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presentation.html
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<!DOCTYPE html>
<html lang="en"><head>
<script src="presentation_files/libs/clipboard/clipboard.min.js"></script>
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<meta name="generator" content="quarto-1.3.450">
<meta name="author" content="Leighton Pritchard">
<title>Three (Rs) Tips for Better Statistical Analysis</title>
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<section id="title-slide" class="quarto-title-block center">
<h1 class="title">Three (Rs) Tips for Better Statistical Analysis</h1>
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<div class="quarto-title-author-name">
Leighton Pritchard
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</section>
<section>
<section id="formalise-your-design" class="title-slide slide level1 center">
<h1>1. Formalise your design</h1>
</section>
<section id="a-simple-experiment" class="slide level2">
<h2>A Simple Experiment</h2>
<p>I am worried that I have a pair of loaded dice: biased to roll one number more often than expected by chance alone.</p>
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<p><strong>My experiment</strong></p>
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<p>I roll my two dice and the “biased” number shows on one die; check if both dice show the same number.</p>
<p>If both dice show the same number more often than chance alone would suggest, I will accept my dice are loaded.</p>
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<p><strong>Let’s set a P-value threshold for accepting the null hypothesis</strong></p>
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<p><span class="math inline">\(H_0\)</span>: both dice are fair and show that same number <em>by chance alone</em>.</p>
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</div>
</section>
<section id="live-demonstration" class="slide level2">
<h2>Live demonstration</h2>
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<p><strong>Ooh! Risky!</strong></p>
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<img data-src="assets/images/loaded_dice.jpg" style="width:60.0%" class="r-stretch quarto-figure-center"><p class="caption">Figure 1: How to bias dice by heating them in an oven at about 121degC for 10min. Don’t use a microwave or blame me for the consequences/if you get caught.</p></section>
<section id="your-predictions-please" class="slide level2">
<h2>Your predictions, please</h2>
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<p><strong>If one die shows the pre-named “bias” number, what is the probability that both dice are fair and showed the same number, by chance alone?</strong></p>
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<aside class="notes">
<p>Use the chalkboard here to tally audience guesses</p>
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</section>
<section id="probability" class="slide level2">
<h2>Probability</h2>
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<p><strong>A definition</strong></p>
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<p><strong>The probability of an event occurring is</strong>: the proportion of all possible outcomes that are that event.</p>
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<p><strong>Tossing a coin</strong></p>
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<p><strong>Outcomes</strong>: heads or tails (two outcomes, assuming a fair coin and toss)</p>
<p><strong>Probability of showing heads</strong>: <span class="math inline">\(\frac{1}{2} = 0.5\)</span> as it is one of two outcomes</p>
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</section>
<section id="outcomes-when-rolling-two-dice" class="slide level2">
<h2>Outcomes when rolling two dice</h2>
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<section id="simulation-1000-rolls" class="slide level2">
<h2>Simulation: 1000 rolls</h2>
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<section id="what-this-means-for-us" class="slide level2">
<h2>What This Means For Us</h2>
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<p><strong>Caution</strong></p>
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<p><strong>Verbal and written experiment descriptions can influence or disguise expected effect sizes, statistical analysis and outcomes</strong></p>
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<p><strong>Talk to a statistician (or other colleague)</strong></p>
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<li>what’s ambiguous to them?</li>
<li>if they explain the experiment back to you, what sounds different to you?</li>
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<p>If I only see your experimental design as a brief written account in a grant application, I can’t always get the full picture.</p>
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<section id="what-this-means" class="slide level2">
<h2>What This Means</h2>
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<p><strong>Caution</strong></p>
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<p><strong>Verbal and written experiment descriptions influence statistical analysis and outcomes</strong></p>
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<p><strong>Experimenter understanding can influence use of language</strong></p>
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<li>We assume through explanatory gaps when we think we understand something.</li>
<li><strong>Clarity and precision are essential when explaining to others</strong></li>
<li>Use the <a href="https://www.nc3rs.org.uk/our-portfolio/experimental-design-assistant-eda">NC3Rs EDA</a> to <strong>formalise unambiguous experimental designs</strong></li>
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<h2>Use NC3Rs EDA</h2>
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<p><strong>Please share the EDA diagram/session with your statistician.</strong></p>
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<img data-src="assets/images/eda1.png" style="width:60.0%" class="r-stretch quarto-figure-center"><p class="caption">Figure 2: NC3Rs EDA forces clarification of concepts and is a focus for discussion.</p></section></section>
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<section id="use-anova" class="title-slide slide level1 center">
<h1>2. Use ANOVA</h1>
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<section id="an-experimental-dataset" class="slide level2">
<h2>An experimental dataset</h2>
<ul>
<li>A control (<code>ctrl</code>) and two treatments (<code>trt1</code>, <code>trt2</code>)</li>
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<li>Does it look like there are differences between the groups?</li>
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<section id="t-tests" class="slide level2">
<h2><em>t</em>-tests</h2>
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<p><strong><em>t</em>-tests assume that datasets are Normal distributions <sup>1</sup></strong></p>
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<p>The only input the test gets:</p>
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<li>mean <span class="math inline">\(\mu\)</span>, standard deviation <span class="math inline">\(\sigma\)</span> for each group</li>
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<aside><ol class="aside-footnotes"><li id="fn1"><p>also that samples are independent, randomly sampled, and have the same variance (Student’s <em>t</em>)</p></li></ol></aside></section>
<section id="t-tests-1" class="slide level2">
<h2><em>t</em>-tests</h2>
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<p><strong><em>t</em>-tests assume that datasets are Normal distributions</strong></p>
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<p>The only input the test gets:</p>
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<li>mean <span class="math inline">\(\mu\)</span>, standard deviation <span class="math inline">\(\sigma\)</span> for each group</li>
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<td style="text-align: left;">ctrl</td>
<td style="text-align: right;">5.032</td>
<td style="text-align: right;">0.5830914</td>
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<td style="text-align: left;">trt1</td>
<td style="text-align: right;">4.661</td>
<td style="text-align: right;">0.7936757</td>
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<td style="text-align: left;">trt2</td>
<td style="text-align: right;">5.526</td>
<td style="text-align: right;">0.4425733</td>
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<section id="t-test-results" class="slide level2">
<h2><em>t</em>-test results</h2>
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<p><strong>Tip</strong></p>
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<p>I’d recommend <code>R</code> for reproducible analyses. <sup>1</sup></p>
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<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode numberSource r number-lines code-with-copy"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1"></a><span class="fu">t.test</span>(weight <span class="sc">~</span> group, data)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<td style="text-align: left;">ctrl.vs.trt1</td>
<td style="text-align: right;">0.371</td>
<td style="text-align: right;">-0.2875162</td>
<td style="text-align: right;">1.0295162</td>
<td style="text-align: right;">0.2503825</td>
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<td style="text-align: left;">ctrl.vs.trt2</td>
<td style="text-align: right;">-0.494</td>
<td style="text-align: right;">-0.9828721</td>
<td style="text-align: right;">-0.0051279</td>
<td style="text-align: right;">0.0478993</td>
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<td style="text-align: left;">trt1.vs.trt2</td>
<td style="text-align: right;">-0.865</td>
<td style="text-align: right;">-1.4809144</td>
<td style="text-align: right;">-0.2490856</td>
<td style="text-align: right;">0.0092984</td>
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<aside><ol class="aside-footnotes"><li id="fn2"><p><code>t.test</code> in <code>R</code> does not assume equal variance by default: Welch’s <em>t</em>-test</p></li></ol></aside></section>
<section id="multiple-tests" class="slide level2">
<h2>Multiple tests</h2>
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<p><strong>These <code>p.values</code> are not correct</strong></p>
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<p>For three groups, there are three pairwise comparisons.</p>
<p>But <em>t</em>-tests calculate probability for a <strong><em>single</em></strong> pairwise comparison!</p>
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<p><strong>Multiple <em>t</em>-tests on your data increase Type I error rate (at P<0.05)</strong></p>
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<li><strong>One test</strong>: P(type I error) = 0.05</li>
<li><strong>Two tests</strong>: P(type I error) = 0.0975</li>
<li><strong>Three tests</strong>: P(type I error) = 0.1427</li>
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<section id="multiple-tests-1" class="slide level2">
<h2>Multiple tests</h2>
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<p><strong>These <code>p.values</code> are not correct</strong></p>
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<p>For three groups, there are three pairwise comparisons.</p>
<p>But <em>t</em>-tests calculate probability for a <strong><em>single</em></strong> pairwise comparison!</p>
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<p><strong>One solution: multiple test correction</strong></p>
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<p>Bonferroni, Benjamini-Hochberg, etc.</p>
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<li><strong>Bonferroni</strong>: divide your P-value significance threshold by number of comparisons, <span class="math inline">\(n\)</span>
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<li>P threshold for one comparison: <span class="math inline">\(0.05\)</span></li>
<li>Adjusted for three comparisons: <span class="math inline">\(0.05 / 3 \approx 0.016\)</span></li>
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<section id="corrected-t-test-results" class="slide level2">
<h2>Corrected <em>t</em>-test results</h2>
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<p><strong>We adjust our threshold for significance.</strong></p>
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<p>Which comparisons are significant at <span class="math inline">\(P=0.05\)</span> for a single comparison, <em>when Bonferroni corrected for three comparisons</em>? (i.e. <span class="math inline">\(P=0.016\)</span>)</p>
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<td style="text-align: left;">ctrl.vs.trt1</td>
<td style="text-align: right;">0.371</td>
<td style="text-align: right;">-0.2875162</td>
<td style="text-align: right;">1.0295162</td>
<td style="text-align: right;">0.2503825</td>
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<td style="text-align: left;">ctrl.vs.trt2</td>
<td style="text-align: right;">-0.494</td>
<td style="text-align: right;">-0.9828721</td>
<td style="text-align: right;">-0.0051279</td>
<td style="text-align: right;">0.0478993</td>
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<td style="text-align: left;">trt1.vs.trt2</td>
<td style="text-align: right;">-0.865</td>
<td style="text-align: right;">-1.4809144</td>
<td style="text-align: right;">-0.2490856</td>
<td style="text-align: right;">0.0092984</td>
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<section id="anova" class="slide level2">
<h2>ANOVA</h2>
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<p><strong>Especially if you have data in three or more groups, use ANOVA</strong></p>
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<li>ANOVA performs all comparisons for all groups simultaneously</li>
<li>ANOVA does not require multiple test correction</li>
<li>ANOVA can give more information than a <em>t</em>-test</li>
<li><em>t</em>-tests are a special case of ANOVA (you get the same answer either way)</li>
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<h2>ANOVA in <code>R</code>:</h2>
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<p><strong>No more difficult than applying a <em>t</em>-test</strong></p>
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<td style="text-align: right;">-0.865</td>
<td style="text-align: right;">-1.48091</td>
<td style="text-align: right;">-0.24909</td>
<td style="text-align: right;">0.0093</td>
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<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode numberSource r number-lines code-with-copy"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1"></a>data.aov <span class="ot"><-</span> <span class="fu">aov</span>(weight <span class="sc">~</span> group, data_pair)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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