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<p>Your survey asked quantities as absolute counts.  But now you need to report them as percentages. 
Here's how to calculate ratios and correctly preserve percentages, frequencies and means: </p>
<p><img src="/images/blog/2018-06-26-ratios/ratio.png" style="width:360px; margin: 0 auto;" />
</p>
<h2 id="a-simple-example">A simple example</h2>
<p>Let's say you have four respondents.  For each respondent, the survey asks
the number of patients treated overall, and on a certain therapy specifically:</p>
<table style="width: 500px;" class="pure-table">
<colgroup>
</colgroup>
<thead style="border-bottom: 2px solid #ccc">
<tr>
<th>ID</th><th>S8</th><th>Q1</th><th>S8/Q1</th>
</tr>
<tr><td>Respondent Id</td><td># pts treated</td><td># pts on GA</td><td>% pts on GA</td></tr>
</thead>
<tbody>
<tr><td>#1</td><td>10</td><td>10</td><td>100%</td></tr>
<tr style="background-color: #eee"><td>#2</td><td>30</td><td>15</td><td>50%</td></tr>
<tr><td>#3</td><td>60</td><td>20</td><td>33%</td></tr>
<tr style="background-color: #eee"><td>#4</td><td>100</td><td>15</td><td>15%</td></tr>
<tbody>
</table>

<h2 id="simple-average-percent">Simple average percent</h2>
<p>A simple average weights each respondent equally: </p>
<p>  (100% + 60% + 33% + 15%) / 4 = 50% </p>
<h2 id="ratio-average-percent">Ratio average percent</h2>
<p>A ratio average weights each respondent by their denominator. It's the same 
as the sum of numerators divided by the sum of denominators : </p>
<p>  (10 + 15 + 20 + 15) / (10 + 30 + 60 + 100) =  30%</p>
<h2 id="why-are-they-different-">Why are they different?</h2>
<p>In this toy example, doctors who treat more patients treat fewer patients with GA.
The simple average treats each respondent equally.
The simple average weights respondents by their denominator.</p>
<h2 id="which-way-to-go-">Which way to go?</h2>
<p>In this toy example the difference between the two is substantial. In practice the two 
are typically closer, but still you want to choose carefully.</p>
<p>A simple average is appropriate when you want to project to the sample of respondents.
E.g. "The average respondent in our sample reported treating 50% of their Condition X patients with GA".</p>
<p>A ratio average is appropriate when you want to refer to the patients.
E.g. "Physicians in our sample reported treating 30% of their patients with GA on average."</p>
<h2 id="see-how">See how</h2>
<p>Protobi can calculate ratios either way, but it's especially simple to create smart ratio averages. 
See how in this tutorial: <a href="https://help.protobi.com/advancededitor/ratios">Calculate ratios in Protobi</a></p>

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