<sect1 id="sect-analysis-statistical">
  <title>Statistical Analysis</title>

  <para>
    The data analysis tools package contains tools for statistical
    data analysis and data sampling.  To use
    these tools select the <guilabel>Data Analysis...</guilabel> item
    in the <guilabel>Tools</guilabel> menu.  This yields a list of
    tools to choose from.  Select one of the tools from the list and
    press the OK button or double-click on the tool.  The tools are
    described below.
  </para>

  <figure id="fig-statistical-analysistools">
    <title>Statistical Analysis Tools </title>
    <screenshot>
      <screeninfo>Gnumeric's Data Analysis Tools</screeninfo>
      <mediaobject>
        <imageobject>
          <imagedata fileref="figures/analysistools-tools.png" 
              format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the statistical analysis tools
              available through the "Tools" menu.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>

  <para>
    All tools have the same output options (see <xref
    linkend="fig-outputoptions" />).  The results can be printed into a
    new sheet, into a new workbook, or into a given output range on a
    sheet of the current workbook.  To select the output method select
    one of the radio buttons inside the <guilabel>Output</guilabel>
    frame. If you have chosen <quote><guibutton>Output
    Range</guibutton></quote> you must also enter a single range in
    the entry field.
  </para>

  <para>Select the <guilabel>Autofit
    Columns</guilabel> option to automatically adjust the widths of
    the columns in the output range.
  </para> 

  <note>
    <para>
      If the chosen output range is too small, some of the results
      will be lost.
    </para>
  </note>

  <note>
    <para>
      The old data in the output range is deleted and cannot be
      recovered.
    </para>
  </note>

  <figure id="fig-outputoptions">
    <title>Common output options of the data analysis tools</title>
    <screenshot id="outputoptions-shot">
      <mediaobject>
        <imageobject>
          <imagedata fileref="figures/analysistools-outputoptions.png" 
              format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the output options dialog used by
              the statistical analysis tools.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>

  <para>
    To enter a range into an entry field, you can either type the
    range specification into the text field, or click in the text
    field and then select the range on the sheet (see <xref
    linkend="specifyingranges" />).
  </para>

  <figure id="specifyingranges">
    <title>Specifying Ranges</title>
    <screenshot>
      <mediaobject>
        <imageobject>
          <imagedata fileref="figures/analysistools-ranges.png" format="PNG" />
      </imageobject>
            <textobject>
              <phrase>An image of the input range text box used by the
              statistical analysis tools.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>

  <para>
    Some entry fields accept lists of ranges. To enter these lists,
    select one range, type a comma, and then select the next range. At
    any time, you may switch to another sheet of the workbook.
  </para>





<sect2 id="anova">
  <title>Analysis of Variance</title>

  <sect3 id="anova-single-factor-tool">
     <title>ANOVA: Single Factor Tool</title>

     <para>
       Use this tool to perform a single factor analysis of the
       variances of given variables. The variables are specified by
       the <quote><guilabel>Input Range:</guilabel></quote> entry.
       The given range can be grouped into the variables either by
       columns, by rows or by areas.  The
       <quote><guilabel>Alpha:</guilabel></quote> entry specifies the
       significance level which is by default 5&#037;.
     </para>

     <para>If the first row or first column of the given range, or the 
     first field of each area contains labels, select the <quote><guibutton>Labels
     </guibutton></quote> option. The names of 
     the variables will be included in the  output table.</para>

     <para>The results of this analysis of variance are presented in 
     a standard ANOVA table. The <quote><guilabel>F critical</guilabel></quote>
     value is the largest value of F that is statistically significant
     using the given significance level (<quote><guilabel>Alpha</guilabel></quote>).</para>

     <para>This tool also calculates the count, sum, average,
     and the variance of each variable.</para>

   <figure id="anova-one-factor-tool-ex1">
    <title>1-factor ANOVA Dialog and Example Data</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-ANOVA1-ex1.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of a multilevel single factor ANOVA
              analysis.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
<example id="usinganovaonefactortool">
 <title>Using the single factor ANOVA</title>
     <para>See <xref linkend="anova-one-factor-tool-ex1" /> for an example 
     of a completed dialog and <xref
     linkend="anova-one-factor-tool-ex2" />
     for the corresponding output.
     </para>
 </example>
  <figure id="anova-one-factor-tool-ex2">
    <title>Output From a 1-factor ANOVA</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-ANOVA1-ex2.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the output from a multilevel single
              factor ANOVA analysis.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
     

  </sect3>

  <sect3 id="anova-two-factor-tool">
     <title>ANOVA: Two-Factor Tool</title>

     <para>&gnum; can perform two factor fixed effects ANOVAs with and 
     without replication. The same dialog is used and the 
     appropriate tool is selected depending on whether the number of rows 
     per sample is 1 or larger than 1.</para> 

  <sect4 id="anova-two-factor-without-tool">
     <title>ANOVA: Two-Factor Without Replication Tool</title>

     <para>If the number of rows per sample is given as 1, &gnum; 
     performs a two factor fixed effects ANOVA without replication. Each
     column of the input range is interpreted as a level of the first 
     factor while each row is interpreted as a level of the second factor.
     </para>
     <para>The first row and column of the range may contain labels for 
     these levels. In this case the <quote><guibutton>Labels</guibutton></quote> option should be selected.
     </para>
     <para> The <quote><guilabel>Alpha:</guilabel></quote> entry specifies the 
     significance level which is by default 5&#037;.</para>
 <example id="usinganovatwofactorwotool">
 <title>Using the 2-factor ANOVA Without Replication Tool</title>
     <para>See <xref linkend="anova-two-factor-without-tool-ex1" /> for an example 
     of a completed dialog and <xref
     linkend="anova-two-factor-without-tool-ex2" />
     for the corresponding output.
     </para>
 </example>
  <figure id="anova-two-factor-without-tool-ex1">
    <title>2-factor ANOVA Without Replication Dialog</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-ANOVA2wo-ex1.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of a two factor ANOVA without
              replication analysis.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
  <figure id="anova-two-factor-without-tool-ex2">
    <title>Output From a 2-factor ANOVA Without Replication</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-ANOVA2wo-ex2.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the output from a two factor ANOVA without
              replication analysis.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
  </sect4>

  <sect4 id="anova-two-factor-with-tool">
     <title>ANOVA: Two-Factor With Replication Tool</title>
     <para>If the number of rows per sample is larger than 1, &gnum; 
     performs a two factor fixed effects ANOVA with replication. Each
     column of the input range is interpreted as a level of the first 
     factor while groups of rows (the number of rows in each group given 
     by the <quote><guilabel>number of rows per sample</guilabel></quote> value) are interpreted as levels 
     of the second factor.
     </para>
     <para>The first row and column of the range may contain labels for 
     these levels. In this case the <quote><guibutton>Labels</guibutton></quote> option should be selected.
     </para>
     <para> The <quote><guilabel>Alpha:</guilabel></quote> entry specifies the 
     significance level which is by default 5&#037;.</para>
     <para>See <xref linkend="anova-two-factor-with-tool-ex1" /> for an example 
     of a completed dialog and <xref
     linkend="anova-two-factor-with-tool-ex2" />
     for the corresponding output.
     </para>
  <figure id="anova-two-factor-with-tool-ex1">
    <title>2-factor ANOVA With Replication Dialog</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-ANOVA2w-ex1.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of a two factor ANOVA with replication
              analysis.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
  <figure id="anova-two-factor-with-tool-ex2">
    <title>Output From a 2-factor ANOVA With Replication</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-ANOVA2w-ex2.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the output from a two factor ANOVA
              with replication analysis.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
     
     <para>&gnum; will estimate missing
     values for each level combination as the mean of the existing
     values in that combination. The degrees of freedom are adjusted
     appropriately. </para>

  </sect4>
  </sect3>

</sect2>

  <sect2 id="correlation-tool">
     <title>Correlation Tool</title>

  <figure id="correlation-tool-dialog">
    <title>Correlation Tool Dialog</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-correlation.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the correlation analysis dialog.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>

     <para>The correlation tool calculates the pairwise Pearson 
     correlation coefficients of the
     given variables.  Use this tool to calculate any number of
     correlation coefficients at the same time.  The variables for
     which the correlations are calculated are specified by the <quote><guilabel>Input
     Range:</guilabel></quote> entry. The input range can consist of either a single 
     range or a comma separated list of ranges. The given range or 
     ranges can be grouped by columns, by rows, or by areas.</para>

     <para>If the first row or column of the given ranges, or the 
     first field of each area contains labels,  the
     <quote><guibutton>Labels</guibutton></quote> option should be selected.
     </para>

  <figure id="correlation-example-1">
    <title>Some Example Data</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-correlation-ex1.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of an example data set for a
              correlation analysis.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>

 <example id="usingcorrelationtool">
 <title>Using the Correlation Tool</title>
    <para>For example, you want to calculate the correlation between
     three variables, one each in columns A, B, and C.
     Both variables have 10 values in rows 2 to 11 with labels in row 1
     (see <xref linkend="correlation-example-1" />).</para>
<orderedlist>
     <listitem><para>
     Enter A1:B11 in the <quote><guilabel>Input Range:</guilabel></quote> entry by typing 
     this directly into the entry or clicking in the entry field and 
     then selecting that range on the sheet. In the latter case the 
     entry will also contain the sheet name. </para></listitem>
     <listitem><para>
     Select the <quote><guibutton>Columns</guibutton></quote> radio button next to 
     <quote><guilabel>Grouped By:</guilabel></quote>, 
     since each variable is in its own column.</para></listitem>
     <listitem><para> Select the <quote><guibutton>Labels</guibutton></quote>
     option since the first row contains labels. (see 
     <xref linkend="correlation-example-2" />).</para></listitem>
     <listitem><para> Specify the output 
     options as described above.</para></listitem>
     <listitem><para> Press the OK button. </para></listitem>
</orderedlist>
     <para>The calculated correlations are given in a table with each column and
     row labeled with the names of the variables.  If the
     names are not given in the input range, &gnum; generates them.
     In our example, the 
     correlation between the variables in column A and B, can be found
     in the second column and third row of the results table (see 
     <xref linkend="correlation-example-3" />).</para>
 </example>
  <figure id="correlation-example-2">
    <title>Completed Correlation Dialog</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-correlation-ex2.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the completed correlation analysis
              dialog.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
  <figure id="correlation-example-3">
    <title>Correlation Tool Output</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-correlation-ex3.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the output of the correlation
              analysis.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
  </sect2>

  <sect2 id="covariance-tool">
     <title>Covariance Tool</title>

  <figure id="covariance-tool-dialog">
    <title>Covariance Tool Dialog</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-covariance.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the covariance analysis
              dialog.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>

     <para>The covariance tool calculates the pairwise 
     covariance coefficients of the
     given variables.  Use this tool to calculate any number of
     covariance coefficients at the same time.  The variables for
     which the covariances are calculated are specified by the <quote><guilabel>Input
     Range:</guilabel></quote> entry. The input range can consist of either a single 
     range or a comma separated list of ranges. The given range or 
     ranges can be grouped by columns, by rows, or by areas.</para>

     <para>If the first row or column of the given ranges, or the 
     first field of each area contains labels,  the
     <quote><guibutton>Labels</guibutton></quote> option should be selected.
     </para>

  <figure id="covariance-example-1">
    <title>Some Example Data</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-covariance-ex1.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image example data for a covariance
              analysis.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>

 <example id="usingcovariancetool">
 <title>Using The Covariance Tool</title>
    <para>For example, you want to calculate the covariance between
     three variables, one each in columns A, B, and C.
     Both variables have 10 values in rows 2 to 11 with labels in row 1
     (see <xref linkend="covariance-example-1" />).</para>
<orderedlist>
     <listitem><para>
     Enter A1:B11 in the <quote><guilabel>Input Range:</guilabel></quote> entry by typing 
     this directly into the entry or clicking in the entry field and 
     then selecting that range on the sheet. In the latter case the 
     entry will also contain the sheet name. </para></listitem>
     <listitem><para>
     Select the <quote><guibutton>Columns</guibutton></quote> radio button next to 
     <quote><guilabel>Grouped By:</guilabel></quote>, 
     since each variable is in its own column.</para></listitem>
     <listitem><para> Select the <quote><guibutton>Labels</guibutton></quote>
     option since the first row contains labels.
     </para></listitem>
     <listitem><para> Specify the output 
     options as described above.</para></listitem>
     <listitem><para> Press the OK button. </para></listitem>
</orderedlist>
     <para>The calculated covariances are given in a table with each column and
     row labeled with the names of the variables.  If the
     names are not given in the input range, &gnum; generates them.
     In our example, the 
     covariance between the variables in column A and B, can be found
     in the second column and third row of the results table (see 
     <xref linkend="covariance-example-2" />).</para>
 </example>
  <figure id="covariance-example-2">
    <title>Covariance Tool Output</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-covariance-ex2.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the output of a covariance analysis.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
  </sect2>


  <sect2 id="descriptive-statistics-tool">
     <title>Descriptive Statistics Tool</title>

  <figure id="descriptive-statistics-tool-dialog">
    <title>Descriptive Statistics Tool Dialog</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-descstats.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the descriptive statistics dialog.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>

     <para>The descriptive statistics tool calculates various statistics 
     for the given variables and a confidence interval for the population
     mean. The variables are specified via the <quote><guilabel>Input
     Range:</guilabel></quote> entry.  The given range or list of ranges can be grouped into 
     variables by columns, rows, or areas.</para>

     <para>This tool can produce four different kinds of statistical
     data.
     </para>
     <itemizedlist>
     <listitem><para>If the <quote><guibutton>Summary Statistics</guibutton></quote> option is selected,  
     this tool calculates the
     mean, standard error, median, mode, standard deviation, sample
     variance, kurtosis, skewness, range, minimum, maximum, sum, and
     count for each variable.</para>
     </listitem>
     <listitem><para>If the <quote><guibutton>Confidence Interval for the Mean</guibutton></quote> option is 
     selected, the tool calculates  confidence intervals for the population
     mean of each variable.
     Specify the confidence level in the entry box.  The default confidence 
     level is 95&#037;.</para> 

     <note><para>The interval given will usually be wider than the 
     interval obtained using the CONFIDENCE function. The CONFIDENCE function
     assumes that the population standard deviation is known. This tool
     estimates the population standard deviation using the sample standard
     deviation.</para></note></listitem>

     <listitem><para>If the <quote><guibutton>Kth Largest:</guibutton></quote> option is selected, the tool finds
     the <parameter>k</parameter>th largest value of each of the variables.  Specify 
     <parameter>k</parameter> in
     the entry box next to the option. The default is 1.
     </para></listitem>

     <listitem><para>If the <quote><guibutton>Kth Smallest:</guibutton></quote> option is selected, the tool finds
     the <parameter>k</parameter>th smallest value of each of the variables.  Specify 
     <parameter>k</parameter> in
     the entry box next to the option. The default is 1.
     </para></listitem>
     </itemizedlist>
     <para>If the first entry for each variable contains the label,
     select the <quote><guibutton>Labels</guibutton></quote> option.
     </para>
  <figure id="descstats-example-1">
    <title>Some Example Data</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-descstats-ex1.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of some example data for descriptive
              statistics.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
 <example id="usingdescstatstool"><title>Using the Descriptive Statistics Tool</title>
     <para><xref linkend="descstats-example-1" /> shows some example data, 
     <xref linkend="descstats-example-1-options" /> the selected options, and 
     <xref linkend="descstats-example-2" /> the corresponding output.
     </para>
</example>
  <figure id="descstats-example-1-options">
    <title>The Options Page For Descriptive Statistics</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-descstats-ex1-options.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of some example data for descriptive
              statistics.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
  <figure id="descstats-example-2">
    <title>Descriptive Statistics Tool Output</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-descstats-ex2.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the output of a descriptive
              statistics analysis.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
  </sect2>

  <sect2 id="exp-smoothing-tool">
     <title>Exponential Smoothing Tool</title>

  <figure id="smoothing-tool-dialog">
    <title>Exponential Smoothing Tool Dialog</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-smoothing.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the exponential smoothing
              dialog.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>

     <para>The Exponential Smoothing tool performs the exponential
     smoothing for the given set or sets of values.  Each value in the
     smoothed set is predicted based on the forecast for the prior
     period.  The formula to calculate the forecast is: 
     F(t+1) = F(t) + (1 - <guilabel>dampingFactor</guilabel>) 
     * (A(t) - F(t)), 
     where <parameter>A(t)</parameter> is the <parameter>t</parameter>th
     value in the original data set.</para>

     <para>Specify the cells containing the datasets in the <quote><guilabel>Input
     Range</guilabel></quote> entry. The entered range or ranges are grouped into 
     datasets either by rows or by columns.</para> 

     <para>If you have labels
     in the first cell of each data set, select the
     <quote><guilabel>Labels</guilabel></quote> option.</para>

     <para>Specify prior forecast adjustment value in the
     <quote><guilabel>Damping factor</guilabel></quote> entry.  
     A value, for example, between 0.2 and 0.3 represents 20 to 30 percent error
     adjustment in the prior forecast.</para>

     <para>If you want to have the standard errors output as well, press the
     checkbutton on before starting the tool. The standard errors are 
     calculated using the following formula: e(t) = SQRT ( ((A(t-3)-F(t-3))^2 +
     (A(t-2)-F(t-2))^2 + (A(t-1)-F(t-1))^2) / 3 ).</para>
 
   <figure id="smoothing-example-1">
    <title>Some Example Data for the Exponential Smoothing Tool</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-smoothing-ex1.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of example data for exponential
              smoothing.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
 <example id="usingsmoothingtool"><title>Using the Exponential Smoothing Tool</title>
     <para><xref linkend="smoothing-example-1" /> shows some example data and 
     <xref linkend="smoothing-example-2" /> the corresponding output.
     </para>
</example>
  <figure id="smoothing-example-2">
    <title>Exponential Smoothing Tool Output</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-smoothing-ex2.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the output of an exponential
              smoothing analysis.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>

  </sect2>

  <sect2 id="fourier-analysis-tool">
     <title>Fourier Analysis Tool</title>

  <figure id="fourier-tool-dialog">
    <title>Fourier Analysis Tool Dialog</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-fourier.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the fourier analysis
              dialog.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>

     <para>
       The Fourier Analysis tool normally performs a Fast Fourier
       Transform to obtain the discrete fourier transform
       F<subscript>s</subscript> of the given sequence
       f<subscript>t</subscript> of real numbers according to the
       formula given in <xref linkend="fourier-tool-formula"
       />.</para> <para>Select the
       <quote><guilabel>Inverse</guilabel></quote> option to calculate
       the inverse discrete fourier transform
       f<subscript>t</subscript> of the given sequence
       F<subscript>s</subscript> of real numbers</para> <note><para>If
       the given sequences does not contain a number of terms that is
       a power of 2 (i.e.  2, 4, 8, 16, 32, 64, 128, etc.), this tool
       will append zeros to reach such a power of 2!</para></note>
     
     <para>Specify the cells containing the datasets in the
     <quote><guilabel>Input Range</guilabel></quote> entry. The
     entered range or ranges are grouped into sequences either by rows
     or by columns.</para>

     <para>If you have labels
     in the first cell of each data set, select the
     <quote><guilabel>Labels</guilabel></quote> option.</para>

  <figure id="fourier-tool-formula">
    <title>Fourier Analysis Formulae</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-fourier-formula.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>The formulae used in a fourier analysis.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>

     <note>
       <para>Before using the numbers obtained by this tool, ensure
       that these are in fact the correct formulae for your
       discipline. In the physical sciences this fourier transform
       tends to be called the inverse fourier transform and vice
       versa. Moreover, frequently the scaling factor varies.</para>
       <para>For example <application>Mathematica</application> uses
       the terms fourier transform and inverse fourier transform with
       the reversed meaning than &gnum;
       and it uses a scaling factor of
       <parameter>1/SQRT(N)</parameter> rather than
       <parameter>1/N</parameter>.</para></note>
  </sect2>

  <sect2 id="ftest-two-sample-for-variances-tool">
     <title>F-Test: Two-Sample for Variances Tool</title>

  <figure id="ftest-tool-dialog">
    <title>F-Test Tool Dialog</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-ftest.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the dialog for an F-test analysis of
              the equality of two variances.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
     <para>Use the F-Test tool to test whether two population  
     variances are different against the null hypothesis that
     they are not.</para>

     <para>Specify the variables in the <quote><guilabel>Variable 1 Range:</guilabel></quote>
     and <quote><guilabel>Variable 2 Range:</guilabel></quote> entries. The <quote><guilabel>Alpha:</guilabel></quote> 
     entry contains the 
     significance level which is by default 5&#037;.</para>

     <para>If the first field of each range contains labels, 
     select the <quote><guibutton>Labels</guibutton></quote> option. The names of 
     the variables will be included in the  output table.</para>

     <para>The results are given in a table.  This table contains
     the mean, variance, count of observations and the degree
     of freedom for both variables. The output table also includes the F-value,
     the one-tailed probability for the F-value, and the F Critical
     value for one-tailed test and the corresponding values for a two 
     tailed test. The one-tailed probability for the
     F-value (<quote><guilabel>P(F&lt;=f) one-tail</guilabel></quote> row) is the probability of making a
     Type I error in the one-tailed test. Similarly, the two-tailed 
     probability for the F-value (<quote><guilabel>P two-tail</guilabel></quote> row)
     is the probability of making a Type I error in the two-tailed test.
     Since in the two-tailed F-Test both critical values are positive, the
     <quote><guilabel>F Critical two-tail</guilabel></quote> row contains two numbers.</para>

     <para>If the output is directed into a specific output range, that
     range should contain at least three columns and eight rows.</para>

   <figure id="ftest-example-1">
    <title>Some Example Data</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-ftest-ex1.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of some example data for an F-test of
              the equality of two variances.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
 <example id="usingftesttool"><title>Using the F-Test Tool</title>
     <para><xref linkend="ftest-example-1" /> shows some example data and 
     <xref linkend="ftest-example-2" /> the corresponding output.
     </para>
</example>
  <figure id="ftest-example-2">
    <title>F-Test Tool Output</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-ftest-ex2.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the output of an F-test analysis of
              the equality of two variances.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
    
  </sect2>

  <sect2 id="histogram-tool">
     <title>Histogram Tool</title>

  <sect3 id="histogram-tool-intro">
     <title>Introduction</title>
     

  <figure id="histogram-tool-dialog">
    <title>Histogram Tool Dialog</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-histogram.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the dialog to generate various
              histograms open to the "Input" tab.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>

     <para>
     The histogram calculates several kinds of histograms for one or more 
     variables. The types of histogram created are determined by the options
     selected.  
     </para>

     <para>As shown in <xref linkend="histogram-tool-dialog" />, the
     histogram dialog has four tabs. We will introduce them in
     sequence.</para>
  </sect3>

  <sect3 id="histogram-tool-inputtab">
     <title>The <quote><guilabel>Input</guilabel></quote> Tab</title>

     <para>The <quote><guilabel>Input</guilabel></quote> tab contains
     the field specifying the data to be used for the
     histogram.</para>
     <para>
     The <quote><guilabel>Input Range</guilabel></quote> entry
     contains a single range or a list of ranges, that can be grouped
     into variables by rows, columns, or areas. The
     <quote><guilabel>Bin Range</guilabel></quote> entry contains a
     single range of cutoff values. Both ranges may also include
     labels.
     </para>
     <para>If the first row or column of the given input ranges, or
     the first field of each area contains labels, the
     <quote><guibutton>Input Labels</guibutton></quote> option should
     be selected.
     </para>

  </sect3>
  <sect3 id="histogram-tool-binstab">
     <title>The <quote><guilabel>Bins</guilabel></quote> Tab</title>
  <figure id="histogram-tool-dialog-bins">
    <title>Histogram Tool Dialog <quote><guilabel>Bins Tab</guilabel></quote></title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-histogram-bins.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the dialog to generate various
              histograms open to the "Bins" tab.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>

  <para>The bins (or classes) for the histogram can either be predetermined by data 
  contained in your workbook or calculated by the histogram tool.</para>

  <para>Select the <quote><guilabel>Predetermined Bins</guilabel></quote> option to specify 
  data on your worksheet in the <quote><guilabel>Bin Range:</guilabel></quote> entry. The
  range should consist of a single column or two columns (the first one containing labels). If the 
  first column of the bin range contains labels, select the <quote><guibutton>Bin 
  Labels</guibutton></quote> option. The values in the last column are used as separators between adjacent bins.</para> 

  <para>Select the <quote><guilabel>Calculated Bins</guilabel></quote> option to have the 
  bins determined by the tool. Enter the desired number of bins in the 
  <quote><guilabel>N:</guilabel></quote> entry. It is recommended (but optional) that you 
  specify the minimum and maximum cutoffs in the <quote><guilabel>Min:</guilabel></quote>
  and <quote><guilabel>Max:</guilabel></quote> entries.</para>
  </sect3>

  <sect3 id="histogram-tool-optionstab">
     <title>The <quote><guilabel>Options</guilabel></quote> Tab</title>

     <para> The options in the options tab modify the appearance of the histogram:</para>
     <itemizedlist>
     <listitem>
     <para> The <quote><guibutton>Pareto</guibutton></quote> option causes the bins to be 
     sorted by decreasing 
     frequency of the first variable.
     </para>
     </listitem>
     <listitem>
     <para> The <quote><guibutton>Percentages</guibutton></quote> option adds a histogram in terms 
     of 
     percentages rather than frequencies.
     </para>
     </listitem>
     <listitem>
     <para> The <quote><guibutton>Cumulative Percentages</guibutton></quote> option adds a 
     cumulative histogram.
     </para>
     </listitem>
     <listitem>
     <para> The <quote><guibutton>Chart</guibutton></quote> option is not implemented.
     </para>
     </listitem>
     </itemizedlist>

  </sect3>


  <sect3 id="histogram-tool-outputtab">
     <title>The <quote><guilabel>Output</guilabel></quote> Tab</title>

      <para>
        The Output tab contains the standard output options and fields
        described at the beginning of <xref
        linkend="sect-analysis-statistical" />.
      </para>
  </sect3>


  <sect3 id="histogram-tool-example">
    <title>A Histogram Example</title>

    <figure id="histogram-example-1">
      <title>Some Example Data</title>
      <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-histogram-ex1.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of some example data for use with the
              histogram tool.</phrase>
            </textobject>
           </mediaobject>
      </screenshot>
    </figure>

    <figure id="histogram-example-3">
      <title>Specifying Bins</title>
      <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-histogram-ex3.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of selecting the bins for the example
              data used with the histogram tool.</phrase>
            </textobject>
           </mediaobject>
      </screenshot>
    </figure>

    <example id="usinghistogramtool">
      <title>Using the Histogram Tool</title>

      <para>
        For example, you want to calculate a histogram and a
        cumulative histogram in percentages for a the number of
        successes in several sequences of trials. The numbers of
        successes are recorded in column A and the classes of interest
        in column D with labels in column C (see <xref
        linkend="histogram-example-1" />).
      </para>

      <orderedlist>
        <listitem>
          <para>
            Enter A1:A21 in the <quote><guilabel>Input
            Range:</guilabel></quote> entry of the
            <quote><guilabel>Input</guilabel></quote> tab by typing
            this directly into the entry or clicking in the entry
            field and then selecting that range on the sheet. In the
            latter case the entry will also contain the sheet
            name. 
          </para>
        </listitem>
        <listitem>
          <para>
            Since you only have one variable select the
            <quote><guibutton>Areas</guibutton></quote> or
            <quote><guibutton>Columns</guibutton></quote> radio button
            next to <quote><guilabel>Grouped By:</guilabel></quote>.
            </para>
        </listitem> 
        <listitem><para> Select the
            <quote><guibutton>Input Labels</guibutton></quote> option
            since the first cell of the Input Range contains a
            label.</para>
        </listitem>
        <listitem><para> Enter C1:D5 in
            the <quote><guilabel>Bin Range:</guilabel></quote> entry
            of the <quote><guilabel>Bins</guilabel></quote> tab. The
            <quote><guilabel>Predetermined Bins</guilabel></quote>
            option will now also be selected (see <xref
            linkend="histogram-example-3" />). </para>
        </listitem>
         <listitem><para> Select the <quote><guibutton>Bin
            Labels</guibutton></quote> option since the first column
            of the Bin Range contains labels.  </para>
        </listitem>
        <listitem><para> Select the
            <quote><guibutton>Percentage</guibutton></quote> and
            <quote><guibutton>Cumulative
            Percentages</guibutton></quote> options of the
            <quote><guilabel>Options</guilabel></quote> tab.
            </para>
        </listitem>
        <listitem>
          <para>
            In the <quote><guilabel>Output</guilabel></quote> tab,
            specify the output options as described at the beginning of
            <xref linkend="sect-analysis-statistical" />.
          </para>
        </listitem>
        <listitem><para>
            Press the OK button. </para>
        </listitem>
      </orderedlist>
     <para> The results are shown in 
     <xref linkend="histogram-example-2" />.</para>
 </example>
  <figure id="histogram-example-2">
    <title>Histogram Tool Output</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-histogram-ex2.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the output from the histogram
              analysis tool.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
  </sect3>
  </sect2>

  <sect2 id="moving-average-tool">
     <title>Moving Average Tool</title>

  <figure id="moving-tool-dialog">
    <title>Moving Average Tool Dialog</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-moving-average.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the dialog for the moving average
              analysis tool.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>

     <para>Use the moving average tool to calculate moving averages of
     one or more data sets.  A moving average provides useful trend
     information of the data that is lost in a simple average.  In
     addition, moving averages can be used to eliminate random
     variance.  For example, use this tool to create a smoother curve
     of a stock prize.</para>

     <para>Specify the cells containing the datasets in the
     <quote><guilabel>Input Range</guilabel></quote> entry. The
     entered range or ranges are grouped into datasets either by rows
     or by columns.</para>

     <para>If you have labels in the first cell of each data set,
     select the <quote><guilabel>Labels</guilabel></quote>
     option.</para>

     <para>Specify the <quote><guilabel>Interval</guilabel></quote>
     for the moving average.  The interval <parameter>i</parameter> is
     the number of consecutive values to be included in each moving
     average.</para>

     <para>The results are given in one column for each dataset Each
     row represents the moving average of the corresponding row or
     column in the input range.  The moving average cannot be
     calculated for the first <parameter>k</parameter> rows in the
     input range where <parameter>k</parameter> is smaller than the
     given interval <parameter>i</parameter>.</para>

   <figure id="moving-example-1">
    <title>Some Example Data for the Moving Average Tool</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-moving-average-ex1.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of some example data for use with the
              moving average analysis tool.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
 <example id="usingmovingtool"><title>Using the Moving Average Tool</title>
     <para><xref linkend="moving-example-1" /> shows some example data and 
     <xref linkend="moving-example-2" /> the corresponding output.
     </para>
</example>
  <figure id="moving-example-2">
    <title>Moving Averages Tool Output</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-moving-average-ex2.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the output from the moving average
              analysis tool.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
  </sect2>

  <sect2 id="rank-and-percentile-tool">
     <title>Rank and Percentile Tool</title>

  <figure id="rank-and-percentile-tool-dialog">
    <title>Rank and Percentile Tool Dialog</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-rank.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the rank and percentile analysis
              tool.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>

     <para>Use this tool to rank given data and to calculate the
     percentiles of each data point.</para>
     <para>Specify the datasets to use in the <quote><guilabel>Input  
     Range:</guilabel></quote> entry.  
     The given range can be grouped into datasets by columns, by rows, or by areas.</para>

     <para>For each dataset, the tool creates three columns in the 
     output table:</para>
     <orderedlist>
     <listitem><para>The first column gives the indices of the 
     ordered data from largest to smallest data value.</para></listitem>
     <listitem><para>The second column 
     gives data values corresponding to the indices in the first column.</para></listitem>
     <listitem><para>The  third column indicates
     the percentile of the  data value in the second column.</para></listitem>
     </orderedlist>

     <para>If you have labels
     in the first cell of each data set, select the
     <quote><guilabel>Labels</guilabel></quote> option.</para>

   <figure id="rank-example-1">
    <title>Some Example Data for the Rank and Percentile Tool</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-rank-ex1.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of example data for use with the rank
              and percentile analysis tool.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
 <example id="usingranktool"><title>Using the Rank and Percentile Tool</title>
     <para><xref linkend="rank-example-1" /> shows some example data and 
     <xref linkend="rank-example-2" /> the corresponding output.
     </para>
</example>
  <figure id="rank-example-2">
    <title>Rank and Percentile Tool Output</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-rank-ex2.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the output from a rank and
              percentile analysis.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
  <note><para>In the case of ties, the rank calculated by this tool differs from the 
  value of the RANK function for the same data. This tool calculates the rank as it is 
  normally used in Statistics: If two values are tied, the assigned rank is the average
  rank for those entries. For example in <xref
  linkend="rank-example-1" /> the two values 10
  are the second and third largest values. Since they are equal each receives the rank of 
  2.5, the average of 2 and 3. The rank function on the other hand assigns the rank as it 
  is normally used to determine placements. The two values 10 would therefore each receive
  a rank of 2.   
  </para></note>
  </sect2>

  <sect2 id="regression-tool">
     <title>Regression Tool</title>
  <figure id="regression-tool-dialog">
    <title>Regression Tool Dialog</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-regression.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the regression tool dialog.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
  <para>The regression tool performs a multiple regression analysis.</para>
  <para>Enter a range or list of ranges containing the independent variables 
  into the <quote><guilabel>X Variables:</guilabel></quote> entry. These ranges 
  can be grouped into the various independent variables by columns, by rows, 
  or by areas. Select the appropriate option.</para>
  <para>Enter a single range containing the dependent variable into the
   <quote><guilabel>Y Variable:</guilabel></quote> entry.</para>
  <para>If the ranges for the independent and dependent variables also contains 
  labels in the first field of each row, column or area, select the <quote>
  <guilabel>Labels</guilabel></quote> option.</para>
  <para> Specify the confidence level in the <quote><guilabel>Confidence
  Level:</guilabel></quote> entry. The default is 95&#037;.</para>
  <para>To force the regression line or plane to pass through the origin, select the
  <quote><guilabel>Force Intercept To Be Zero</guilabel></quote> option.</para>
  <para>Specify the output options as described above. If the output is directed 
  into a specific output range, that
  range should contain at least seven columns and 17 rows more than there are 
  independent variables.</para>

  <figure id="regression-example-1">
    <title>Regression Example Data</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-regression-ex1.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of example data for use with the
              regression tool.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>

 <example id="usingregressiontool">
 <title>Using the Regression Tool</title>

  <para>
    Suppose you want to perform a regression analysis on the data
    given in <xref linkend="regression-example-1" /> using
    <parameter>v</parameter> and <parameter>y</parameter> as
    independent variables and <parameter>u</parameter> as dependent
    variable.</para>
<orderedlist>
     <listitem><para>
     Enter B1:B9,E1:E9 in the <quote><guilabel>X Variables:</guilabel></quote> 
     entry by typing 
     this directly into the entry or clicking in the entry field and 
     then selecting the first part range on the sheet, typing comma, and then 
     selecting the second range. In the latter case the 
     entry will also contain the sheet name. </para></listitem>
     <listitem><para>
     Enter A1:A9  in the <quote><guilabel>Y Variable:</guilabel></quote> 
     entry. </para></listitem>
     <listitem><para>
     Select the <quote><guibutton>Columns</guibutton></quote> or 
     <quote><guibutton>Areas</guibutton></quote> option 
     since each variable is in its own column and also its own area.</para></listitem>
     <listitem><para> Select the <quote><guibutton>Labels</guibutton></quote>
     option since the first row contains labels. (see 
     <xref linkend="regression-example-2" />).</para></listitem>
     <listitem><para> Specify the output 
     options as described above.</para></listitem>
     <listitem><para> Press the OK button. </para></listitem>
</orderedlist>
     <para> The output of this regression analysis is shown in
     <xref linkend="regression-example-3" />.</para>
 </example>
  <figure id="regression-example-2">
    <title>Completed Regression Dialog</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-regression-ex2.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the regression tool dialog with the
              required fields completed.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
  <figure id="regression-example-3">
    <title>Regression Tool Output</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-regression-ex3.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the output from a regression
              analysis.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
  </sect2>

  <sect2 id="sampling-tool">
     <title>Sampling Tool</title>
     <figure>
        <title>Sampling Tool Dialog</title>
	<screenshot>
	   	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-sampling.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the sampling tool.</phrase>
            </textobject>
           </mediaobject>
	</screenshot>
      </figure>
     <para>Use the sampling tool to take a sample of a data set.  This
     tool can take both a random sample of a given size or a periodic
     sample:</para>
     <variablelist>
     <varlistentry><term>random sample</term>
     <listitem><para>A random sample is a subset of the population such that 
     every subset of that size has the same chance of being picked.</para></listitem>
     </varlistentry>
     <varlistentry><term>periodic sample</term>
     <listitem><para>In a periodic sample every <parameter>k</parameter>th element in 
     the population is selected.</para></listitem>
     </varlistentry>
     </variablelist>

     <para>To use this tool, first specify the data set or data sets by setting the
     <quote><guilabel>Input Range:</guilabel></quote> entry. The range or ranges 
     given can be grouped into datasets by rows, by columns, or by areas.</para>
     <para>If the first entry in each data set contains a variable, select the 
     <quote><guilabel>Labels</guilabel></quote> option.</para>

     <para>Select the sampling method which
     can be either periodic or random.</para>
     <variablelist>
     <varlistentry><term>random sample</term>
     <listitem><para>Specify the size of the random sample in the <quote><guilabel>Size 
     of Sample:</guilabel></quote> entry.</para></listitem>
     </varlistentry>
     <varlistentry><term>periodic sample</term>
     <listitem><para>Specify the period in the <quote><guilabel>Period:</guilabel></quote>
     entry.</para></listitem>
     </varlistentry>
     </variablelist>

     <para>Specify the number of samples you would like to obtain in the <quote><guilabel>
     Number of Samples:</guilabel></quote> entry.</para>
     <note><para> Since the period uniquely determines a periodic sample, if you specify 
     that you would like 2 samples you will be given the identical sample twice.</para></note>
     <note><para>If the dataset for a periodic sample is a two dimensional range, &gnum; 
     will enumerate the data points by row first.</para></note>

   <figure id="sampling-example-1">
    <title>Some Example Data for the Sampling Tool</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-sampling-ex1.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of example data for use with the
              sampling tool.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
 <example id="usingsamplingtool"><title>Using the Sampling Tool</title>
     <para><xref linkend="sampling-example-1" /> shows some example data and 
     <xref linkend="sampling-example-2" /> the corresponding output.
     </para>
</example>
  <figure id="sampling-example-2">
    <title>Sampling Tool Output</title>
    <screenshot>
	<mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-sampling-ex2.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the output from the sampling
              tool.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
  </sect2>


<sect2 id="t-test">
     <title>Comparing Means of 2 Populations</title>
     <para>&gnum; provides 4 similar
     tools to test whether the difference of two population means is
     equal to a hypothesized value. These four tools use the same
     dialog (see <xref linkend="ttest-dialog" />).</para>

  <figure id="ttest-dialog">
    <title><parameter>t</parameter>- and <parameter>z</parameter>-Test
    Tool Dialog</title>

    <screenshot>
      <mediaobject>
        <imageobject>
          <imagedata fileref="figures/analysistools-ttest.png" format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the t-test and z-test dialog.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>

     <para>Depending on the options settings, the appropriate test
     will be performed. The entries in the
     <quote><guilabel>Input</guilabel></quote>,
     <quote><guilabel>Test</guilabel></quote>, and
     <quote><guilabel>Output</guilabel></quote> frames are independent
     from the specific test.</para>

     <para>Enter the first variable in the <quote><guilabel>Variable 1
     Range</guilabel></quote> entry and the second variable in the
     <quote><guilabel>Variable 2 Range</guilabel></quote>
     entry.</para> <para>Enter the hypothesized difference between the
     population means in the <quote><guilabel>Hypothesized Mean
     Difference</guilabel></quote> entry, which has a default of 0.
     Enter the significance level in the
     <quote><guilabel>Alpha</guilabel></quote> entry, which has a
     default of 5 &#037;.</para> <para> Specify the output options as
     described above. If the output is printed into a range, it should
     have at least three columns and ten rows.</para>

     <para>There are up to three possible options that can be selected:</para>
     <variablelist>
     <varlistentry><term><quote><guilabel>Paired</guilabel></quote> versus <quote><guilabel>Unpaired</guilabel></quote>
     </term><listitem><para>
     If the variables are dependent (or paired) select the <quote><guilabel>Paired</guilabel></quote>
     option.
     </para></listitem>
     </varlistentry>
     <varlistentry><term><quote><guilabel>Known</guilabel></quote> versus <quote><guilabel>Unknown</guilabel></quote>
     </term><listitem><para>
     For unpaired or independent variables, the population variances may be known 
     or unknown. In the latter case they will be estimated using the sample variances.
     Select the <quote><guilabel>Known</guilabel></quote> option if you in fact know the population 
     variances prior to collecting the sample.
     </para></listitem>
     </varlistentry>
     <varlistentry><term><quote><guilabel>Equal</guilabel></quote> versus <quote><guilabel>Unequal</guilabel></quote>
     </term><listitem><para>
     For paired variables with unknown population variances, we may either assume 
     that the population variances are equal or not. If the population variances are
     assumed to be equal, &gnum; will estimate the common variance by pooling the 
     sample variances. Select the <quote><guilabel>Equal</guilabel></quote> option to assume that
     the population variances are equal.
     </para></listitem>
     </varlistentry>
     </variablelist>

  <sect3 id="t-test-paired-two-samples-for-means-tool">
     <title><parameter>t</parameter>-Test: Paired Two Sample for Means Tool</title>
  <figure id="ttest-dialog-paired">
    <title><parameter>t</parameter>-Test (Paired) Tool Dialog Options</title>
    <screenshot>
      <mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-ttest-paired.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the options for the t-test.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
     <para>For paired variables, when you click on 
     <quote><guibutton>OK</guibutton></quote>, &gnum; will test whether the 
     mean of the difference between the paired variables is equal to 
     the given hypothesized mean difference.</para>

 <example id="usingttestpairedtool">
 <title>Using the <parameter>t</parameter>-Test (Paired) Tool</title>
     <para>See <xref linkend="ttest-paired-tool-ex1" /> for an example 
     of a completed dialog and <xref linkend="ttest-paired-tool-ex2" />
     for the corresponding output.
     </para>
 </example>
  <figure id="ttest-paired-tool-ex1">
    <title><parameter>t</parameter>-Test (Paired) Example Data</title>
    <screenshot>
      <mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-ttest-paired-ex1.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the example for a t-test.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
  <figure id="ttest-paired-tool-ex2">
    <title>Output from the <parameter>t</parameter>-Test (Paired) Tool</title>
    <screenshot>
      <mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-ttest-paired-ex2.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the output results from a t-test.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>

  </sect3>

  <sect3 id="t-test-two-sample-equal-variances-tool">
     <title><parameter>t</parameter>-Test: Two-Sample Assuming Equal Variances Tool</title>
  <figure id="ttest-dialog-equal">
    <title><parameter>t</parameter>-Test (Equal Variances) Tool Dialog
    Options</title>
    <screenshot>
      <mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-ttest-equal.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the options for a t-test
              analysis of two samples with equal variances.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
     <para>For unpaired variables with unknown but assumed equal population variances,
     when you click on <quote><guibutton>OK</guibutton></quote>, &gnum; will test whether the 
     mean of the difference between the paired variables is equal to the given hypothesized
     mean difference.</para>

 <example id="usingttestequaltool">
 <title>Using the <parameter>t</parameter>-Test (Unknown but Equal Variances) Tool</title>
     <para>See <xref linkend="ttest-equal-tool-ex1" /> for an example 
     of a completed dialog and <xref linkend="ttest-equal-tool-ex2" />
     for the corresponding output.
     </para>
 </example>
  <figure id="ttest-equal-tool-ex1">
    <title><parameter>t</parameter>-Test (Unknown but Equal Variances) Example Data</title>
    <screenshot>
      <mediaobject>
        <imageobject>
          <imagedata fileref="figures/analysistools-ttest-equal-ex1.png" 
              format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of example data for use with a t-test
              with unknown but equal variances.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
  <figure id="ttest-equal-tool-ex2">
    <title>Output from the <parameter>t</parameter>-Test (Unknown but Equal Variances) Tool</title>
    <screenshot>
      <mediaobject>
        <imageobject>
          <imagedata fileref="figures/analysistools-ttest-equal-ex2.png" 
              format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the output from a t-test
              with unknown but equal variances.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
  </sect3>

  <sect3 id="t-test-two-samples-unequal-variances">
     <title><parameter>t</parameter>-Test: Two-Sample Assuming Unequal Variances Tool</title>
  <figure id="ttest-dialog-unequal">
    <title><parameter>t</parameter>-Test (Unknown and Unequal Variances) Tool 
    Dialog Options</title>
    <screenshot>
      <mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-ttest-unequal.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the options in a t-test of two
              samples with unknown and possibly unequal
              variances.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
     <para>For unpaired  variables with unknown and assumed unequal population variances,
     when you click on <quote><guibutton>OK</guibutton></quote>, &gnum; will test whether the 
     mean of the difference between the paired variables is equal to the given hypothesized
     mean difference.</para> 

 <example id="usingttestunwqualtool">
 <title>Using the <parameter>t</parameter>-Test (Unknown and Unequal Variances) Tool</title>
     <para>See <xref linkend="ttest-unequal-tool-ex1" /> for an example 
     of a completed dialog and <xref linkend="ttest-unequal-tool-ex2" />
     for the corresponding output.
     </para>
 </example>
  <figure id="ttest-unequal-tool-ex1">
    <title><parameter>t</parameter>-Test (Unknown and Unequal Variances) Example Data</title>
    <screenshot>
      <mediaobject>
        <imageobject>
          <imagedata fileref="figures/analysistools-ttest-unequal-ex1.png" 
              format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of example data for use in a t-test of two
              samples with unknown and possibly unequal
              variances.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
  <figure id="ttest-unequal-tool-ex2">
    <title>Output from the <parameter>t</parameter>-Test (Unknown and Unequal Variances) 
    Tool</title>
    <screenshot>
      <mediaobject>
        <imageobject>
          <imagedata fileref="figures/analysistools-ttest-unequal-ex2.png" 
              format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the output of a t-test of two
              samples with unknown and possibly unequal
              variances.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
  </sect3>

  <sect3 id="ztest-two-samples-for-means-tool">
     <title><parameter>z</parameter>-Test: Two Samples for Means Tool</title>
  <figure id="ztest-dialog">
    <title><parameter>z</parameter>-Test Tool Dialog Options</title>
    <screenshot>
      <mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-ztest.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of the options in a z-test of two
              samples.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
     <para>For unpaired  variables with known population variances, enter those variances 
     in the <quote><guilabel>Variable 1 Pop. Variance</guilabel></quote> and 
     <quote><guilabel>Variable 2 Pop. Variance</guilabel></quote> entries.
     When you click on <quote><guibutton>OK</guibutton></quote>, &gnum; will test whether the 
     mean of the difference between the paired variables is equal to the given hypothesized
     mean difference.</para> 

 <example id="usingztesttool">
 <title>Using the <parameter>z</parameter>-Test Tool</title>
     <para>See <xref linkend="ztest-tool-ex1" /> for an example 
     of a completed dialog and <xref linkend="ztest-tool-ex2" />
     for the corresponding output.
     </para>
 </example>
  <figure id="ztest-tool-ex1">
    <title><parameter>z</parameter>-Test Example Data</title>
    <screenshot>
      <mediaobject>
            <imageobject>
              <imagedata fileref="figures/analysistools-ztest-ex1.png" 
                  format="PNG" />
            </imageobject>
            <textobject>
              <phrase>An image of example data for use in a z-test of two
              samples.</phrase>
            </textobject>
           </mediaobject>
    </screenshot>
  </figure>
  <figure id="ztest-tool-ex2">
    <title>Output from the <parameter>z</parameter>-Test Tool</title>
    <screenshot>
      <screeninfo>Output from the <parameter>z</parameter>-Test
              Tools
      </screeninfo>
      <mediaobject>
        <imageobject>
          <imagedata fileref="figures/analysistools-ztest-ex2.png" 
              format="PNG" />
          </imageobject>
          <textobject>
            <phrase>An image of the output from a z-test of two
            samples.</phrase>
          </textobject>
      </mediaobject>
    </screenshot>
  </figure>
  </sect3>
</sect2>
</sect1>
