bound").value);
if (offset == 0) {
//document.getElementById("result").innerHTML = "<p>Invalid input: SESOI must not be zero.</p>";
//return;
}
if (document.getElementById('sesoi_verify').checked) sign = Math.sign(offset);
else sign = -Math.sign(offset);
} else if (document.getElementById('tost_test').checked) {
test_type = "one_sided";
lower_bound = parseFloat(document.getElementById("tost_lower_bound").value);
upper_bound = parseFloat(document.getElementById("tost_upper_bound").value);
} else {
return; // do nothing.
}
var output = "<table class='w3-table' border='1' width='500' cellspacing='0'cellpadding='5'>";
output = output + "<tr>";
output = output + "<td>" + "ctrl \\ exp" + "</td>";
var temp = 1.0;
for (j = M1_min; j <= M1_max; j++)
{
output = output + "<td>" + j + "</td>";
}
output = output + "</tr>";
for(i = M0_min; i <= M0_max; i++)
{
output = output + "<tr>";
output = output + "<td>" + i + "</td>";
for (j = M1_min; j <= M1_max; j++)
{
if (document.getElementById('tost_test').checked) {
temp = Math.min((calcBetaRaw(i, j, N0, N1, a0, a1, b0, b1, alpha, test_type, upper_bound, -1) +
calcBetaRaw(i, j, N0, N1, a0, a1, b0, b1, alpha, test_type, lower_bound, 1)),
1);
} else {
temp = calcBetaRaw(i, j, N0, N1, a0, a1, b0, b1, alpha, test_type, offset, sign);
}
if (temp < beta) output = output + "<td bgcolor=#E0E0E0>" + round(temp, 3) + "</td>";
else output = output + "<td>" + round(temp, 3) + "</td>";
}
output = output + "</tr>";
}
output = output + "</table>";
document.getElementById("result").innerHTML = output;
//document.getElementById("results").scrollIntoView();
}
function calcBetaRawPaired(M, N0, N1, a0, a1, b0, b1, alpha, rho, test_type, offset, sign)
{
Ep0 = a0 / (a0 + b0);
Ep1 = a1 / (a1 + b1);
Vp0 = a0 * b0 * (a0 + b0 + N0) / ((N0 * (a0 + b0) * (a0 + b0)) * (a0 + b0 + 1));
Vp1 = a1 * b1 * (a1 + b1 + N1) / ((N1 * (a1 + b1) * (a1 + b1)) * (a1 + b1 + 1));
cov = rho * Math.sqrt(a0 * b0 / ((a0 + b0) * (a0 + b0) * (a0 + b0 + 1))) * Math.sqrt(a1 * b1 / ((a1 + b1) * (a1 + b1) * (a1 + b1 + 1)));
Et = (Ep1 - (Ep0 + offset)) * Math.sqrt(M) / Math.sqrt(Vp0 + Vp1 - 2 * cov);
if (sign == 0) {
Et = Math.abs(Et);
} else {
Et = sign * Et;
}
nu = M-1;
if (test_type === "one_sided") t_star = jStat.studentt.inv(1 - alpha, nu);
else t_star = jStat.studentt.inv(1 - alpha / 2, nu);
console.log("paired", M, Et);
// return jStat.normal.cdf(t_star - Et, 0, 1)
return jStat.studentt.cdf(t_star - Et, nu)
}
function execCalcBetaPaired()
{
var M_min = parseFloat(document.getElementById("M_min_paired").value);
var M_max = parseFloat(document.getElementById("M_max_paired").value);
var N0 = parseFloat(document.getElementById("N0_paired").value);
var N1 = parseFloat(document.getElementById("N1_paired").value);
var a0 = parseFloat(document.getElementById("a0_paired").value);
var a1 = parseFloat(document.getElementById("a1_paired").value);
var b0 = parseFloat(document.getElementById("b0_paired").value);
var b1 = parseFloat(document.getElementById("b1_paired").value);
var alpha = parseFloat(document.getElementById("alpha_paired").value);
var rho = parseFloat(document.getElementById("rho_paired").value);
var beta = parseFloat(document.getElementById("beta_paired").value);
var test_type = "";
var sign = 0;
var offset = 0.0;
var lower_bound = 0.0;
var upper_bound = 0.0;
if (document.getElementById('one_sided_paired').checked) {
test_type = "one_sided";
sign = 0;
offset = 0.0;
} else if (document.getElementById('two_sided_paired').checked) {
test_type = "two_sided";
sign = 0;
offset = 0.0;
} else if (document.getElementById('sesoi_test_paired').checked) {
test_type = "one_sided";
offset = parseFloat(document.getElementById("sesoi_bound_paired").value);
if (offset == 0) {
//document.getElementById("result").innerHTML = "<p>Invalid input: SESOI must not be zero.</p>";
//return;
}
if (document.getElementById('sesoi_verify_paired').checked) sign = Math.sign(offset);
else sign = -Math.sign(offset);
} else if (document.getElementById('tost_test_paired').checked) {
test_type = "one_sided";
lower_bound = parseFloat(document.getElementById("tost_lower_bound_paired").value);
upper_bound = parseFloat(document.getElementById("tost_upper_bound_paired").value);
} else {
return; // do nothing.
}
var output = "<table class='w3-table' border='1' width='500' cellspacing='0'cellpadding='5'>";
output = output + "<tr>";
output = output + "<td>" + "Sample Size" + "</td>";
var temp = 1.0;
for (j = M_min; j <= M_max; j++)
{
output = output + "<td>" + j + "</td>";
}
output = output + "</tr>";
output = output + "<tr>";
output = output + "<td>False Negative Rate</td>";
for (j = M_min; j <= M_max; j++)
{
if (document.getElementById('tost_test_paired').checked) {
temp = Math.min((calcBetaRawPaired(j, N0, N1, a0, a1, b0, b1, alpha, rho, test_type, upper_bound, -1) +
calcBetaRawPaired(j, N0, N1, a0, a1, b0, b1, alpha, rho, test_type, lower_bound, 1)),
1);
} else {
temp = calcBetaRawPaired(j, N0, N1, a0, a1, b0, b1, alpha, rho, test_type, offset, sign);
}
if (temp < beta) output = output + "<td bgcolor=#E0E0E0>" + round(temp, 3) + "</td>";
else output = output + "<td>" + round(temp, 3) + "</td>";
}
output = output + "</tr>";
output = output + "</table>";
document.getElementById("result_paired").innerHTML = output;
//document.getElementById("results").scrollIntoView();
}
function plotBetaPaired()
{
var a0 = parseFloat(document.getElementById("a0_paired").value);
var a1 = parseFloat(document.getElementById("a1_paired").value);
var b0 = parseFloat(document.getElementById("b0_paired").value);
var b1 = parseFloat(document.getElementById("b1_paired").value);
var rho = parseFloat(document.getElementById("rho_paired").value);
x = [];
y = [];
for (i = 0.0; i <= 1.0; i = i + 0.005) x.push(i);
for (i = 0; i < x.length; i++) y.push(jStat.beta.pdf(x[i], a1, b1))
var exp = {
x: x,
y: y,
type: 'scatter',
name: 'Experimental'
};
if (document.getElementById('one_sided_paired').checked || document.getElementById('two_sided_paired').checked) {
y = [];
for (i = 0; i < x.length; i++) y.push(jStat.beta.pdf(x[i], a0, b0));
var ctrl = {
x: x,
y: y,
type: 'scatter',
name: 'Control'
};
var data = [ctrl, exp];
} else if (document.getElementById('sesoi_test_paired').checked) {
offset = parseFloat(document.getElementById("sesoi_bound_paired").value);
y = [];
x1 = [];
for (i = 0; i < x.length; i++) {
y.push(jStat.beta.pdf(x[i], a0, b0));
x1.push(x[i] + offset);
}
var ctrl = {
x: x,
y: y,
type: 'scatter',
name: 'Control'
};
var sesoi = {
x: x1,
y: y,
type: 'scatter',
name: 'Control with SESOI',
line: {
dash: 'dot',
color: '#1f77b4'
}
};
var data = [ctrl, exp, sesoi];
} else if (document.getElementById('tost_test_paired').checked) {
lower_bound = parseFloat(document.getElementById("tost_lower_bound_paired").value);
upper_bound = parseFloat(document.getElementById("tost_upper_bound_paired").value);
y = [];
x1 = [];
x2 = [];
for (i = 0; i < x.length; i++) {
y.push(jStat.beta.pdf(x[i], a0, b0));
x1.push(x[i] + lower_bound);
x2.push(x[i] + upper_bound);
}
var ctrl = {
x: x,
y: y,
type: 'scatter',
name: 'Control'
};
var lb = {
x: x1,
y: y,
type: 'scatter',
name: 'Lower',
line: {
dash: 'dot',
color: '#1f77b4'
}
};
var ub = {
x: x2,
y: y,
type: 'scatter',
name: 'Upper',
line: {
dash: 'dash',
color: '#1f77b4'
}
};
var data = [ctrl, exp, lb, ub];
} else {
return; // do nothing.
}
var layout = {showlegend: true, legend: {"orientation": "h"}, height: 300, width: 400,
margin: {
l: 50,
r: 50,
b: 50,
t: 50,
pad: 4
}
};
Plotly.newPlot('plot_paired', data, layout)
}
function plotBeta()
{
var a0 = parseFloat(document.getElementById("a0").value);
var a1 = parseFloat(document.getElementById("a1").value);
var b0 = parseFloat(document.getElementById("b0").value);
var b1 = parseFloat(document.getElementById("b1").value);
x = [];
y = [];
for (i = 0.0; i <= 1.0; i = i + 0.005) x.push(i);
for (i = 0; i < x.length; i++) y.push(jStat.beta.pdf(x[i], a1, b1))
var exp = {
x: x,
y: y,
type: 'scatter',
name: 'Experimental'
};
if (document.getElementById('one_sided').checked || document.getElementById('two_sided').checked) {
y = [];
for (i = 0; i < x.length; i++) y.push(jStat.beta.pdf(x[i], a0, b0));
var ctrl = {
x: x,
y: y,
type: 'scatter',
name: 'Control'
};
var data = [ctrl, exp];
} else if (document.getElementById('sesoi_test').checked) {
offset = parseFloat(document.getElementById("sesoi_bound").value);
y = [];
x1 = [];
for (i = 0; i < x.length; i++) {
y.push(jStat.beta.pdf(x[i], a0, b0));
x1.push(x[i] + offset);
}
var ctrl = {
x: x,
y: y,
type: 'scatter',
name: 'Control'
};
var sesoi = {
x: x1,
y: y,
type: 'scatter',
name: 'Control with SESOI',
line: {
dash: 'dot',
color: '#1f77b4'
}
};
var data = [ctrl, exp, sesoi];
} else if (document.getElementById('tost_test').checked) {
lower_bound = parseFloat(document.getElementById("tost_lower_bound").value);
upper_bound = parseFloat(document.getElementById("tost_upper_bound").value);
y = [];
x1 = [];
x2 = [];
for (i = 0; i < x.length; i++) {
y.push(jStat.beta.pdf(x[i], a0, b0));
x1.push(x[i] + lower_bound);
x2.push(x[i] + upper_bound);
}
var ctrl = {
x: x,
y: y,
type: 'scatter',
name: 'Control'
};
var lb = {
x: x1,
y: y,
type: 'scatter',
name: 'Lower',
line: {
dash: 'dot',
color: '#1f77b4'
}
};
var ub = {
x: x2,
y: y,
type: 'scatter',
name: 'Upper',
line: {
dash: 'dash',
color: '#1f77b4'
}
};
var data = [ctrl, exp, lb, ub];
} else {
return; // do nothing.
}
var layout = {showlegend: true, legend: {"orientation": "h"}, height: 300, width: 400,
margin: {
l: 50,
r: 50,
b: 50,
t: 50,
pad: 4
}
};
Plotly.newPlot('plot', data, layout)
}
</script>
</head>
<body>
<button class="tablink" onclick="openPage('main', this, 'green')" id="defaultOpen">Unpaired t-Test</button>
<button class="tablink" onclick="openPage('paired', this, 'green')">Paired t-Test</button>
<button class="tablink" onclick="openPage('instructions', this, 'green')">Instructions</button>
<div class="tabcontent" id="main">
<div class="row">
<div class="column30">
<h2>Control group</h2>
<div class="block">
<label for=""><a class="glossaryLink" title="Number of patients you plan to recruit">Range of samples M<sub>0</sub></a></label>
<input type="number" id="M0_min" value="" style="width: 45px;">
~
<input type="number" id="M0_max" value="" style="width: 45px;">
</div>
<div class="block">
<label for="N0"><a class="glossaryLink" title="Number of cells in each sample. Reasonable numbers are: Smart-seq: 100~300 10x Chromium: 3,000~5,000 CyTOF: 3 × 10⁶">Number of cells N<sub>0</sub></a></label>
<input type="number" id="N0" value="" step=100>
</div>
<h4><a class="glossaryLink" title="If you have a pilot study, these can be set to the mean and standard deviation of the cell type abundance. Otherwise, these are some reasonable values for PBMCs (mean ± std): CD4 T cells: 40% ± 5% CD8 T cells: 20% ± 5% B cells: 10% ± 5% NK cells: 20 ± 3% Monocytes: 8 ± 2% Dendritic cells: 1.5% ± 0.2%">Expected cell abundance</a></h4>
<div class="block">
<label for="mean0">Mean</label>
<input type="number" id="mean0" value="" step="0.05" min="0.05" max="0.95" onchange="execBetaStatParam(0); plotBeta();">
</div>
<div class="block">
<label for="">Standard deviation</label>
<input type="number" id="std0" value="" step="0.01" min="0.001" onchange="execBetaStatParam(0); plotBeta();">
</div>
<button class="collapsible">Or a<sub>0</sub> and b<sub>0</sub> for the underlying <a class="glossaryLink" title="We assume that the cell abundance follow a beta distribution, a distribution commonly used for modeling proportions. It is not far from a normal distribution in most cases.">beta distribution</a></button>
<div class="content">
<div class="block">
Beta(a<sub>0</sub> =
<input type="number" id="a0" value="" step="1" min="1" style="width: 70px" onchange="execBetaParamStat(0); plotBeta();">
, b<sub>0</sub> =
<input type="number" id="b0" value="" step="1" min="1" style="width: 70px" onchange="execBetaParamStat(0); plotBeta();">
)
<p><small>The mean and standard deviation will change when you change a<sub>0</sub> and b<sub>0</sub>,
and vice versa.</small></p>
</div>
</div>
<h4></h4>
</div>
<div class="column30">
<h2>Experimental group</h2>
<label for="">Range of samples M<sub>1</sub></label>
<input type="number" id="M1_min" value="" style="width: 45px;">
~
<input type="number" id="M1_max" value="" style="width: 45px;">
<div class="block">
<label for="N1">Number of cells N<sub>1</sub></label>
<input type="number" id="N1" value="" step=100>
</div>
<h4>Expected cell abundance</h4>
<div class="block">
<label for="mean1">Mean</label>
<input type="number" id="mean1" value="" step="0.05" min="0.05" max="0.95" onchange="execBetaStatParam(1); plotBeta();">
</div>
<div class="block">
<label for="">Standard deviation</label>
<input type="number" id="std1" value="" step="0.01" min="0.001" onchange="execBetaStatParam(1); plotBeta();">
</div>
<button class="collapsible">Or a<sub>0</sub> and b<sub>0</sub> for the underlying beta distribution</button>
<div class="content">
<div class="block">
Beta(a<sub>0</sub> =
<input type="number" id="a1" value="" step="1" min="1" style="width: 70px" onchange="execBetaParamStat(1); plotBeta();">
, b<sub>0</sub> =
<input type="number" id="b1" value="" step="1" min="1" style="width: 70px" onchange="execBetaParamStat(1); plotBeta();">
)
<p><small>The mean and standard deviation will change when you change a<sub>0</sub> and b<sub>0</sub>,
and vice versa.</small></p>
</div>
</div>
</div>
<div class="column40">
<h2>Visualize Beta-distributions</h2>
<div id='plot'><!-- Plotly chart will be drawn inside this DIV --></div>
<div><small>The graph will update when the Beta-distributions change.</small></div>
</div>
</div>
<div class="row">
<div class="column30">
<h2>Statistical Test</h2>
<div>
<div class="block">
<label for="alpha"><a class="glossaryLink" title="The significance level to be used in your study, usuall 0.01 or 0.05.">False positive rate</a> α</label>
<input type="number" id="alpha" value="" step=0.01>
</div>
<div class="block">
<label for="beta"><a class="glossaryLink" title="The chance of getting a false negative result in your study.">False negative threshold</a> β<sub>th</sub></label>
<input type="number" id="beta" value="" step=0.01>
</div>
<div>
<h3>Type</h3>
<div>
<input type="radio" id="one_sided" name="test_type" value="one_sided" onchange="displayParams();" checked>
<label class="radio" for="one_sided"><a class="glossaryLink" title="Useful when prior knowledge supports a direction of change, and only that direction is tested for.">One-sided</a> t-test</label>
</div>
<div>
<input type="radio" id="two_sided" name="test_type" value="two_sided" onchange="displayParams();">
<label class="radio" for="two_sided"><a class="glossaryLink" title="Useful when you only want to know if the two samples are different, but do not know which way it will go.">Two-sided t-test</a></label>
</div>
<div>
<input type="radio" id="sesoi_test" name="test_type" value="sesoi_test" onchange="displayParams();">
<label class="radio" for="sesoi_test">t-Test with <a class="glossaryLink" title="SESOI: smallest effect size of interest.
Useful when you want to test for an effect with a difference other than 0.
E.g., a drug is considered effective if the number of T cells raise by at least 1 percent points.">SESOI</a></label>
</div>
<div>
<input type="radio" id="tost_test" name="test_type" value="sesoi_test" onchange="displayParams();">
<label class="radio" for="tost_test"><a class="glossaryLink" title="TOST: two one-sided t-tests.
Useful when you want to test if two samples has effectively the same value by asserting that the change is no larger than a percentage.">TOST</a> for equivalence</label>
</div>
<div id="sesoi_param">
<h3>Parameters for SESOI</h3>
<div>
<input type="radio" id="sesoi_verify" name="sesoi_type" value="sesoi_verify" checked>
<label class="radio" for="sesoi_verify"><a class="glossaryLink" title="test if the effect is significantly greater than specified">Verify</a></label>
</div>
<div>
<input type="radio" id="sesoi_falsify" name="sesoi_type" value="sesoi_falsify">
<label class="radio" for="sesoi_falsify"><a class="glossaryLink" title="test if the effect is significantly smaller than specified">Falsify</a></label>
</div>
<div>
<label for="sesoi_bound">SESOI (≠ 0)</label>
<input type="number" id="sesoi_bound" value="0.01" step=0.005>
</div>
</div>
<div id="tost_param">
<h3>Parameters for TOST</h3>
<div>
<label for="tost_upper_bound"><a class="glossaryLink" title="Upper bound is set to (control + upper_bound_offset)">Upper bound offset</a></label>
<input type="number" id="tost_upper_bound" value="0.1" step=0.01 min=0.0>
</div>
<div>
<label for="tost_lower_bound"><a class="glossaryLink" title="Lower bound is set to (control - |lower_bound_offset|)">Lower bound offset</a></label>
<input type="number" id="tost_lower_bound" value="-0.1" step=0.01 max=0.0>
</div>
</div>
</div>
</div>
<!--<input type="button" id="create" value="Calculate beta table" onclick="execCalcBeta(); "/>-->
</div>
<div class="column70">
<h2>Result: False-negative rate β</h2>
<div>
<div id="result">
Results pending calculating...
</div>
</div>
<div><small>Lower is better. Each row correponds to a fixed number of control samples.
Each row correponds to a fixed number of experimental samples. Values pass β<sub>th</sub> are shaded.</small>
</div>
</div>
</div>
</div>
<div class="tabcontent" id="paired">
<div class="row">
<div class="column60dummy">
<div class = "row">
<div class="column60">
<h2>Control Group and Case Group</h2>
<div class="block2">
<label for="">Range of samples M</label>
<input type="number" id="M_min_paired" value="" style="width: 45px;">
~
<input type="number" id="M_max_paired" value="" style="width: 45px;">
</div>
<div class="block2">
<label for="rho_paired">Correlation 𝜌</label>
<input type="number" id="rho_paired" value="" step="0.05">
</div>
</div>
</div>
<div class="row">
<div class="column30">
<h2>Control Group</h2>
<div class="block">
<label for="N0_paired">Number of cells N<sub>0</sub></label>
<input type="number" id="N0_paired" value="" step=100>
</div>
<h4>Expected cell abundance</h4>
<div class="block">
<label for="mean0_paired">Mean</label>
<input type="number" id="mean0_paired" value="" step="0.05" min="0.05" max="0.95" onchange="execBetaStatParam('0_paired');">
</div>
<div class="block">
<label for="std0_paired">Standard deviation</label>
<input type="number" id="std0_paired" value="" step="0.01" min="0.001" onchange="execBetaStatParam('0_paired');">
</div>
<button class="collapsible">Or a<sub>0</sub> and b<sub>0</sub> for the underlying <a class="glossaryLink" title="We assume that the cell abundance follow a beta distribution, a distribution commonly used for modeling proportions. It is not far from a normal distribution in most cases.">beta distribution</a></button>
<div class="content">
<div class="block">
Beta(a<sub>0</sub> =
<input type="number" id="a0_paired" value="" step="1" min="1" style="width: 70px" onchange="execBetaParamStat('0_paired');">
, b<sub>0</sub> =
<input type="number" id="b0_paired" value="" step="1" min="1" style="width: 70px" onchange="execBetaParamStat('0_paired');">
)
</div>
</div>
</div>
<div class="column30">
<h2>Case Group</h2>
<div class="block">
<label for="N1_paired">Number of cells N<sub>1</sub></label>
<input type="number" id="N1_paired" value="" step=100>
</div>
<h4>Expected cell abundance</h4>
<div class="block">
<label for="mean1_paired">Mean</label>
<input type="number" id="mean1_paired" value="" step="0.05" min="0.05" max="0.95" onchange="execBetaStatParam('1_paired');">
</div>
<div class="block">
<label for="std1_paired">Standard deviation</label>
<input type="number" id="std1_paired" value="" step="0.01" min="0.001" onchange="execBetaStatParam('1_paired');">
</div>
<button class="collapsible">Or a<sub>0</sub> and b<sub>0</sub> for the underlying <a class="glossaryLink" title="We assume that the cell abundance follow a beta distribution, a distribution commonly used for modeling proportions. It is not far from a normal distribution in most cases.">beta distribution</a></button>
<div class="content">
<div class="block">
Beta(a<sub>1</sub> =
<input type="number" id="a1_paired" value="" step="1" min="1" style="width: 70px" onchange="execBetaParamStat('1_paired');">
, b<sub>1</sub> =
<input type="number" id="b1_paired" value="" step="1" min="1" style="width: 70px" onchange="execBetaParamStat('1_paired');">
)
</div>
</div>
</div>
</div>
</div>
<div class="column40">
<h2>Visualization</h2>
<div id='plot_paired'><!-- Plotly chart will be drawn inside this DIV --></div>
<div><small>The graph will update when the Beta-distributions change.</small></div>
</div>
</div>
<div class="row">
<div class="column30">
<h2>Statistical Test</h2>
<div>
<div class="block">
<label for="alpha_paired"><a class="glossaryLink" title="The significance level to be used in your study, usuall 0.01 or 0.05.">False positive rate</a> α</label>
<input type="number" id="alpha_paired" value="" step=0.01>
</div>
<div class="block">
<label for="beta_paired"><a class="glossaryLink" title="The chance of getting a false negative result in your study.">False negative threshold</a> β<sub>th</sub></label>
<input type="number" id="beta_paired" value="" step=0.01>
</div>
<div>
<h3>Type</h3>
<div>
<input type="radio" id="one_sided_paired" name="test_type_paired" value="one_sided" onchange="displayParamsPaired();" checked>
<label class="radio" for="one_sided_paired">One-sided t-test</label>
</div>
<div>
<input type="radio" id="two_sided_paired" name="test_type_paired" value="two_sided" onchange="displayParamsPaired();">
<label class="radio" for="two_sided_paired">Two-sided t-test</label>
</div>
<div>
<input type="radio" id="sesoi_test_paired" name="test_type_paired" value="sesoi_test" onchange="displayParamsPaired();">
<label class="radio" for="sesoi_test_paired">t-Test with <a class="glossaryLink" title="SESOI: smallest effect size of interest">SESOI</a></label>
</div>
<div>
<input type="radio" id="tost_test_paired" name="test_type_paired" value="sesoi_test" onchange="displayParamsPaired();">
<label class="radio" for="tost_test_paired"><a class="glossaryLink" title="TOST: two one-sided t-tests">TOST</a> for equivalence</label>
</div>
<div id="sesoi_param_paired">
<h3>Parameters for SESOI</h3>
<div>
<input type="radio" id="sesoi_verify_paired" name="sesoi_type_paired" value="sesoi_verify" checked>
<label class="radio" for="sesoi_verify"><a class="glossaryLink" title="test if the effect is significantly greater than specified">Verify</a></label>
</div>
<div>
<input type="radio" id="sesoi_falsify_paired" name="sesoi_type_paired" value="sesoi_falsify">
<label class="radio" for="sesoi_falsify"><a class="glossaryLink" title="test if the effect is significantly smaller than specified">Falsify</a></label>
</div>
<div>
<label for="sesoi_bound_paired">SESOI (≠ 0)</label>
<input type="number" id="sesoi_bound_paired" value="0.01" step=0.005>
</div>
</div>
<div id="tost_param_paired">
<h3>Parameters for TOST</h3>
<div>
<label for="tost_upper_bound_paired"><a class="glossaryLink" title="Upper bound is set to (control + upper_bound_offset)">Upper bound offset</a></label>
<input type="number" id="tost_upper_bound_paired" value="0.1" step=0.01 min=0.0>
</div>
<div>
<label for="tost_lower_bound_paired"><a class="glossaryLink" title="Lower bound is set to (control - |lower_bound_offset|)">Lower bound offset</a></label>
<input type="number" id="tost_lower_bound_paired" value="-0.1" step=0.01 max=0.0>
</div>
</div>
</div>
</div>
<!--<input type="button" id="create" value="Calculate beta table" onclick="execCalcBeta(); "/>-->
</div>
<div class="column70">
<h2>Result: False-negative rate β</h2>
<div>
<div id="result_paired">
Results pending calculating...
</div>
</div>
<div><small>Lower is better. Each row correponds to a fixed number of control samples.
Each row correponds to a fixed number of experimental samples. Values pass β<sub>th</sub> are shaded.</small>
</div>
</div>
</div>