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anova.html
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<!DOCTYPE html>
<html>
<head>
<!-- Global site tag (gtag.js) - Google Analytics -->
<script async src="https://www.googletagmanager.com/gtag/js?id=UA-131282143-1"></script>
<script>
window.dataLayer = window.dataLayer || [];
function gtag(){dataLayer.push(arguments);}
gtag('js', new Date());
gtag('config', 'UA-131282143-1');
</script>
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<title>EZ Statistics: ANOVA</title>
<meta name="description" content="EZ Statistics ANOVA">
<link rel="stylesheet" href="style/stats.css">
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery-csv/0.71/jquery.csv-0.71.min.js"></script>
<script src="https://cdn.plot.ly/plotly-latest.min.js"></script>
<script src="jstat.js"></script>
<script src="ezstatistics-0.30.js"></script>
</head>
<body>
<center><img class="round" src="style/logo.png" height="105"/></center>
<div style="text-align: right"><a href="index.html">Back to main page</a></div>
<h3 class="f18b">One-way Analysis of Variance (ANOVA)</h3>
Requires that the samples are independent and normally distributed and have equal variances.<br> <br>
Tests the hypotheses:
<table>
<tr>
<th class="dark" width="30">H<sub>0</sub></th>
<td class="border">The means of the samples are equal </td>
</tr>
<tr>
<th class="dark">H<sub>1</sub></th>
<td class="border">The means of the samples are different </td>
</tr>
</table>
<div class="smalltext">
<div class="label16">
<h3 class="f16"> Data Entry</h3>
</div>
<br/>
<table>
<tr>
<td width="110">No samples:</td>
<td><input class="value" name="no" id="no" value="3"> <button onclick="javascript:update_no_samples()">Update</button></td>
</tr>
</table>
<table id="samples">
<tr>
<td width="110">Sample A:</td>
<td><input class="sample" name="sampA" id="samp1" value="42, 53, 49, 53, 43, 44, 45, 52, 54, 46"></td>
</tr>
<tr>
<td width="110">Sample B:</td>
<td><input class="sample" name="sampB" id="samp2" value="49, 54, 58, 64, 57, 55, 56, 62, 58, 54"></td>
</tr>
<tr>
<td width="110">Sample C:</td>
<td><input class="sample" name="sampC" id="samp3" value="35, 40, 49, 42, 50, 49, 55, 39, 40, 46"></td>
</tr>
</table>
<table>
<tr>
<td width="110">Significance level α</td>
<td><input class="value" name="alpha" id="alpha" value="0.05"></td>
</tr>
<tr>
<td width="110">Upload CSV file:</td>
<td>
<input type="file" name="File Upload" id="txtFileUpload" accept=".csv" />
</td>
</tr>
<tr>
<td width="110">Post-test:</td>
<td>
<select name="posttest" id="posttest">
<option value="tukeys">Tukey's HSD</option>
<option value="scheffes">Scheffe's</option>
</select>
Correction:
<select name="correction" id="correction">
<option value="none">None</option>
<option value="bonferroni">Bonferroni</option>
</select>
</td>
</tr>
</table>
<br>
<button class="test" onclick="javascript:run_anova()">Run Test</button>
<button class="clear" onclick="javascript:clear_fields(-1)">Clear</button>
<div id="error">
</div>
<div id="test_results" style="display: none;">
<div class="label16">
<h3 class="f16"> Test Result</h3>
</div>
<br/>
<table class="border">
<thead>
<tr>
<th colspan=4 class="dark">Data Summary</th>
</tr>
<tr>
<th class="dark" width="70">Sample</th>
<th class="dark" width="40">N</th>
<th class="dark" width="100">Mean</th>
<th class="dark" width="100">Stdev</th>
</tr>
</thead>
<tbody id ="summary">
<tr>
<th class="dark">A</th>
<td class="border" id="n1"> </td>
<td class="border" id="mean1"> </td>
<td class="border" id="stdev1"> </td>
</tr>
<tr>
<th class="dark">B</th>
<td class="border" id="n2"> </td>
<td class="border" id="mean2"> </td>
<td class="border" id="stdev2"> </td>
</tr>
<tr>
<th class="dark">C</th>
<td class="border" id="n3"> </td>
<td class="border" id="mean3"> </td>
<td class="border" id="stdev3"> </td>
</tr>
</tbody>
</table>
<br>
<table class="border">
<thead>
<tr>
<th class="dark" width="550" colspan="2">Result</th>
</tr>
</thead>
<tbody>
<tr>
<td class="dark" width="130"><b>Significance level α:</b></td>
<td class="border" width="420" id="sign_level"> </td>
</tr>
<tr>
<td class="dark"><b>P-value:</b></td>
<td class="border" id="p"> </td>
</tr>
<tr>
<td class="dark"><b>F-score:</b></td>
<td class="border" id="f"> </td>
</tr>
<tr>
<td class="dark"><b>Result:</b></td>
<td class="border" id="res"> </td>
</tr>
</tbody>
</table>
<br>
<div id="postres">
<div class="label16">
<h3 class="f16"> Post-test</h3>
</div>
<br/>
The post-test shows which pairs of samples that have different means (if any).
<div id="post">
</div>
</div>
<div id="power">
<div class="label16">
<h3 class="f16"> Power Analysis <button class="help" onclick="javascript:toggle('pahelp')";>?</button></h3>
</div>
<div id="pahelp" style="display: none;">
<br>
The first table shows the minimum required sample sizes for low, medium and high statistical power respectively.
The second table shows the current statistical power for the samples and test type.
<p class="tab">The power and required sample sizes are for the pair of samples with the smallest difference in means.
The power analysis is affected by the correction specified for the post-test.</p>
</div>
<br>
<table class="border">
<thead>
<tr>
<th colspan=3 class="dark">Required sample sizes</th>
</tr>
<tr>
<th class="dark" width="120">Power</th>
<th class="dark" width="150">Min sample size</th>
</tr>
</thead>
<tbody>
<tr>
<td class="border">Low (20%)</td>
<td class="border" id="n_low"> </td>
</tr>
<tr>
<td class="border">Medium (50%)</td>
<td class="border" id="n_medium"> </td>
</tr>
<tr>
<td class="border">High (80%)</td>
<td class="border" id="n_high"> </td>
</tr>
</tbody>
</table>
<br>
<table class="border">
<thead>
<tr>
<th class="dark" width="150">Current power</th>
</tr>
</thead>
<tbody>
<tr>
<td class="border" id="pwr"> </td>
</tr>
</tbody>
</table>
</div>
<div id="assumptions">
<div class="label16">
<h3 class="f16"> Check test assumptions <button class="help" onclick="javascript:toggle('ashelp')";>?</button></h3>
</div>
<div id="ashelp" style="display: none;">
<br>
The samples should be normally distributed. If not, consider using the <a href="kruskalwallis.html">Kruskal-Wallis test</a> instead.
Note that the normality test is not entirely accurate for sample sizes under 20.
<p class="tab">The samples should also have equal variances.</p>
</div>
<br>
<div id="vartest">
<table class="border">
<thead>
<tr>
<th class="dark" width="550" colspan="2">Bartlett's test for equal variances</th>
</tr>
</thead>
<tbody>
<tr>
<td class="dark" width="100"><b>Result:</b></td>
<td class="border" id="v_res"> </td>
</tr>
<tr>
<td class="dark"><b>P-value:</b></td>
<td class="border" id="v_p"> </td>
</tr>
</tbody>
</table>
<br>
</div>
<div id="normtest">
<table class="border">
<thead>
<tr>
<th class="dark" width="550" colspan="2">Shapiro-Wilk test for normally distributed samples</th>
</tr>
</thead>
<tbody id="normtest_cont">
</tbody>
</table>
</div>
</div>
<div id="viz">
<div class="label16">
<h3 class="f16"> Data Visualization</h3>
</div>
<div id="chart"></div>
</div>
</div>
</div>
</body>
</html>