View source for XY Comparison

[[Category:Analytica User Guide]] 
[[Category: Windows and dialogs]] 
[[Category: Graphs]]

<breadcrumbs>Analytica User Guide > Formatting Numbers, Tables, and Graphs > {{PAGENAME}}</breadcrumbs>

==About XY comparison==
When you display a standard (non XY) graph of a variable, '''V''', it plots the values of '''V '''up the vertical (y) axis against an index of '''V '''along the horizontal (x) axis. If '''V '''has more than one dimension, you can choose which index to plot horizontally from the '''Horizontal Axis '''menu. In contrast, with '''''XY comparison '''''you can plot '''V '''against another variable, '''U''', along the horizontal (x) axis, over a '''Common Index '''of '''V '''and '''U'''. You can also plot one slice of '''V '''against another slice over a '''Comparison Index'''. (See [[Scatter plots]] to use XY comparison for scatter plots.)

== XY comparison sources dialog ==
This dialog lets you set options for XY comparison and extends or adds menus to the XY graph described below.

:[[File:Chapter7 28.png]]

'''To open the dialog''': Click the '''XY '''button in top-right corner of [[Result window]] (graph or table). You must be in edit or arrow mode, so it is not available in Analytica editions or models confined to browse mode.

'''Use comparison index''': Check this box if you want to compare one slice of the variable against another slice, slices selected from the comparison index. The graph shows the '''Comparison Index '''menu from which you can select the index you want. The '''Vertical Axis '''and '''Horizontal Axis '''menus then offer slices from the comparison index so that you can choose which two slices to plot against each other.

'''Use another variable''': Check this box if you would like to compare the base variable by plotting it against one or more other variables (or simple expressions). When you check it, the following items appear:

'''Add''': Click this button to open the [[Object Finder dialog]] to select a variable against which to plot the base variable. You can also use the [[Object Finder]] to select a function or operation from one of the relevant libraries. You can add up to five items.

'''Remove''': Select a item from the list of other variables, and click this button to remove it from the list of variables for comparison.

== Menus added to XY Comparison graph ==
An XY comparison graph adds a '''Common Index '''and, sometimes, a '''Comparison Index '''to the usual graphing roles menus on a graph or table.

:[[File:Chapter7 29.png]]

'''Comparison index''': This menu lists the indexes of the base variable. The '''Horizontal Axis '''and '''Vertical Axis '''menus each let you choose a slice from the selected comparison index to plot against each other. It appears on the graph when ''Use comparison index ''is checked in the '''XY comparison sources '''dialog.

'''Common index''': This defines the correspondence among the variables or slices to be plotted against each other. Each value of the common index identifies a data point on the graph, with vertical (X) and horizontal (Y) values from the variables or slices you have selected for those graphing roles. For a scatter plot, the common index should be '''Iteration '''('''Run'''). It appears on the graph when one or both checkboxes on the '''XY comparison sources '''dialog are selected.

If ''Use another variable ''is checked in the '''XY comparison sources '''dialog, '''Common Index '''is an index in common to the base variable and other variable(s). If the variables have more than one index in common, '''Common Index '''is a menu from which you can choose the index you want.

If ''Use comparison index ''is checked in the '''XY comparison sources '''dialog, '''Common Index '''shows the index(es) of the base variable not selected for '''Comparison Index'''. '''Common Index '''is a menu if the variable has more than two indexes — leaving more than one for '''Common Index'''.

== Example: Plot one variable against another ==
For example, suppose you have an index and two variables: 
:<code>Index Degrees := Sequence(0, 360, 5) </code>
:<code>Variable V := Sin(Degrees)</code>
:<code>Variable U := Cos(Degrees)</code>

For a standard graph of '''V '''against its index, '''Degrees''', select '''V '''from the diagram and click the '''Result '''button (''Control+r''). Repeat with '''U '''to display the graph for '''U '''against '''Degrees'''.

:[[File:Chapter7 30.png]]

For these graphs, we selected the ''symbol plus line'' '''line style''' from [[Graph setup dialog|Graph setup]] to show the data points for each value of '''Degrees'''.

With '''XY Comparison''', you can graph '''U '''against '''V''', instead of against its index '''Degrees''':

# Change to ''edit mode''. In the '''Graph '''window for '''U''', click the '''XY '''button in the top-right corner (above) to open the '''XY Comparison sources '''dialog. <br /> [[File:Chapter7 31.png]]
# Select the checkbox ''Use another variable''.
# Click the '''Add '''button to open the '''Object Finder '''dialog. <br /> [[File:Chapter7 32.png]]
# Select the variable '''V''', and click '''OK'''. You can now see '''V '''listed in the '''XY comparison sources''' dialog. <br /> [[File:Chapter7 33.png]]
# Click '''OK'''.  <br /> [[File:Chapter7 34.png]]

The graph of '''U '''now plots the values of '''U '''on the vertical (y) axis against corresponding values of '''V '''on the horizontal (x) axis. By “corresponding” we mean for each value of '''Degrees''', in the '''Common Index'''. If '''U '''and '''V '''had more than one index in common, it would show a menu from which you could select the index you want.

== Example: Compare variables using comparison index ==
You can also use '''XY comparison '''to compare one slice of a variable against another slice of the same variable. This is especially useful when you combine several variables as a list. Let’s add a third variable to '''U '''and '''V '''defined above:
:<code>Variable W := Sin(2*Degrees)</code>

The parameter <code>2*Degrees</code> creates a sine curve with twice the frequency. Here is an easy way to create a list to compare several variables.

:[[File:Chapter7 35.png]]

# Select the three nodes for the variables to compare, '''U''', '''V''', and '''W''', and click '''Result '''(''Control+r'').
# When it prompts ''“Do you want to compare more than one result?” ''click '''OK'''. It creates a new variable '''Compare1''', and shows the standard (not XY) graph comparing '''U''', '''V''', and '''W '''against index '''Degrees'''. <br /> [[File:Chapter7 36.png]]
# Make sure you are in ''edit mode''. In the graph window for '''Compare1''', click the '''XY '''button in the top-right corner to open the '''XY comparison sources '''dialog. <br /> [[File:Chapter7 37.png]]
# Select the checkbox ''Use comparison index ''and click '''OK'''. <br /> [[File:Chapter7 38.png]]

This sideways figure 8 results because '''W '''is a sine wave with twice the frequency of '''V'''. You can select other pairs of variables to compare, from '''U''', '''V''', and '''W''', from the '''Vertical '''and '''Horizontal Axis '''menus — for example, changing to '''W '''against '''V '''puts the figure 8 the right way up.

:[[File:Chapter7 39.png]]

You can also select '''Degrees '''from the '''Horizontal Axis '''menu to revert to a standard (non XY) graph of the selected variable against '''Degrees'''.

==See Also==
* [[XY comparison]]
* [[Graph settings]]
* [[Graph setup dialog]]
* [[Graph templates]]
* [[Graph Style Templates]]
*  [[Scatter plots]]
* [[Making a Multi-D Scatter Plot]]
* [[Comparing results]]


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