<p>
	OVERVIEW</p>
<p>
	&nbsp;</p>
<p>
	&nbsp;</p>
<p>
	This activity will produce the information students need to determine whether their hypothesis was supported or not. Students will calculate basic descriptive statistics and then will analyze the data using two basic principles: whether two things are related (correlation) or whether groups of things are different. Which technique is used depends in part on the data. The primary goal is for students to produce meaningful graphs depicting results, and to interpret the results to judge whether the hypothesis was supported or not.</p>
<p>
	&nbsp;</p>
<p>
	&nbsp;</p>
<h3>
	<a name="TOC-Materials"></a>Materials</h3>
<ul>
	<li>
		<span style="font-size: 11pt; font-family: Calibri,sans-serif;">data spreadsheet or table produced in Activity A</span></li>
	<li>
		Either of the following:
		<ul>
			<li>
				Graph paper &amp; calculators</li>
			<li>
				or Computers with Spreadsheet software (e.g., MS Excel)</li>
		</ul>
	</li>
</ul>
<div>
	<h2>
		<a name="TOC-ACTIVITY-PROCEDURE"></a>ACTIVITY PROCEDURE</h2>
	<p>
		&nbsp;</p>
	<h3>
		<a name="TOC-Getting-Ready"></a>Getting Ready</h3>
	This activity will use the data spreadsheet or table produced in Activity A.</div>
<div>
	<ul>
		<li>
			If using a spreadsheet program, students will need access to computers and that program.</li>
		<li>
			If using hard copy data sheets, students will need calculators.</li>
		<li>
			Graphs can be created manually by plotting on paper (graph paper is especially handy) or on the board. Some students might have access to and facility with graphing programs on computers, which can also be used. This activity describes manual graphing of the data; computer graphing will need to be explored and tested by the teacher as each school&rsquo;s computer and software combination is unique. Completing the manual graphing process will encourage a better understanding of why the results and datapoints show up where they do on a graph instead of &lsquo;magically&rsquo; appearing via the software.</li>
		<li>
			Depending on the research question and class dynamics this can be a small group activity, or the class can work as a whole.</li>
		<li>
			This activity requires teacher explanation of basic statistical operations &ndash; like calculating a mean &ndash; and an explanation of relationships and differences among groups.</li>
	</ul>
</div>
<div>
	<h3>
		<a name="TOC-Doing-the-Activity"></a>Doing the Activity</h3>
	<p>
		First, students will calculate and record basic descriptive statistics about their data. Begin with a brief description of what the following variables are, and then ask students to calculate these statistics for mercury in their data set.</p>
	<p style="text-indent: 0.5in;">
		Example Dataset:</p>
	<div align="center">
		<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse; border: medium none;">
			<tbody>
				<tr>
					<td style="border: 1pt solid black; padding: 0in 5.4pt; text-align: center; width: 30.6px; height: 43px;" valign="top">
						<p>
							1</p>
					</td>
					<td style="border-width: 1pt 1pt 1pt medium; border-style: solid solid solid none; border-color: black black black -moz-use-text-color; padding: 0in 5.4pt; text-align: center; width: 32.6px; height: 43px;" valign="top">
						<p>
							3</p>
					</td>
					<td style="border-width: 1pt 1pt 1pt medium; border-style: solid solid solid none; border-color: black black black -moz-use-text-color; padding: 0in 5.4pt; text-align: center; width: 30.6px; height: 43px;" valign="top">
						<p>
							4</p>
					</td>
					<td style="border-width: 1pt 1pt 1pt medium; border-style: solid solid solid none; border-color: black black black -moz-use-text-color; padding: 0in 5.4pt; text-align: center; width: 27.6px; height: 43px;" valign="top">
						<p>
							8</p>
					</td>
					<td style="border-width: 1pt 1pt 1pt medium; border-style: solid solid solid none; border-color: black black black -moz-use-text-color; padding: 0in 5.4pt; text-align: center; width: 31.6px; height: 43px;" valign="top">
						<p>
							12</p>
					</td>
				</tr>
			</tbody>
		</table>
	</div>
	<p>
		&nbsp;</p>
	<ul style="margin-top: 0in;">
		<li style="color: rgb(79, 98, 40);">
			<i><span style="color: windowtext;">Mean</span></i><span style="color: windowtext;">: The average of all the data values for a given variable. Add all the data values together (sum), then divide by n, the number of data values there are. </span><b>If the data were 1,3,4,8,12 then n is 5 (there are 5 numbers), the sum is 28, and the mean would be 5.6</b></li>
		<li style="color: rgb(79, 98, 40);">
			<i><span style="color: windowtext;">Median</span></i><span style="color: windowtext;">: The median is the value halfway through the ordered data set, below and above which there lies an equal number of data values. </span><b>In our example, the median would be 4, the middle value</b></li>
		<li style="color: rgb(79, 98, 40);">
			<i><span style="color: windowtext;">Minimum</span></i><span style="color: windowtext;">: The smallest value. </span><b>The minimum would be 1</b></li>
		<li style="color: rgb(79, 98, 40);">
			<i><span style="color: windowtext;">Maximum</span></i><span style="color: windowtext;">: The largest value. </span><b>The maximum would be 12</b></li>
		<li style="color: rgb(79, 98, 40);">
			<i><span style="color: windowtext;">Range</span></i><span style="color: windowtext;">: A measure of the spread or the dispersion of the observations. It is the difference between the largest and the smallest observed value of some quantitative characteristic and is very easy to calculate. </span><b>If the data were 1,3,4,8,12 then the range would be 12-1 = 11</b></li>
		<li>
			<i>Standard Deviation</i> (for more advanced analysis/classes): This is another measure of the spread of the data set. It tells you how tightly all the various data points are clustered around the mean in a set of data. The formula is more complex, and can be found in any statistics text. <b><span style="color: rgb(79, 98, 40);">The standard deviation of the number set above = 4.39</span></b></li>
	</ul>
	<p>
		&nbsp;Next, students will work on techniques that allow them to find patterns and relationships in the data. Two key techniques will be used.</p>
	<ol style="margin-top: 0in;">
		<li>
			<font size="3"><b>Are two things related?</b></font> You must have two columns of data that are numbers (or continuous variables, also called a <i>ratio scale</i>). Say students think that bigger fish will have more mercury. One way to evaluate whether that is the case or not is to graph fish size and mercury on paper or on the computer.<br />
			&nbsp;</li>
	</ol>
	<div style="margin-left: 80px;">
		<b>a. </b>Set up a graph with an X (horizontal) and Y (vertical) axis. Typically we put the response or dependent variable on the Y axis, and the predictor or independent variable on the X axis. Ask students to identify which is the independent and which is the dependent variable. In our example, fish size is independent and mercury content is dependent &ndash; we&rsquo;re asking if mercury content depends on fish size. Don&rsquo;t forget to label the axes with what they represent and the units of measure. The graph should look something like this:</div>
	<p style="margin-left: 1in; text-indent: 0.5in;">
		&nbsp;</p>
	<div style="display: block; text-align: left;">
		<span><a href="https://sites.google.com/site/mercuryourwatershedfriends/watershed-experiences/unit-5/b-presenting-data/1_a.jpg?attredirects=0" imageanchor="1"><img border="0" height="289" src="https://sites.google.com/site/mercuryourwatershedfriends/_/rsrc/1290099011590/watershed-experiences/unit-5/b-presenting-data/1_a.jpg?height=289&amp;width=320" width="320" /></a></span></div>
	<div style="margin-left: 80px;">
		<b>b. </b>Now plot the data points. The graph that results will be called a scatterplot, or an X-Y plot. For each fish size value, trace up to the corresponding mercury value. The graph might look something like this (although where the points are will be different, based on your data):</div>
	<p style="margin-left: 1in; text-indent: 0.5in;">
		&nbsp;</p>
	<div style="display: block; text-align: left;">
		<span><a href="https://sites.google.com/site/mercuryourwatershedfriends/watershed-experiences/unit-5/b-presenting-data/1_b.jpg?attredirects=0" imageanchor="1"><img border="0" height="291" src="https://sites.google.com/site/mercuryourwatershedfriends/_/rsrc/1290099044863/watershed-experiences/unit-5/b-presenting-data/1_b.jpg?height=291&amp;width=320" width="320" /></a><span> </span></span></div>
	<div style="margin-left: 80px;">
		<b>c. </b>To assess whether the two things are related, students need to understand a bit more about what the relationship might look like. There are three main types of relationship:</div>
	<p>
		<span><span><span style="font: 7pt &quot;Times New Roman&quot;;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<b>&nbsp; </b></span><b>i.</b><span style="font: 7pt &quot;Times New Roman&quot;;"><b>&nbsp;&nbsp;&nbsp;</b>&nbsp;&nbsp; </span></span></span>Positive. As size increases, so does mercury:</p>
	<p style="margin-left: 1.9134in;">
		&nbsp;</p>
	<div style="display: block; text-align: left;">
		<span><a href="https://sites.google.com/site/mercuryourwatershedfriends/watershed-experiences/unit-5/b-presenting-data/1_c_i.jpg?attredirects=0" imageanchor="1"><img border="0" height="291" src="https://sites.google.com/site/mercuryourwatershedfriends/_/rsrc/1290099114929/watershed-experiences/unit-5/b-presenting-data/1_c_i.jpg?height=291&amp;width=320" width="320" /></a></span></div>
	<p>
		<span><span><span style="font: 7pt &quot;Times New Roman&quot;;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<b> </b></span><b>ii.</b><span style="font: 7pt &quot;Times New Roman&quot;;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span>Negative. As size decreases, mercury increases:</p>
	<p style="margin-left: 1.9134in;">
		&nbsp;</p>
	<div style="display: block; text-align: left;">
		<span><a href="https://sites.google.com/site/mercuryourwatershedfriends/watershed-experiences/unit-5/b-presenting-data/1_c_ii.jpg?attredirects=0" imageanchor="1"><img border="0" height="291" src="https://sites.google.com/site/mercuryourwatershedfriends/_/rsrc/1290099136628/watershed-experiences/unit-5/b-presenting-data/1_c_ii.jpg?height=291&amp;width=320" width="320" /></a></span></div>
	<p>
		<span><span><span style="font: 7pt &quot;Times New Roman&quot;;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<b>&nbsp;&nbsp;&nbsp;&nbsp; </b></span><b>iii.</b><span style="font: 7pt &quot;Times New Roman&quot;;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span>No relationship. There&rsquo;s no clear pattern between size and mercury:</p>
	<p style="margin-left: 1.5in;">
		&nbsp;</p>
	<div style="display: block; text-align: left;">
		<span><a href="https://sites.google.com/site/mercuryourwatershedfriends/watershed-experiences/unit-5/b-presenting-data/1_c_iii.jpg?attredirects=0" imageanchor="1"><img border="0" height="291" src="https://sites.google.com/site/mercuryourwatershedfriends/_/rsrc/1290099161744/watershed-experiences/unit-5/b-presenting-data/1_c_iii.jpg?height=291&amp;width=320" width="320" /></a></span></div>
	<div style="margin-left: 80px;">
		<b>d. </b>If time and the class dynamic permits you might ask students to find the best fit line for the data. If using software such as Microsoft Excel, the software can display an equation and an R<sup>2</sup> value on the chart. If plotting by hand, students can use a piece of string and manipulate the two ends so the string appears to cross the center of the data points. It is recommended that you practice this manual technique before completing the exercise on data analysis software.<br />
		&nbsp;</div>
	<div style="margin-left: 80px;">
		<b>e. </b>Here is an example of a scatterplot with a best fit line:</div>
	<p style="margin-left: 1in; text-indent: 0.5in;">
		&nbsp;</p>
	<div style="display: block; text-align: left;">
		<span><a href="https://sites.google.com/site/mercuryourwatershedfriends/watershed-experiences/unit-5/b-presenting-data/1_e.jpg?attredirects=0" imageanchor="1"><img border="0" height="291" src="https://sites.google.com/site/mercuryourwatershedfriends/_/rsrc/1290099213780/watershed-experiences/unit-5/b-presenting-data/1_e.jpg?height=291&amp;width=320" width="320" /></a></span></div>
	<ol style="margin-top: 0in;">
		<li>
			<b><font size="3">Are groups of things different?</font> </b>You will need numeric data for one variable, and a categorical variable &ndash; named groups &ndash; for the other. For example, students might be looking to find whether different fish species had different mercury concentrations. Their hypothesis might be that perch have more mercury than bass.<br />
			&nbsp;</li>
	</ol>
	<div style="margin-left: 80px;">
		<b>a. </b>Set up a graph with an X (horizontal) and Y (vertical) axis. OR &ndash; use the boxplot or dot density graph introduced in the Warmup activities, above. Typically we put the response or dependent variable on the Y axis, and the predictor or independent variable on the X axis. Ask students to identify which is the independent and which is the dependent variable. In our example, fish species is independent and mercury content is dependent &ndash; we&rsquo;re asking if mercury content depends on fish species. Don&rsquo;t forget to label the axes with what they represent and the units of measure. The graph should look something like this:</div>
	<p style="margin-left: 0.5866in; text-indent: 0.5in;">
		&nbsp;</p>
	<div style="display: block; text-align: left;">
		<span><a href="https://sites.google.com/site/mercuryourwatershedfriends/watershed-experiences/unit-5/b-presenting-data/2_a.jpg?attredirects=0" imageanchor="1"><img border="0" height="322" src="https://sites.google.com/site/mercuryourwatershedfriends/_/rsrc/1290099267634/watershed-experiences/unit-5/b-presenting-data/2_a.jpg?height=322&amp;width=400" width="400" /></a></span></div>
	<div style="margin-left: 80px;">
		<b>b. </b>Calculate the mean for each group. In our example, the mean mercury in Perch was 307 ng/g; the mean mercury in Bass was 719 ng/g.</div>
	<div style="margin-left: 80px;">
		<b>c. </b>Start by plotting the mean for each group as a dot on the graph:</div>
	<p style="margin-left: 1in;">
		&nbsp;</p>
	<div style="display: block; text-align: left;">
		<span><a href="https://sites.google.com/site/mercuryourwatershedfriends/watershed-experiences/unit-5/b-presenting-data/2_c.jpg?attredirects=0" imageanchor="1"><img border="0" height="342" src="https://sites.google.com/site/mercuryourwatershedfriends/_/rsrc/1290099533406/watershed-experiences/unit-5/b-presenting-data/2_c.jpg?height=342&amp;width=400" width="400" /></a></span></div>
	<div style="margin-left: 80px;">
		<b>d. </b>We need to get an idea of how variable the data are for each species. Plot the minimum and maximum above and below the mean, and fill in with the other values, like this:</div>
	<p style="margin-left: 1in;">
		&nbsp;</p>
	<div style="display: block; text-align: left;">
		<span><a href="https://sites.google.com/site/mercuryourwatershedfriends/watershed-experiences/unit-5/b-presenting-data/2_d.jpg?attredirects=0" imageanchor="1"><img border="0" height="336" src="https://sites.google.com/site/mercuryourwatershedfriends/_/rsrc/1290099380452/watershed-experiences/unit-5/b-presenting-data/2_d.jpg?height=336&amp;width=400" width="400" /></a></span></div>
	<div style="margin-left: 80px;">
		<b>e. </b>If time and lesson plans permit, students can plot standard deviation rather than the range as a more appropriate measure of variability:</div>
	<div style="display: block; text-align: left; margin-left: 80px;">
		<a href="https://sites.google.com/site/mercuryourwatershedfriends/watershed-experiences/unit-5/b-presenting-data/2_e.jpg?attredirects=0" imageanchor="1"><img border="0" height="332" src="https://sites.google.com/site/mercuryourwatershedfriends/_/rsrc/1290099407692/watershed-experiences/unit-5/b-presenting-data/2_e.jpg?height=332&amp;width=400" width="400" /></a></div>
	<p>
		Now that you have some statistics about the data and a graph showing the patterns or differences, it&rsquo;s time to interpret what the results mean. Think of the graph and data as evidence, and the scientists (students) now need to judge whether the hypothesis was supported or not. In the graph above, showing perch versus bass mercury, the means are different, and there&rsquo;s not much overlap in the data. So the scientists would conclude that bass had more mercury than perch in their study, and that fish species does matter. If the hypothesis was that perch would have more mercury, it would not be supported by the data.</p>
	<p>
		Note that scientists avoid the terms &ldquo;right&rdquo; and &ldquo;wrong&rdquo; and do not say that we &ldquo;prove a hypothesis&rdquo;. Try to encourage students to adopt the language of supporting a hypothesis (or not).</p>
</div>
<div>
	<h3>
		<a name="TOC-Enrichment"></a>Enrichment</h3>
	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse; border: medium none;">
		<tbody>
			<tr>
				<td style="width: 7.45in; border: 1pt solid black; padding: 0in 5.4pt;" valign="top" width="715">
					<p>
						Question Set</p>
				</td>
			</tr>
			<tr>
				<td style="width: 7.45in; border-width: medium 1pt 1pt; border-style: none solid solid; border-color: -moz-use-text-color black black; padding: 0in 5.4pt;" valign="top" width="715">
					<ul style="margin-top: 0in;">
						<li>
							Why would a scientist avoid the terms &ldquo;right&rdquo; and &ldquo;wrong&rdquo; and rather use &ldquo;support a hypothesis&rdquo;?</li>
					</ul>
				</td>
			</tr>
			<tr>
				<td style="width: 7.45in; border-width: medium 1pt 1pt; border-style: none solid solid; border-color: -moz-use-text-color black black; padding: 0in 5.4pt;" valign="top" width="715">
					<ul style="margin-top: 0in;">
						<li>
							What kinds of things are useful to label on graphs?</li>
					</ul>
				</td>
			</tr>
			<tr>
				<td style="width: 7.45in; border-width: medium 1pt 1pt; border-style: none solid solid; border-color: -moz-use-text-color black black; padding: 0in 5.4pt;" valign="top" width="715">
					<ul style="margin-top: 0in;">
						<li>
							What kind of traits does a &ldquo;line of best fit&rdquo; have?</li>
					</ul>
				</td>
			</tr>
		</tbody>
	</table>
	<p>
		&nbsp;</p>
	<h2>
		<a name="TOC-DOCUMENTS"></a>DOCUMENTS</h2>
	<p>
		These documents can be viewed by clicking the links below.&nbsp; Individual PDFs of each document can be downloaded from the &quot;Attachments&quot; at the bottom of this web page.</p>
	<h3>
		<a name="TOC-Handouts"></a>Handouts</h3>
	<ul>
		<li>
			<a href="https://docs.google.com/viewer?a=v&amp;pid=sites&amp;srcid=ZGVmYXVsdGRvbWFpbnxtZXJjdXJ5b3Vyd2F0ZXJzaGVkZnJpZW5kc3xneDo2YTMyMDVhZGViYjg5MmI0" target="_blank">Student Worksheet</a></li>
	</ul>
</div>
