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<title>Overview</title>
<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>
<para>You will normally want to select the <guilabel>Clear
Output Range</guilabel> option, since otherwise some of the cells with
existing content will remain in the output range.
</para>
<para> The <guilabel>Retain Output Range Formatting</guilabel> and
<guilabel>Retain Output Range Comments</guilabel> options are useful
if you have already preformatted the output range.
</para>
<para>All analysis tools also provide a choice whether
they will enter formulæ or just values in the cells. By default
&gnum; will usually enter formulæ. These formulæ will automatically
reevaluate when the data change. For some tools, the formulæ also
permit modification of certain parameters.
</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>
</sect1>
<sect1 id="descriptive_statistics">
<title>Descriptive Statistics</title>
<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%.</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="frequencies-tools">
<title>Frequency Tables</title>
<para>
&gnum; provides two types of frequencies tables:
</para>
<itemizedlist>
<listitem><para>The frequency table tools is primarily useful for non-numeric data
(data of nominal and ordinal level of measurement). It allows to determine
frequencies for given values.
</para></listitem>
<listitem><para> The histogram tool is useful for numeric data that is supposed to be
classified into a certain number of intervals. These intervals can be either
specified or calculated.
</para></listitem>
</itemizedlist>
<sect3 id="frequency-tool">
<title>Frequency Tables Tool</title>
<sect4 id="frequency-tool-intro">
<title>Introduction</title>
<para> The frequency tool can be used to create frequency tables for
non-numerical data. It presents this table
numerically as well as graphically.
</para>
<note><para>
If your data are numeric and you want to accumulate whole intervals of values into
frequency counts then this tool is not appropriate. In that case you may
want to use the histogram table tool described in section <xref linkend="histogram-tool" />.
</para></note>
<figure id="frequency-tool-dialog">
<title>Frequency Tool Dialog</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-frequency.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the dialog to generate various
frequency tables open to the "Input" tab.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<para>As shown in <xref linkend="frequency-tool-dialog" />, the
frequency table dialog has four tabs. We will introduce them in
sequence.
</para>
</sect4>
<sect4 id="frequency-tool-inputtab">
<title>The <quote><guilabel>Input</guilabel></quote> Tab</title>
<para>The <quote><guilabel>Input</guilabel></quote> tab shown in
<xref linkend="frequency-tool-dialog" /> 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.
</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>Labels</guibutton></quote> option should
be selected.
If the input is grouped by areas and the top left cell contains a label, the
other cells in the first row are being ignored.
</para>
</sect4>
<sect4 id="frequency-tool-catstab">
<title>The <quote><guilabel>Categories</guilabel></quote> Tab</title>
<para>The <quote><guilabel>Categories</guilabel></quote> tab permits the specification
of a range that contains the possible values that are supposed to be counted in the
input range.
</para>
<note><para>The <quote><guilabel>Automatic categories</guilabel></quote> option is
disabled since it is not yet implemented.
</para></note>
<figure id="frequency-tool-dialog-cats">
<title>Frequency Tool Dialog Categories Tab</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-frequency-cats.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the dialog to generate various
frequency tables open to the "Categories" tab.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
</sect4>
<sect4 id="frequency-tool-optionstab">
<title>The <quote><guilabel>Graphs & Options</guilabel></quote> Tab</title>
<para>The <quote><guilabel>Graphs & Options</guilabel></quote> tab allows various
options to be set. In the top half of the tab you can choose whether you would like
a graph to be created. If you choose to have a graph created you can specify whether
you would like to see a bar chart or a column chart.
</para>
<para>In the bottom part of the tab you
can select the <quote><guilabel>percentages</guilabel></quote> option. This option
replaces the frequency counts with percentages.
</para>
<note><para>If the categories range contains repeated values, then the percentages may
add up to more than 100%. If the categories range does not contain all values that
occur in the input range, the percentages may sum to less than 100%.
</para></note>
<para>The <quote><guilabel>Use exact comparisons</guilabel></quote> checkbox determines how
category values and input range values are compared. If it is checked then the function
<function>EXACT</function> is used for the comparison. If it isn't checked then simple
equality is used. In this latter case, empty cells and cells containing the numerical
value 0 are considered equal. As a consequence you usually want that checkbox to be selected.
</para>
<figure id="frequency-tool-dialog-graphs">
<title>Frequency Tool Dialog Graphs & Options Tab</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-frequency-graphs.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the dialog to generate various
frequency tables open to the "Graphs & Options" tab.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
</sect4>
<sect4 id="frequency-tool-results-sect">
<title>Frequency Tool Results</title>
<figure id="frequency-tool-results">
<title>Frequency Tool Results</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-frequency-results.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>Sample results of the frequencies tool.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
</sect4>
</sect3>
<sect3 id="histogram-tool">
<title>Histogram Tool</title>
<sect4 id="histogram-tool-intro">
<title>Introduction</title>
<para> The histogram tool can be used to create histograms or frequency tables for
numerical data. Using this tool you can define intervals, or <quote>bins</quote>.
The tool determines how many data points belong to each bin and presents this number
numerically as well as graphically.
</para>
<note><para>
If your data are non-numeric this tool is not appropriate. In that case you may
want to use the frequency table tool described in section <xref linkend="frequency-tool" />.
</para></note>
<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>As shown in <xref linkend="histogram-tool-dialog" />, the
histogram dialog has five tabs. We will introduce them in
sequence.
</para>
</sect4>
<sect4 id="histogram-tool-inputtab">
<title>The <quote><guilabel>Input</guilabel></quote> Tab</title>
<para>The <quote><guilabel>Input</guilabel></quote> tab shown in
<xref linkend="histogram-tool-dialog" /> 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.
</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>Labels</guibutton></quote> option should
be selected.
If the input is grouped by areas and the top left cell contains a label, the
other cells in the first row are being ignored.
</para>
</sect4>
<sect4 id="histogram-tool-cutoffsstab">
<title>The <quote><guilabel>Cutoffs</guilabel></quote> Tab</title>
<figure id="histogram-tool-dialog-cutoffs">
<title>Histogram Tool Dialog <quote><guilabel>Cutoffs</guilabel></quote> Tab</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-histogram-cutoffs.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the dialog to generate various
histograms open to the "Cutoffs" tab.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<para>The cutoffs for the histogram can either be predetermined by data
contained in your workbook or calculated by the histogram tool. These cutoffs
determine bins as defined
by the selection on the <quote><guilabel>Bins</guilabel></quote> tab.
</para>
<para>Select the <quote><guilabel>Predetermined Cutoffs</guilabel></quote> option to specify
data on your worksheet in the <quote><guilabel>Cutoff Range:</guilabel></quote> entry. The
values in this range will be used as cutoffs <parameter>c<subscript>1</subscript></parameter>,
<parameter>c<subscript>2</subscript></parameter>, and so on
to <parameter>c<subscript>n</subscript></parameter>.
</para>
<para>Select the <quote><guilabel>Calculated Cutoffs</guilabel></quote> option to have the
cutoffs determined by the tool. Enter the desired number of cutoffs in the
<quote><guilabel>Number of Cutoffs</guilabel></quote> entry. It is strongly recommended
(but optional) that you
specify the minimum and maximum cutoffs in the <quote><guilabel>Minimum cutoff</guilabel></quote>
and <quote><guilabel>Maximum cutoff</guilabel></quote> entries. If the minimum or maximum
cutoff is not specified, the tool will use the minimum and/or maximum of the current data.
</para>
</sect4>
<sect4 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 tab is used to determine how the cutoffs <parameter>c<subscript>1</subscript></parameter>,
<parameter>c<subscript>2</subscript></parameter>, and so on
to <parameter>c<subscript>n</subscript></parameter> are translated into bins. Specifically,
it has to be determined whether first and/or last bins reaching from −∞ to
<parameter>c<subscript>1</subscript></parameter> and from
<parameter>c<subscript>n</subscript></parameter> to ∞ are added and whether data points that much
cutoffs exactly are included in the bin to the right or the left.
</para>
<para> For example the option
<quote><guilabel>[∙,∙),[∙,∙),⋯,
[∙,∙),[∙,∞)
</guilabel></quote>
indicates that the first bin starts at the first cutoff while the last bin ends at ∞. Moreover,
each cutoff value belongs to the bin on its right.
</para>
</sect4>
<sect4 id="histogram-tool-optionstab">
<title>The <quote><guilabel>Graphs & Options</guilabel></quote> Tab</title>
<figure id="histogram-tool-dialog-options">
<title>Histogram Tool Dialog <quote><guilabel>Graphs & Options Tab</guilabel></quote></title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-histogram-graphs.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the dialog to generate various
histograms open to the "Graphs & Options" tab.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<para> The options in the graphs and options tab specify any graph to be created and modify
the appearance of the histogram:</para>
<itemizedlist>
<listitem>
<para> The <quote><guibutton>No chart</guibutton></quote> option causes the chart to be omitted.
</para>
</listitem>
<listitem>
<para> The <quote><guibutton>Bar chart</guibutton></quote> option causes a bar chart to be
added to the histogram. For each bin, the bar chart shows a horizontal bar indicating the frequency.
</para>
<para> The <quote><guibutton>Column chart</guibutton></quote> option causes a column chart to be
added to the histogram. For each bin, the column chart shows a vertical bar indicating the frequency.
</para>
<para> The <quote><guibutton>Histogram chart</guibutton></quote> option causes a histogram chart to be
added to the histogram. For each bin, the histogram chart shows a vertical bar indicating the density
(that is the frequency divided by the width of the bin).
</para>
</listitem>
<listitem>
<para> The <quote><guibutton>Percentages</guibutton></quote> option causes the frequencies to be
expressed as percentages.
</para>
</listitem>
<listitem>
<para> The <quote><guibutton>Cumulative answers</guibutton></quote> option causes a cumulative
frequency table (either with counts or with pecentages) to be created.
</para>
</listitem>
<listitem>
<para> The <quote><guibutton>Count numbers only</guibutton></quote> option determines whether only numbers are counted. If also non-numbers are counted they are first converted into numbers, usually into 0.
</para>
</listitem>
</itemizedlist>
</sect4>
<sect4 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 in <xref
linkend="sect-stat-analysis-overview" />.
</para>
</sect4>
<sect4 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>
<example id="usinghistogramtool">
<title>Using the Histogram Tool</title>
<para>
For example, you want to calculate a histogram for the number of
successes in several sequences of trials. The numbers of
successes are recorded in column A and the cutoffs of interest
in column C (see <xref linkend="histogram-example-1" />).
</para>
<orderedlist>
<listitem>
<para>
Enter A1:A31 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 may 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>Labels</guibutton></quote> option
since the first cell of the Input Range contains a
label.</para>
</listitem>
<listitem><para> Enter C2:C5 in
the <quote><guilabel>Cutoff Range:</guilabel></quote> entry
of the <quote><guilabel>Cutoffs</guilabel></quote> tab. The
<quote><guilabel>Predetermined Cutoffs</guilabel></quote>
option will now also be selected (see <xref
linkend="histogram-example-2" />). </para>
</listitem>
<listitem><para> In the <quote><guilabel>Bins</guilabel></quote> tab
select the second option since we want to add two bins reaching to ∓∞ and
we want to count each cutoff value in the bin to its right (see <xref
linkend="histogram-example-3" />).</para>
</listitem>
<listitem><para> Select the
<quote><guibutton>Percentage</guibutton></quote> option of the
<quote><guilabel>Graphs &Options</guilabel></quote> tab to have
the frequencies expressed as percentages.
</para>
</listitem>
<listitem><para> Select the
<quote><guibutton>Column Chart</guibutton></quote> option of the
<quote><guilabel>Graphs &Options</guilabel></quote> tab to have
a column chart added to the histogram (see <xref
linkend="histogram-example-4" />).
</para>
</listitem>
<listitem>
<para>
In the <quote><guilabel>Output</guilabel></quote> tab,
specify the output options as described in
<xref linkend="sect-stat-analysis-overview" />.
</para>
</listitem>
<listitem><para>
Press the OK button. </para>
</listitem>
</orderedlist>
<para> The results are shown in
<xref linkend="histogram-example-5" />. Note that the graph will by default appear on top
of the histogram table. It usually needs to be moved in to proper position. That has
already been done here.
</para>
</example>
<figure id="histogram-example-2">
<title>Histogram Tool: Specifying Cutoffs</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-histogram-ex2.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of selecting the cutoffs for the example
data used with the histogram tool.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<figure id="histogram-example-3">
<title>Histogram Tool: Specifying Bins</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-histogram-ex3.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of selecting a certain bins type.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<figure id="histogram-example-4">
<title>Histogram Tool: Specifying Options</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-histogram-ex4.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of specifying the required options.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<figure id="histogram-example-5">
<title>Histogram Tool Output</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-histogram-ex5.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the output from the histogram
analysis tool.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
</sect4>
</sect3>
</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>
</sect1>
<sect1 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>
</sect1>
<sect1 id="dependent_observations">
<title>Dependent Observations</title>
<sect2 id="forecast-tools">
<title>Forecast Tools</title>
<sect3 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. It provides the choice of 5
different exponential smoothing methods:
</para>
<itemizedlist>
<listitem>
<para>Simple exponential smoothing according to (Hunter, 1968).</para>
</listitem>
<listitem>
<para>Simple exponential smoothing according to (Roberts, 1959).</para>
</listitem>
<listitem>
<para>Holt's trend corrected exponential smoothing (occasionally also
referred to as double exponential smoothing)</para>
</listitem>
<listitem>
<para>Additive Holt-Winters exponential smoothing</para>
</listitem>
<listitem>
<para>Multiplicative Holt-Winters exponential smoothing (occasionally also
referred to as triple exponential smoothing)</para>
</listitem>
</itemizedlist>
<para>Since the kind of options available depend on the type of exponential
smoothing desired, you can choose the type on the <quote><guilabel>Input
</guilabel></quote>
page.
</para>
<sect4 id="exp-smoothing-tool-common">
<title>Common Options of the Exponential Smoothing Tool</title>
<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> If you select the <quote><guilabel>Include chart</guilabel></quote>
option, &gnum;
will also create a chart showing both the data and corresponding smoothed
values.
</para>
</sect4>
<sect4 id="exp-smoothing-tool-hunter">
<title>Exponential Smoothing According to Hunter</title>
<para> Each value in the
smoothed set is predicted based on the forecast for the prior
period. The formula is given in <xref linkend="exp-smoothing-tool-formula-hunter" />.
α is the value given as <quote><guilabel>Damping factor</guilabel></quote>.
<parameter>y<subscript>t</subscript></parameter> is the <parameter>t</parameter>th
value in the original data set and <parameter>l<subscript>t</subscript></parameter>
the corresponding smoothed value.</para>
<figure id="exp-smoothing-tool-formula-hunter">
<title>Exponential Smoothing Formula According To Hunter</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-exp-smoothing-hunter-formula.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>The formula used in exponential smoothing according to Hunter.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<para>For example, a value for α between 0.2 and 0.3 represents 20 to 30 percent error
adjustment in the prior forecast.
</para>
<note><para>
If you choose to have the tool enter formulæ rather than values into the output region,
then you can modify the damping factor α even after you executed the tool.
</para></note>
<para>To have the standard errors output as well, check the
<quote><guilabel>Standard error</guilabel></quote> check box. The formula
used is given in <xref linkend="exp-smoothing-tool-formula-hunter-stderr" />.
The denominator can be adjusted by selecting the appropriate radio button. Since
there are <parameter>t−1</parameter> terms in the sum of the denominator,
selecting <quote><guilabel>n−1</guilabel></quote> means that the denominator
will be <parameter>t−2</parameter>.
</para>
<figure id="exp-smoothing-tool-formula-hunter-stderr">
<title>The Standard Error Formula For Exponential Smoothing According To Hunter</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-exp-smoothing-hunter-stderr.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>The formula used to calculate the standard error of exponential
smoothing according to Hunter
</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<para>If you check the <quote><guilabel>Include chart</guilabel></quote> check box, a line
graph showing the observations <parameter>y<subscript>t</subscript></parameter> and the
predicted values <parameter>l<subscript>t</subscript></parameter> will also be created.
</para>
<example id="usingsmoothingtool"><title>Using the Exponential Smoothing Tool</title>
<para><xref linkend="smoothing-example-1" /> shows some example data, <xref linkend="smoothing-example-2" /> the selected options and
<xref linkend="smoothing-example-3" /> the corresponding output.
</para>
</example>
<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>
<figure id="smoothing-example-2">
<title>The Options for the Exponential Smoothing Tool</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-smoothing-ex3.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the options tab of the exponential smoothing tool.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<figure id="smoothing-example-3">
<title>Exponential Smoothing Tool Output (Hunter)</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 according to Hunter.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
</sect4>
<sect4 id="exp-smoothing-tool-roberts">
<title>Exponential Smoothing According to Roberts</title>
<para>The simple exponential smoothing method according to Roberts is used for
forecasting a time series without a trend or seasonal pattern, but for which
the level is nevertheless slowly changing over time. The predicted values are
calculated according to the formula given in
<xref linkend="exp-smoothing-tool-formula-roberts" />. α is the value
given as <quote><guilabel>Damping factor</guilabel></quote>.
<parameter>y<subscript>t</subscript></parameter> is the <parameter>t</parameter>th
value in the original data set and <parameter>l<subscript>t</subscript></parameter>
the predicted value. <parameter>l<subscript>0</subscript></parameter> is the
predicted value at time 0 and must be estimated. This tool uses the average
value of the first 5 observations as estimate.
</para>
<note><para>
If you choose to have the tool enter formulæ rather than values into
the output region,
then you can modify the damping factor α and the estimated value
at time 0 after executing the tool.
</para></note>
<figure id="exp-smoothing-tool-formula-roberts">
<title>Exponential Smoothing Formula According To Roberts</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-exp-smoothing-roberts-formula.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>The formula used in exponential smoothing according to Roberts.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<para>To have the standard errors output as well, check the
<quote><guilabel>Standard error</guilabel></quote> check box. The formula used is
given in <xref linkend="exp-smoothing-tool-formula-roberts-stderr" />. The
denominator can be adjusted by selecting the appropriate radio button.
</para>
<figure id="exp-smoothing-tool-formula-roberts-stderr">
<title>The Standard Error Formula For Exponential Smoothing According To Roberts</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-exp-smoothing-roberts-stderr.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>The formula used to calculate the standard error of exponential
smoothing according to Roberts
</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<para>If you check the <quote><guilabel>Include chart</guilabel></quote> check box, a line
graph showing the observations <parameter>y<subscript>t</subscript></parameter> and the
predicted values <parameter>l<subscript>t</subscript></parameter> will also be created.
</para>
<example id="usingsmoothingtool-roberts"><title>Using the Exponential Smoothing Tool</title>
<para>
<xref linkend="smoothing-example-4" /> shows example output for the exponential smoothing
tool using the formula according to Roberts. Cell A4 contains the estimated level at time 0.
If you requested to have formulæ rather than values entered into the sheet, then changing
the estimate in A4 and/or the value for α in A2 will result in an immediate change to
the predicted values.
</para>
</example>
<figure id="smoothing-example-4">
<title>Exponential Smoothing Tool Output (Roberts)</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-smoothing-ex4.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the output of an exponential
smoothing analysis according to Roberts.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
</sect4>
<sect4 id="exp-smoothing-tool-holt">
<title>Holt's Trend Corrected Exponential Smoothing</title>
<para>Holt's trend corrected exponential smoothing is appropriate when both the level and the growth rate of a time series are changing. (If the time series has a fixed growth rate and therefore exhibits a linear trend, a linear regression model is more appropriate.)
</para>
<para><parameter>y<subscript>t</subscript></parameter> is the true value at time
<parameter>t</parameter>, <parameter>l<subscript>t</subscript></parameter>
is the estimated level at time <parameter>t</parameter> and <parameter>b<subscript>t
</subscript></parameter>
is the estimated growth rate at time <parameter>t</parameter>. We use the two smoothing equations
given in <xref linkend="exp-smoothing-tool-formula-holt" /> to update our estimates.
α is the value
given as <quote><guilabel>Damping factor</guilabel></quote> and γ is the value
given as <quote><guilabel>Growth damping factor</guilabel></quote>.
</para>
<para>This tool obtains initial (time 0) estimates for the level and growth rate by performing
a linear regression using the first 5 data values.
</para>
<figure id="exp-smoothing-tool-formula-holt">
<title>Formulae Of Holt's Trend Corrected Exponential Smoothing</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-exp-smoothing-holt-formula.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>The formulae used in Holt's trend corrected exponential smoothing.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<note><para>
If you choose to have the tool enter formulæ rather than values into
the output region,
then you can modify the damping factors α and γ as well as the estimated level and growth rate
at time 0 after executing the tool.
</para></note>
<para>To have the standard errors output as well, check the
<quote><guilabel>Standard error</guilabel></quote> check box. The formula used is
given in <xref linkend="exp-smoothing-tool-formula-holt-stderr" />. The
denominator can be adjusted by selecting the appropriate radio button.
</para>
<figure id="exp-smoothing-tool-formula-holt-stderr">
<title>The Standard Error Formula For Holt's Trend Corrected Exponential Smoothing</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-exp-smoothing-holt-stderr.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>The formula used to calculate the standard error for Holt's trend
corrected exponential smoothing.
</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<para>If you check the <quote><guilabel>Include chart</guilabel></quote> check box, a line
graph showing the observations <parameter>y<subscript>t</subscript></parameter> and the
estimated level values <parameter>l<subscript>t</subscript></parameter> will also be created.
</para>
<example id="usingsmoothingtool-holt"><title>Using the Exponential Smoothing Tool</title>
<para>
<xref linkend="smoothing-example-5" /> shows example output for Holt's trend corrected
exponential smoothing. Cell A4 contains the estimated level at time 0 and B4 the estimated
growth rate at time 0.
If you requested to have formulæ rather than values entered into the sheet, then changing
the estimates in A4, B4, the values for α in A2 and/or for γ in B2 will result
in an immediate change to
the predicted values.
</para>
</example>
<figure id="smoothing-example-5">
<title>Exponential Smoothing Tool Output (Holt's)</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-smoothing-ex5.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the output of Holt's trend corrected exponential
smoothing.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
</sect4>
<sect4 id="exp-smoothing-tool-additive-holt-winters">
<title>Additive Holt-Winters Method</title>
<para>The additive Holt-Winters method of exponential smoothing is appropriate when a time
series with a linear trend has an additive seasonal pattern for which the level, the growth
rate and the seasonal pattern may be changing. An additive seasonal pattern is a pattern in
which the seasonal variation can be explained by the addition of a seasonal constant
(although we allow for this constant to change slowly.)
</para>
<para><parameter>y<subscript>t</subscript></parameter> is the true value at time
<parameter>t</parameter>, <parameter>l<subscript>t</subscript></parameter>
is the estimated level at time <parameter>t</parameter>, <parameter>b<subscript>t
</subscript></parameter>
is the estimated growth rate at time <parameter>t</parameter> and <parameter>s<subscript>t
</subscript></parameter>
is the estimated seasonal adjustment for time <parameter>t</parameter>.
We use the three smoothing equations
given in <xref linkend="exp-smoothing-tool-formula-a-holt-winters" /> to update our estimates.
α is the value
given as <quote><guilabel>Damping factor</guilabel></quote>, γ is the value
given as <quote><guilabel>Growth damping factor</guilabel></quote> and δ is the value
given as <quote><guilabel>Seasonal damping factor</guilabel></quote>. <parameter>L</parameter>
is the value
given as <quote><guilabel>Seasonal period</guilabel></quote>. If your data consist of monthly
values, then <parameter>L</parameter> should be 12, if it consist of quarterly values then
<parameter>L</parameter> should be 4.
</para>
<para>This tool obtains initial (time 0) estimates for the level and growth rate by performing
a linear regression using all data values. It obtains estimates
for the seasonal adjustments by averaging the appropriate seasonal differences from values
predicted by linear regression alone.
</para>
<figure id="exp-smoothing-tool-formula-a-holt-winters">
<title>Exponential Smoothing Formulae Of The Additive Holt-Winters Method</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-exp-smoothing-a-holt-winters-formula.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>The formulae used in the additive Holt-Winters Method.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<note><para>
If you choose to have the tool enter formulæ rather than values into
the output region,
then you can modify the damping factors α, γ and δ as well as all
estimates after executing the tool.
</para></note>
<para>To have the standard errors output as well, check the
<quote><guilabel>Standard error</guilabel></quote> check box. The formula used is
given in <xref linkend="exp-smoothing-tool-formula-a-holt-winters-stderr" />.
The denominator can be adjusted by selecting the appropriate radio button.
</para>
<figure id="exp-smoothing-tool-formula-a-holt-winters-stderr">
<title>The Standard Error Formula Of The Additive Holt-Winters Method</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-exp-smoothing-a-holt-winters-stderr.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>The formula used to calculate the standard error in the additive
Holt-Winters Method
</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<para>If you check the <quote><guilabel>Include chart</guilabel></quote> check box, a line
graph showing the observations <parameter>y<subscript>t</subscript></parameter> and the
estimated level values <parameter>l<subscript>t</subscript></parameter> will also be created.
</para>
<example id="usingsmoothingtool-ahw"><title>Using the Exponential Smoothing Tool</title>
<para>
<xref linkend="smoothing-example-6" /> shows the options' tab of the exponential smoothing
tool for the additive Holt-Winters method. The data is expected to have a seasonal period
of 4 (this would for example happen if we have a data value for each quarter of a year).
<xref linkend="smoothing-example-7" /> shows the corresponding example output for the
additive Holt-Winters method. Cell C7 contains the estimated level at time 0, D7 the
estimated growth rate at time 0, and E4 to E7 the initial seasonal adjustments for each
of the 4 seasons preceding our data time period.
If you requested to have formulæ rather than values entered into the sheet, then changing
any of these estimates, the values for α in A2, for γ in B2 and/or for δ
in C2 will result in an immediate change to the estimated values.
</para>
</example>
<figure id="smoothing-example-6">
<title>Exponential Smoothing Tool Options (Additive Holt-Winters)</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-smoothing-ex6.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the options' tab for the additive Holt-Winters method.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<figure id="smoothing-example-7">
<title>Exponential Smoothing Tool Output (Additive Holt-Winters)</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-smoothing-ex7.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the output of the additive Holt-Winters method.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
</sect4>
<sect4 id="exp-smoothing-tool-multiplicative-holt-winters">
<title>Multiplicative Holt-Winters Method</title>
<para>The multiplicative Holt-Winters method of exponential smoothing is appropriate when a time
series with a linear trend has a multiplicative seasonal pattern for which the level, the growth
rate and the seasonal pattern may be changing. A multiplicative seasonal pattern is a pattern in
which the seasonal variation can be explained by the multiplication of a seasonal constant
(although we allow for this constant to change slowly.)
</para>
<para><parameter>y<subscript>t</subscript></parameter> is the true value at time
<parameter>t</parameter>, <parameter>l<subscript>t</subscript></parameter>
is the estimated level at time <parameter>t</parameter>, <parameter>b<subscript>t
</subscript></parameter>
is the estimated growth rate at time <parameter>t</parameter> and <parameter>s<subscript>t
</subscript></parameter>
is the estimated seasonal adjustment for time <parameter>t</parameter>.
We use the three smoothing equations
given in <xref linkend="exp-smoothing-tool-formula-m-holt-winters" /> to update our estimates.
α is the value
given as <quote><guilabel>Damping factor</guilabel></quote>, γ is the value
given as <quote><guilabel>Growth damping factor</guilabel></quote> and δ is the value
given as <quote><guilabel>Seasonal damping factor</guilabel></quote>. <parameter>L</parameter>
is the value
given as <quote><guilabel>Seasonal period</guilabel></quote>. If your data consist of monthly
values, then <parameter>L</parameter> should be 12, if it consist of quarterly values then
<parameter>L</parameter> should be 4.
</para>
<para>This tool obtains initial (time 0) estimates for the level and growth rate by performing
a linear regression using the data values of the first 4 seasonal periods. It obtains estimates
for the seasonal adjustments by averaging the appropriate seasonal differences from values
predicted by linear regression alone during the first 4 seasonal periods.
</para>
<figure id="exp-smoothing-tool-formula-m-holt-winters">
<title>Exponential Smoothing Formulae Of The Multiplicative Holt-Winters Method</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-exp-smoothing-m-holt-winters-formula.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>The formulae used in the multiplicative Holt-Winters Method</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<note><para>
If you choose to have the tool enter formulæ rather than values into
the output region,
then you can modify the damping factors α, γ and δ as well as all
estimates after executing the tool.
</para></note>
<para>To have the standard errors output as well, check the
<quote><guilabel>Standard error</guilabel></quote> check box. The formula used is given in
<xref linkend="exp-smoothing-tool-formula-m-holt-winters-stderr" />. The denominator
can be adjusted by selecting the appropriate radio button.
</para>
<figure id="exp-smoothing-tool-formula-m-holt-winters-stderr">
<title>The Standard Error Formula Of The Multiplicative Holt-Winters Method</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-exp-smoothing-m-holt-winters-stderr.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>The formula used to calculate the standard error in the multiplicative
Holt-Winters Method
</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<para>If you check the <quote><guilabel>Include chart</guilabel></quote> check box, a line
graph showing the observations <parameter>y<subscript>t</subscript></parameter> and the
estimated level values <parameter>l<subscript>t</subscript></parameter> will also be created.
</para>
<example id="usingsmoothingtool-mhw"><title>Using the Exponential Smoothing Tool</title>
<para>
<xref linkend="smoothing-example-8" /> shows the example output for the
multiplicative Holt-Winters method, assuming 4 seasons. Cell C7 contains the estimated level
at time 0, D7 the estimated growth rate at time 0, and E4 to E7 the initial seasonal
adjustments for each of the 4 seasons preceding our data time period.
If you requested to have formulæ rather than values entered into the sheet, then changing
any of these estimates, the values for α in A2, for γ in B2 and/or for δ
in C2 will result in an immediate change to the estimated values.
</para>
</example>
<figure id="smoothing-example-8">
<title>Exponential Smoothing Tool Output (Multiplicative Holt-Winters)</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-smoothing-ex8.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the output of the multiplicative Holt-Winters method.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
</sect4>
</sect3>
<sect3 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>Choose the type of moving average you would like to calculate. The tool can
determine 4 types of moving averages:
</para>
<orderedlist spacing="compact">
<listitem><para>
Simple moving average
</para></listitem>
<listitem><para>
Cumulative moving average
</para></listitem>
<listitem><para>
Weighted moving average
</para></listitem>
<listitem><para>
Spencer's 15 point moving average
</para></listitem>
</orderedlist>
<figure id="moving-tool-dialog-options">
<title>
Moving Average Tool Dialog: The
<quote><guilabel>Options</guilabel></quote> Tab
</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-moving-average-options.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the <quote><guilabel>Options</guilabel></quote>
tab of the moving average
analysis tool.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<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. This options is only available for the simple and weighted
moving averages.
</para>
<para>Check the <quote><guilabel>Standard errors</guilabel></quote>
checkbox if you would also like the standard error to be calculated.
Since there is no general agreement on the denominator for the standard
error you can choose the appropriate radio button.
</para>
<para>In the case of the simple moving average, you can also choose between
a prior moving average and a central moving average, or you may even specify
any other desired offset.
</para>
<orderedlist>
<listitem><para>
<quote><guilabel>Prior moving average</guilabel></quote>: Each average
takes into account the current observation and the most recent prior
observations for a total of <parameter>i</parameter> observations.
</para></listitem>
<listitem><para>
<quote><guilabel>Central moving average</guilabel></quote>
with <parameter>i</parameter> being odd: Each average
takes into account the current observation and the same number of most recent prior
observations and closest future observations for a total of
<parameter>i</parameter> observations.
</para></listitem>
<listitem><para>
<quote><guilabel>Central moving average</guilabel></quote>
with <parameter>i</parameter> being even:
This is calculated according to the formula given in
<xref linkend="moving-formula-central" />.
<parameter>a<subscript>t</subscript></parameter> is the moving average
at time <parameter>t</parameter> and
<parameter>y<subscript>t</subscript></parameter> is the observation at
time <parameter>t</parameter>.
</para></listitem>
<listitem><para>
<quote><guilabel>Other offset</guilabel></quote>: If the offset is 0,
this is just the prior moving average. Otherwise the offset indicates
the number of closest future observations to include in the average.
Correspondingly, the number of most recent past observations is decreased.
</para></listitem>
</orderedlist>
<figure id="moving-formula-central">
<title>Formula For The Central Moving Average With Even Interval</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-moving-average-formula-central.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>The formula for the central moving average if the interval
length is even.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<para>The results are given in one column for each dataset (with a second
column added if you have chosen standard errors to be calculated). Each
row represents the moving average of the corresponding row or
column in the input range. Depending on the type of average and
the offset, the moving average cannot be
calculated for the first rows in the
input range.
</para>
<sect4 id="moving-averages-simple">
<title>Simple Moving Average</title>
<para>
A simple moving average is the unweighted average of a collection of
observations. Exactly which observations are included depends on whether
a prior or central moving average is calculated.
</para>
</sect4>
<sect4 id="moving-averages-cumulative">
<title>Cumulative Moving Average</title>
<para>A cumulative moving average is a prior moving average in which the current
and all prior observations are included.</para>
</sect4>
<sect4 id="moving-averages-weighted">
<title>Weighted Moving Average</title>
<para>A weighted moving average with an interval <parameter>i</parameter> is a prior
moving average calculated according to formula
<xref linkend="moving-formula-central" />.
<parameter>a<subscript>t</subscript></parameter> is the moving average
at time <parameter>t</parameter> and
<parameter>y<subscript>t</subscript></parameter> is the observation at
time <parameter>t</parameter>.
</para>
<figure id="moving-averages-weighted-formula">
<title>Formula For The Weighted Moving Average With Interval
<parameter>i</parameter></title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-moving-average-formula-weighted.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>The formula for the weighted moving average if the interval
length is <parameter>i</parameter>.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
</sect4>
<sect4 id="moving-averages-spencer">
<title>Spencer's 15 Point Moving Average</title>
<para>Spencer's 15 point moving average is a central moving average calculated
according to formula
<xref linkend="moving-formula-spencer" />.
<parameter>a<subscript>t</subscript></parameter> is the moving average
at time <parameter>t</parameter> and
<parameter>y<subscript>t</subscript></parameter> is the observation at
time <parameter>t</parameter>.
</para>
<figure id="moving-formula-spencer">
<title>Formula For Spencer's 15 Point Moving Average</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-moving-average-formula-spencer.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>The formula for the Spencer's 15 point moving average.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
</sect4>
<sect4 id="moving-averages-example">
<title>A Moving Average Example</title>
<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,
<xref linkend="moving-example-2" /> shows the option settings, and
<xref linkend="moving-example-3" /> the corresponding output.
</para>
</example>
<figure id="moving-example-2">
<title>Moving Averages Tool Options</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-moving-average-ex2.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the option settings of the moving averages
example.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<figure id="moving-example-3">
<title>Moving Averages Tool Output</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-moving-average-ex3.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the output from the moving average
analysis tool.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
</sect4>
</sect3>
</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 number of terms in the given sequence is not
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="kaplan-meier-tool">
<title>Kaplan Meier Estimates Tool</title>
<para/>
<sect3 id="kaplan-meier-tool-inputtab">
<title>The <quote><guilabel>Input</guilabel></quote> Tab</title>
<para>The <quote><guilabel>Input</guilabel></quote> tab shown in
<xref linkend="kaplan-meier-tool-dialog" /> contains
the fields specifying the data to be used for the
Kaplan Meier Estimates. The time column contains the times or dates
at which the subjects died or were censored. If any of the subjects
were censored, the <guilabel>Permit censorship</guilabel> checkbox is
checked and the Censor column contained the censorship marks. Censorship
marks are typically 0s or 1s. The range of censor marks or labels can be
set using the
remaining two spinboxes.</para>
<figure id="kaplan-meier-tool-dialog">
<title>Kaplan-Meier Tool Dialog</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-kaplan.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the .Kaplan-Meier tool dialog.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
</sect3>
<sect3 id="kaplan-meier-tool-group-tab">
<title>The <quote><guilabel>Groups</guilabel></quote> Tab</title>
<para>
If the subjects belong to several groups and the groups are supposed to be
analyzed separately, the groups tab can be used.
</para>
<figure id="kaplan-meier-tool-dialog-groups">
<title>Kaplan-Meier Tool Dialog Groups Tab</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-kaplan-groups.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the Kaplan-Meier tool dialog groups tab.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<para>
The groups tab can be enabled via the <guilabel>Define multiple groups
</guilabel> checkbox. The groups column entry contains the address of
the column specifying the group membership. Groups can then be defined
or deleted via the <guilabel>Add</guilabel> and <guilabel>Remove
</guilabel> buttons.
</para>
</sect3>
<sect3 id="kaplan-meier-tool-optionstab">
<title>The <quote><guilabel>Options</guilabel></quote> Tab</title>
<para>The options tab of the Kaplan-Meier tools dialog is used to set
various options of the Kaplan-Meier tool.
</para>
<figure id="kaplan-meier-tool-dialog-options">
<title>Kaplan-Meier Tool Dialog Options Tab</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-kaplan-options.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the Kaplan-Meier tool dialog options tab.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
</sect3>
<sect3 id="kaplan-meier-tool-outputtab">
<title>The <quote><guilabel>Output</guilabel></quote> Tab</title>
<para>
The Output tab contains the standard output options and fields
described in <xref linkend="sect-stat-analysis-overview" />.
</para>
</sect3>
<sect3 id="kaplan-meier-tool-example">
<title>A Kaplan-Meier Example</title>
<figure id="kaplan-meier-tool-example-1">
<title>Kaplan-Meier Tool Example Input</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-kaplan-ex1.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the input to the Kaplan-Meier estimate example
and of the input
tab of the Kaplan-Meier analysis tool.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<example id="usingkaplan-meiertool">
<title>Using the Kaplan-Meier Tool</title>
<para>
Suppose you want to calculate Kaplan-Meier Estimates
for the as given in <xref linkend="kaplan-meier-tool-example-1" />. Each
row contains the data for one subject. Column A contains the survival time,
i.e. the time until death or censure. Column B contains the group number,
we are considering two groups of subjects. Column C indicates whether the
subject died (0) or was censured (1).
</para>
<para>
We complete the fields of the <guilabel>Input</guilabel> tab as shown in
<xref linkend="kaplan-meier-tool-example-1" />. The time column is A2:A21
and the censure column is C2:C21.
</para>
<para>
Since we have two groups of subjects, on the <guilabel>Groups</guilabel>
tab we check the <guilabel>Define multiple groups</guilabel> check box and
set up two groups with identifiers 1 and 2 in column B2:B21:
<figure id="kaplan-meier-tool-tool-example-3">
<title>Kaplan-Meier Tool Example Group Tab</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-kaplan-ex3.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the group tab of the Kaplan-Meier
analysis tool.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
</para>
<para>On the <guilabel>Options</guilabel> tab all checkboxes are pre-checked
and we leave them that way to obtain a maximum amount of information.
</para>
<para>On the output tab we choose where we would like the output to be placed. For
the purposes of this example we retain the <guilabel>New Sheet</guilabel> target.
After clicking <guilabel>OK</guilabel> we get the output shown in
<xref linkend="kaplan-meier-tool-example-2" />. Note that the graph initially
always appears on top of the numerical result and was moved for the
screen shot.
</para>
<para>
B1:F17 shows the results of the first group, G1 to K17 the results of the
second group. The graph shows the Kaplan-Meier survival curves for both
groups.
</para>
<para>
M4:N7 shows the result of the Mantel-Haenszel Log-Rank Test. In this case
the p-value is larger than 0.3 and we would fail to reject the Null
hypothesis. There is no evidence that the survival times differ.
</para>
</example>
<figure id="kaplan-meier-tool-example-2">
<title>Kaplan-Meier Tool Example Output</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-kaplan-ex2.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the output of the Kaplan-Meier
analysis tool.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
</sect3>
</sect2>
<sect2 id="principal-component-tool">
<title>Principal Component Analysis</title>
<figure id="pcanalysis-tool-dialog">
<title>Principal Component Analysis Tool Dialog</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-pcanalysis.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the principal component analysis tool dialog.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<para>Principal Component Analysis Tool performs a principal component analysis (PCA).
PCA is a useful statistical technique with application in
fields such as face recognition and image compression. It is a common technique for
finding patterns in data of high dimension.
</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 the factors either by rows
or by columns.</para>
<para>If you have labels
in the first cell of each factor, select the
<quote><guilabel>Labels</guilabel></quote> option.</para>
<figure id="pcanalysis-example-1">
<title>Principal Component Analysis Example Data</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-pcanalysis-ex1.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of example data for use with the
principal component analysis tool.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<example id="usingpcanalysistool">
<title>Using the Principal Component Analysis Tool</title>
<para>
Suppose you want to perform a principal component analysis on the data
given in <xref linkend="pcanalysis-example-1" /> having the two dimensions (factors)
<inlineequation><mathphrase>x</mathphrase></inlineequation> and
<inlineequation><mathphrase>y</mathphrase></inlineequation>.</para>
<orderedlist>
<listitem><para>
Enter Sheet1!$A$1:$B$11 (or just 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 the range on the sheet.</para></listitem>
<listitem><para> Select the <quote><guibutton>Labels</guibutton></quote>
option since the first row contains labels. (see
<xref linkend="pcanalysis-tool-dialog" />).</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 principal component analysis is shown in
<xref linkend="regression-example-3" />. The output shows the covariance matrix,
the eigenvalues and corresponding eigenvectors. The principal component is the
constructed factor with the highest percent of trace,
<inlineequation><mathphrase>ξ1</mathphrase></inlineequation>.</para>
</example>
<figure id="pcanalysis-example-2">
<title>Principal Component Analysis Tool Output</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-pcanalysis-ex2.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the output from a principal component
analysis.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
</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.</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%.</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:C11 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 range on the sheet.</para></listitem>
<listitem><para>
Enter A1:A11 in the <quote><guilabel>Y Variable:</guilabel></quote>
entry. </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>
</sect1>
<sect1 id="one_sample_tests">
<title>One Sample Tests</title>
<sect2 id="normality-tool">
<title>Normality Tests</title>
<para>The normality test tool provides for four tests of normality.</para>
<orderedlist spacing="compact">
<listitem><para>Anderson Darling Test</para></listitem>
<listitem><para>Cramér-von Mises Test</para></listitem>
<listitem><para>Lilliefors (Kolmogorov-Smirnov) Test</para></listitem>
<listitem><para>Shapiro-Francia Test</para></listitem>
</orderedlist>
<figure id="normality-tool-dialog">
<title>Normality Test Dialog</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-normality.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the normality test dialog.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<para>The data range is specified via the <quote><guilabel>Input
Range:</guilabel></quote> entry
(see <xref linkend="normality-tool-dialog" />). The given range
or list of ranges can be grouped into
separate data sets by columns, rows, or areas. The tool performs a
separate test for each data set.</para>
<figure id="normality-tool-testspec-dialog">
<title>Test Tab of the Normality Test Dialog</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-normality-testspec.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the test tab of the normality
test dialog.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<para>On the test tab one specifies which of the four tests to
perform, the significance level for the test and whether to include
a normal probability plot of the data
(see <xref linkend="normality-tool-testspec-dialog" />).</para>
<figure id="normality-example-1">
<title>Normality Test Example Data</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-normality-ex1.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of example data for a normality test.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<example id="usingnormalitytesttool">
<title>Using the Normality Test Tool</title>
<para>
Suppose you want to perform a Lilliefors (Kolmogorov-Smirnov) Test
for Normality on the data
given in <xref linkend="normality-example-1" />.</para>
<orderedlist>
<listitem><para>
Enter A1:A50 (or Sheet1!$A$1:$A$50) 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 the range on the sheet.</para></listitem>
<listitem><para> Select the <quote><guibutton>Labels</guibutton></quote>
option since the first row contains a label (see
<xref linkend="normality-example-2" />).</para></listitem>
<listitem><para> On the test tab of the dialog
(see <xref linkend="normality-example-3" />) select the
Lilliefors (Kolmogorov-Smirnov) Test.</para></listitem>
<listitem><para> Specify an appropriate significance level
Alpha, say 0.05.</para></listitem>
<listitem><para> Select the <quote><guibutton>Create Normal
Probability Plot</guibutton></quote>
option to include a normal
probability plot in the output.</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 normality test is shown in
<xref linkend="normality-example-4" />. Note that the graph appears
initially on top of the output data and needs to be moved to make
the data visible.</para>
</example>
<figure id="normality-example-2">
<title>Completed Input Tab of the Normality Test Dialog</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-normality-ex2.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the completed input tab of the normality
test dialog.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<figure id="normality-example-3">
<title>Completed Test Tab of the Normality Test Dialog</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-normality-ex3.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the completed test tab of the normality
test dialog.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<figure id="normality-example-4">
<title>Normality Test Output</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-normality-ex4.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the output from a normality test.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
</sect2>
<sect2 id="one-median-tool">
<title>One Median</title>
<para>The One Median test tool provides two non-parametric
tests that test the null hypothesis that the sample comes from a
population with a given median:</para>
<orderedlist spacing="compact">
<listitem><para>Sign Test</para></listitem>
<listitem><para>Wilcoxon Signed Rank Test</para></listitem>
</orderedlist>
<para>Selecting the appropriate submenu item opens the dialog with
the respective test preselected.</para>
<sect3 id="sign-test-tool">
<title>Sign Test</title>
<note>
<para>
This section describes the one sample sign test to test the
null hypothesis that the sample comes from a
population with the given median. The tool to perform a sign test to
test the null hypothesis that two paired samples come from populations
with the same median is in section
<xref linkend="two-median-sign-test-tool" />.
</para>
</note>
<figure id="one-median-tool-dialog">
<title>One-Median Test Dialog</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-signtest.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the one-median test dialog used by
the Sign Test and the Wilcoxon Signed Rank Test.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<para>The Sign Test tool performs a one-sample sign test whether
the sample comes from a population with a given median.</para>
<para>The sample data range is specified via the <quote><guilabel>Input
Range:</guilabel></quote> entry
(see <xref linkend="one-median-tool-dialog" />). The given range
or list of ranges can be grouped into
separate data sets by columns, rows, or areas. The tool performs a
separate test for each data set.</para>
<para>On the <quote><guilabel>Test</guilabel></quote>tab of the dialog
(see <xref linkend="one-median-tool-dialog-test-tab" />) the predicted
median as well as the significance level are specified.</para>
<figure id="one-median-tool-dialog-test-tab">
<title>The Test Tab of the One-Median Test Dialog</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-signtest-ex1.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the test tab of the one-median test
dialog.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
<example id="usingsigntesttool">
<title>Using the Sign Test Tool</title>
<para>
Suppose you want to perform a Sign Test
on the data
given in <xref linkend="one-median-tool-dialog" /> to determine whether
the sample comes from a population of mean 3.</para>
<orderedlist>
<listitem><para>
Enter A1:A19 (or Sheet1!$A$1:$A$19) 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 the range on the sheet.</para></listitem>
<listitem><para> Select the <quote><guibutton>Labels</guibutton></quote>
option since the first row contains a label. (see
<xref linkend="one-median-tool-dialog" />).</para></listitem>
<listitem><para> On the <quote><guibutton>Test</guibutton></quote> tab
of the dialog
(see <xref linkend="one-median-tool-dialog-test-tab" />) select the
Sign Test.</para></listitem>
<listitem><para> Specify an appropriate significance level
Alpha, say 0.05.</para></listitem>
<listitem><para> Select thepecify the median of the null hypothesis (3)
in the <quote><guibutton>Predicted Median</guibutton></quote> entry.
</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 sign test is shown in
<xref linkend="sign-test-dialog-output" />.</para>
</example>
<figure id="sign-test-dialog-output">
<title>Output of a Sign Test</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-signtest-ex2.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the output of a Sign Test.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
</sect3>
<sect3 id="wilcoxon-sign-test-tool">
<title>Wilcoxon Signed Rank Test</title>
<note>
<para>
This section describes the one sample Wilcoxon signed rank test to
test the
null hypothesis that the sample comes from a
population with the given median. The tool to perform a Wilcoxon
signed rank test to
test the null hypothesis that two paired samples come from populations
with the same median is in section
<xref linkend="two-median-wilcoxon-sign-test-tool" />.
</para>
</note>
<para>The Wilcoxon Signed Rank TTest tool performs a one-sample
sign test whether
the sample comes from a population with a given median.</para>
<para>The sample data range is specified via the <quote><guilabel>Input
Range:</guilabel></quote> entry
(see <xref linkend="one-median-tool-dialog" />). The given range
or list of ranges can be grouped into
separate data sets by columns, rows, or areas. The tool performs a
separate test for each data set.</para>
<para>On the <quote><guilabel>Test</guilabel></quote>tab of the dialog
(see <xref linkend="one-median-tool-dialog-test-tab" />) the predicted
median as well as the significance level are specified.</para>
<note>
<para>
The p-values given by this tool are determined using a normal
approximation. This approximation is only valid if the sample
size is at least 12.
</para>
</note>
<example id="usingwilcoxonsignedranktesttool">
<title>Using the Wilcoxon Signed Rank Test Tool</title>
<para>
Suppose you want to perform a Wilcoxon Signed Rank Test
on the data
given in <xref linkend="one-median-tool-dialog" /> to determine whether
the sample comes from a population of mean 3.</para>
<orderedlist>
<listitem><para>
Enter A1:A19 (or Sheet1!$A$1:$A$19) 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 the range on the sheet.</para></listitem>
<listitem><para> Select the <quote><guibutton>Labels</guibutton></quote>
option since the first row contains a label. (see
<xref linkend="one-median-tool-dialog" />).</para></listitem>
<listitem><para> On the <quote><guibutton>Test</guibutton></quote> tab
of the dialog
(see <xref linkend="one-median-tool-dialog-test-tab" />) select the
Wilcoxon Signed Rank Test.</para></listitem>
<listitem><para> Specify an appropriate significance level
Alpha, say 0.05.</para></listitem>
<listitem><para> Select thepecify the median of the null hypothesis (3)
in the <quote><guibutton>Predicted Median</guibutton></quote> entry.
</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 sign test is shown in
<xref linkend="wilcoxon-sign-test-dialog-output" />.</para>
</example>
<figure id="wilcoxon-sign-test-dialog-output">
<title>Output of a Wilcoxon Signed Rank Test</title>
<screenshot>
<mediaobject>
<imageobject>
<imagedata fileref="figures/analysistools-signtest-ex3.png"
format="PNG" />
</imageobject>
<textobject>
<phrase>An image of the output of a Wilcoxon Signed Rank
Test.</phrase>
</textobject>
</mediaobject>
</screenshot>
</figure>
</sect3>
</sect2>
</sect1>
<sect1 id="two_sample_tests">
<title>Two Sample Tests</title>
<sect2 id="t-test-tool">
<title>Comparing Means of Two Populations</title>
<para>&gnum; provides four 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 %.</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>
<sect2 id="two-medians-tool">
<title>Comparing Medians of Two Populations</title>
<para>&gnum; provides three non-parametric tests to test the null
hypothesis that the two samples come from
populations with the same median. Two tests, performed through the same
tool, apply in the case of paired samples:</para>
<itemizedlist spacing="compact">
<listitem><para>Sign Test</para></listitem>
<listitem><para>Wilcoxon Signed Rank Test</para></listitem>
</itemizedlist>
<para>One test applies in the case of unpaired samples:</para>
<itemizedlist spacing="compact">
<listitem><para>Wilcoxon-Mann-Whitney Test</para></listitem>
</itemizedlist>
<para></para>
<sect3 id="two-median-sign-test-tool">
<title>Sign Test</title>
<note>
<para>
This section describes the two sample (paired) sign test to test the
null hypothesis that the two samples come from
populations with the same median. The tool to perform a sign test to
test the null hypothesis that the single sample comes from a population
with a given median is in section <xref linkend="sign-test-tool" />.
</para>
</note>
<note>
<para>This section needs to be written.</para>
</note>
</sect3>
<sect3 id="two-median-wilcoxon-sign-test-tool">
<title>Wilcoxon Signed Rank Test</title>
<note>
<para>
This section describes the two sample (paired) Wilcoxon signed rank
test to test the
null hypothesis that the two samples come from
populations with the same median. The tool to perform a Wilcoxon
signed rank test to
test the null hypothesis that the single sample comes from a population
with a given median is in section
<xref linkend="wilcoxon-sign-test-tool" />.
</para>
</note>
<note>
<para>This section needs to be written.</para>
</note>
</sect3>
<sect3 id="two-median-wilcoxon-mann-whitney-test-tool">
<title>Wilcoxon-Mann-Whitney Test</title>
<note>
<para>This section needs to be written.</para>
</note>
</sect3>
</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%.</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><inlineequation><mathphrase>P(F≤f)</mathphrase></inlineequation> one-tail</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>
</sect1>
<sect1 id="multiple_sample_tests">
<title>Multiple Sample Tests</title>
<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%.
</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%.</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%.</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="chi-square-tool">
<title>Tests for a Contingency Table</title>
<sect3 id="homogeneity-tool">
<title>Test of Homogeneity</title>
<para></para>
</sect3>
<sect3 id="independence-tool">
<title>Test of Independence</title>
<para></para>
</sect3>
</sect2>
</sect1>
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