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<title>Sampling</title>
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<h1 class="center">Sampling</h1>
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/people.gif" alt="People" width="250" height="112" /></p>
<ul>
<li>Population: The whole group&nbsp;we are interested in</li>
<li>Census: A collection of data from the whole population</li>
<li>Sample: A collection of data from <b>part</b> of the population</li>
</ul><div style="clear:both"></div>
<p>But how do we choose what members of the population to sample?</p>
<p>There are 4 main methods:</p>
<div class="center">
<div class="boxa"><img src="images/sample-random.svg" alt="Random Sample" /><br>
<b>Random Sample</b><br>
(pick randomly from list)</div>
<div class="boxa"> <img src="images/sample-systematic.svg" alt="sytematic Sample" /><br>
<b>Systematic Sample</b><br>
(such as every 4th)
</div>
<div class="boxa"> <img src="images/sample-stratified.svg" alt="stratified Sample" /><br>
<b>Stratified Sample</b><br>
(randomly, but in ratio to group size)
</div>
<div class="boxa"> <img src="images/sample-cluster.svg" alt="cluster Sample" /><br>
<b>Cluster Sample</b><br>
(choose whole groups randomly)
</div>
</div>
<h2>Random Sampling</h2>
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/sample-random.svg" alt="Random Sample" /></p>
<p>The <b>best</b> way is to choose <b>randomly</b></p>
<p>Imagine slips of paper each with a person's name, put all the slips into a barrel, mix them up, then dive your hand in and choose some slips of paper.</p>
<p>But this means you need a <b>full list of the population</b> to choose from.</p>
<p>Computer databases can be a big help here!</p>
<div class="example">
<h3>Example: You want to know the favorite colors for people at your school, but don't have the time to ask everyone.</h3>
<p>Somehow get a full list of students printed out, then</p>
<ul>
<li>place all pages on the ground, drop a pencil and note down the student's name. </li>
<li> repeat until you have 50 names.</li>
</ul>Now survey those 50.
<p>Your results will <i><b>hopefully</b></i> be nearly as good as if you had asked everyone.</p>
</div>
<p>Random surveys are the best way to avoid <a href="../accuracy-precision.html">bias</a>.</p>
<p>And your results are better when you ask more people. </p>
<div class="example">
<p>Example: nationwide opinion polls survey around 2,000 people, and the results are nearly as good (within about 1%) as asking everyone.</p>
</div>
<h2>Systematic Sampling</h2>
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/sample-systematic.svg" alt="Systematic Sample" /></p>
<p>This is where we follow some system of selection like &quot;every 10th person&quot;</p>
<div class="example">
<h3>Example: You want to know the favorite colors for people at your school, but don't have the time to ask everyone.</h3>
<p>Solution: stand at the gate and choose &quot;every 4th person to arrive&quot;</p>
<p>Not perfect, as you will miss out on people who are away.</p>
<p>You could improve this by selecting from a full list of people then go and find them.</p>
</div>
<h2>Stratified Sampling</h2>
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/sample-stratified.svg" alt="Stratified Sample" /></p>
<p>This is where we divide the population into groups by some characteristic&nbsp;such as age or occupation or gender.</p>
<p>Then make sure our survey includes people from each group in proportion to how many there are in the whole population.</p>
<div class="example">
<h3>Example: Survey 100 People in Our Town </h3>
<p>We know that teachers make up 7% of our town's population, so we should include:</p>
<p class="center larger">100 x 7% = 7 teachers</p>
</div>
<div class="example">
<h3>Example: We want to survey 300 people in the USA</h3>
<p>This is the population breakdown for the USA in 2010:</p>
<table border="0" align="center">
<tr>
<th width="100" height="25" align="center">Age Range</th>
<th width="100" align="center">Percent </th>
</tr>
<tr>
<td height="25" align="center">0-4</td>
<td align="center">6.5%</td>
</tr>
<tr>
<td height="25" align="center">5-17</td>
<td align="center">17.5%</td>
</tr>
<tr>
<td height="25" align="center">18-23</td>
<td align="center">9.9%</td>
</tr>
<tr>
<td height="25" align="center">24-44</td>
<td align="center">26.6%</td>
</tr>
<tr>
<td height="25" align="center">45-64</td>
<td align="center">26.4%</td>
</tr>
<tr>
<td height="25" align="center">65+</td>
<td align="center">13.0%</td>
</tr>
<tr>
<td height="25" align="center">&nbsp;</td>
<td align="center"><b>100%</b></td>
</tr>
</table>
<p>We want to survey 300 people, so we choose:</p>
<table border="0" align="center">
<tr>
<th width="100" height="25" align="center">Age Range</th>
<th width="100" align="center">Percent </th>
<th width="100" align="center">People</th>
</tr>
<tr>
<td height="25" align="center">0-4</td>
<td align="center">6.5%</td>
<td align="center">20</td>
</tr>
<tr>
<td height="25" align="center">5-17</td>
<td align="center">17.5%</td>
<td align="center">52</td>
</tr>
<tr>
<td height="25" align="center">18-23</td>
<td align="center">9.9%</td>
<td align="center">30</td>
</tr>
<tr>
<td height="25" align="center">24-44</td>
<td align="center">26.7%</td>
<td align="center">80</td>
</tr>
<tr>
<td height="25" align="center">45-64</td>
<td align="center">26.4%</td>
<td align="center">79</td>
</tr>
<tr>
<td height="25" align="center">65+</td>
<td align="center">13.0%</td>
<td align="center">39</td>
</tr>
<tr>
<td height="25" align="center">&nbsp;</td>
<td align="center"><b>100%</b></td>
<td align="center"><b>300</b></td>
</tr>
</table>
<p>I am not sure how to ask the 0-4 range, but we will think of something.</p>
</div>
<h2>Cluster Sampling</h2>
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/sample-cluster.svg" alt="Cluster Sample" /></p>
<p>We break the population into many groups, then randomly choose whole groups.</p>
<div class="example">
<p>Example: we divide the town into many different zones, then randomly choose 5 zones and survey everyone in those zones.</p>
</div>
<p>Cluster sampling works best when the clusters are similar in character to each other.</p>
<div class="example">
<p>Example: if the town has rich and poor zones then try to create a new way of dividing the town into fairer regions. Also a good idea in general!</p>
</div>
<p>&nbsp;</p>
<p>&nbsp;</p>
<div class="related"><a href="index.html">Data Index</a></div>
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