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<article>
<h1>Levels of Measurement</h1>
<section>
<address class="h-card">
by
<a rel="author" class="u-url" href="http://changelog.ca/"><span class="p-given-name">Charles</span> <span class="p-additional-name">Iliya</span> <span class="p-family-name">Krempeaux</span></a>
</address>
</section>
<section>
<p>
The <strong>levels of measurement</strong> are a way of categorizing a <ziba-link>data</ziba-link> as one of four different categories:
</p>
<ul>
<li><ziba-link>nominal data</ziba-link>,</li>
<li><ziba-link>ordinal data</ziba-link>,</li>
<li><ziba-link>interval data</ziba-link>, and</li>
<li><ziba-link>ratio data</ziba-link>.</li>
</ul>
</section>
<section>
<h2>Ratio Data</h2>
</section>
<section>
<h2>Interval Data</h2>
</section>
<section>
<h2>Ordinal Data</h2>
</section>
<section>
<h2>Nominal Data</h2>
<section>
<p>
An example of <strong>nominal data</strong> is <em>blood types</em>:
</p>
<ul>
<li>type A+</li>
<li>type A-</li>
<li>type B+</li>
<li>type B-</li>
<li>type AB+</li>
<li>type AB-</li>
<li>type O+</li>
<li>type O-</li>
</ul>
</section>
<section>
<p>
Another example of <strong>nominal data</strong> is <em>sex</em>:
</p>
<ul>
<li>female</li>
<li>male</li>
</ul>
</section>
<section>
<p>
Another example of <strong>nominal data</strong> is <em>family names</em>:
</p>
<ul>
<li>Alves</li>
<li>Beg</li>
<li>Chen</li>
<li>Cho</li>
<li>Choi</li>
<li>da Silva</li>
<li>Dickson</li>
<li>dos Santos</li>
<li>Esfahani</li>
<li>Fernández</li>
<li>Ferreira</li>
<li>García</li>
<li>Jung</li>
<li>Kang</li>
<li>Kerr</li>
<li>Kim</li>
<li>Krempeaux</li>
<li>Li</li>
<li>Liu</li>
<li>Martin</li>
<li>Müller</li>
<li>Pahlavi</li>
<li>Park</li>
<li>Parsi</li>
<li>Pereira</li>
<li>Rodríguez</li>
<li>Safavi</li>
<li>Sasani</li>
<li>Wang</li>
<li>Yun</li>
<li>Zhang</li>
<li><em>etc</em></li>
</ul>
</section>
<section>
<p>
Another example of <strong>nominal data</strong> is <em>hair color</em>:
</p>
<ul>
<li>brown</li>
<li>black</li>
<li>blond</li>
<li>gray</li>
<li>red</li>
<li><em>etc</em></li>
</ul>
</section>
<section>
<p>
Another example of <strong>nominal data</strong> is <em>cities</em>:
</p>
<ul>
<li>Beijing</li>
<li>Bangalore</li>
<li>Bangkok</li>
<li>Bogotá</li>
<li>Buenos Aires</li>
<li>Cairo</li>
<li>Chennai</li>
<li>Chicago</li>
<li>Chongqing</li>
<li>Dallas</li>
<li>Delhi</li>
<li>Dhaka</li>
<li>Guangzhou</li>
<li>Hyderabad</li>
<li>Kinshasa</li>
<li>Kolkata</li>
<li>Isfahan</li>
<li>Istanbul</li>
<li>Jakarta</li>
<li>Karachi</li>
<li>Lagos</li>
<li>Lahore</li>
<li>Lima</li>
<li>London</li>
<li>Los Angeles</li>
<li>Moscow</li>
<li>Nagoya</li>
<li>New York City</li>
<li>Osaka</li>
<li>Manila</li>
<li>Mexico City</li>
<li>Mumbai</li>
<li>Paris</li>
<li>Rio de Janeiro</li>
<li>São Paulo</li>
<li>Seoul</li>
<li>Shanghai</li>
<li>Shenzhen</li>
<li>Tehran</li>
<li>Tianjin</li>
<li>Tokyo</li>
<li>Toronto</li>
<li>Vancouver</li>
<li><em>etc</em></li>
</ul>
</section>
</section>
<section>
<h2>Operations</h2>
<p>
One way of understanding the <strong>levels of measurement</strong> is — what type of <strong>operations</strong> are meaningful and valid for that type of data‽
</p>
<p>
Here is a table that summarizes what <strong>operations</strong> are and are <em>not</em >meaningful and valid for each <strong>levels of measurement</strong> category:
</p>
<table>
<thead>
<tr>
<th></th>
<th>nominal</th>
<th>ordinal</th>
<th>interval</th>
<th>ratio</th>
</tr>
</thead>
<tbody>
<tr>
<td>can × and ÷ ?</td>
<td>no</td>
<td>no</td>
<td>no</td>
<td>YES</td>
</tr>
<tr>
<td>can + and - ?</td>
<td>no</td>
<td>no</td>
<td>YES</td>
<td>YES</td>
</tr>
<tr>
<td>can &lt; and &gt; ?</td>
<td>no</td>
<td>YES</td>
<td>YES</td>
<td>YES</td>
</tr>
<tr>
<td>can = and ≠ ?</td>
<td>YES</td>
<td>YES</td>
<td>YES</td>
<td>YES</td>
</tr>
</tbody>
</table>
</section>
</article>