Modeling & Analysis with Fathom Software
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Dynamic Statistics™ Software for Deeper Understanding Software Authors: William Finzer, Tim Erickson,
& Jill Binker; |
Fathom is a
statistical software package that promotes exploration, investigation, and
discovery understanding. Fathom is
similar in its vision for statistics education to the vision that Geometer’s
Sketchpad has given dynamic study of geometry. The software is appropriate for both secondary and
post-secondary study, and can be used in a variety of courses. |
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Website: http://www.keypress.com/fathom/ |
In this workshop, we will provide a “hands-on” overview of Fathom. The goal is not to provide detailed instruction in every feature of the software package; rather, the goal is to demonstrate ways in which the software can be used to promote modeling and visualization. We have used the software with both pre-service & in-service mathematics and science teachers to promote conceptual understanding of data analysis, and concepts of model building.
With Fathom software, one can:
v View data in multiple representations—as attributes of individual cases; in “spreadsheet-like” tables; in summary tables; in graphs
v Bring data into Fathom files in multiple ways—directly inputting data in spreadsheet format; importing data from various text files (e.g., tab-delimited, comma-separated); copying and pasting from other files; and most excitingly, importing data directly from the Internet!
v Create contingency tables—cross tabulation of data intuitively
v Create dynamic graphs and explore data graphically—that help students understand which types of graphs are appropriate for various forms of data. If “unlocked”, the data may be altered through directly manipulation of the graph; if “locked”, the data are not alterable.
v Create a variety of functional plots and explore data graphically —Linear regression—manual moveable line fits showing sum of squares, median-median fit, least squares fit; Build more complex mathematical models with an extensive collection of functions; plot specific values; plot most probability distributions; establish model parameters (sliders)
v Perform a variety of statistical tests—Descriptive statistics; estimate population parameters; test hypotheses
v Investigate probability and statistics dynamically—collect random samples with replacement; collect measures from a sample; create simulations
The
essential basics of Fathom:
Collections—Treats collections of cases as a collection of gold balls; each gold ball represents one case: e.g., each individual subject in a human study is a case, and the variables about which data are collected
are attributes.
One can scroll through each case in the data file by double-clicking on a collection; this view is called the Inspector. It is similar to a database view and from here, one can create measures, make comments, and control advanced features, such as sampling.
Data are summarized in a case table—similar to a spreadsheet view of the data. Each row is a case and each column is an attribute.
Graphs are displayed inside a separate window
within the file. In fact, any of the
views—a collection, case table, inspector, graph, or summary table—can be collapsed
to an icon such as the graph icon to the right by dragging the bottom
right corner to the top left corner.
This gives a Fathom file the feel of a desktop workspace with moveable,
collapsible windows inside of the file.
Sliders allow the user to establish
parameters for coefficients in a model, in order to explore change effects of specific parameters.
Summary tables are contingency tables or
cross-tabulation tables
that are easily built by dragging and dropping attributes into summary rows or
columns.
Exploration # 1:
Population Data
Goal of
activity: Examining Data Collections,
Data Inspectors, Case Tables Creating Summary Tables, Basic Graphs
Fathom
software comes with hundreds of data sets ready to be explored. Many data sets come from census files.
v Under File, choose Open… and search for “BeverlyHills.ftm”. Note the extension for Fathom files (.ftm).
Either the file is loaded under presentation examples on the conference
computer, or search the Sample Documents sub-directory under Fathom Program
files, or download the file from http://www.mste.uiuc.edu/hendrix/FathomSC2002/
v Once you have opened the file, drag the
corners of the collection to collapse and expand the collection. Double-click on a gold ball to open the Case
Inspector. Use the arrows at the bottom to scroll
through the cases. What attributes have
been collected for each case?
v 
With the collection highlighted, drag a
case table from the Tool Bar
to the file window. Whoosh! The data are displayed in a spreadsheet-like
table.
v Drag a
graph icon from the Tool Bar
to the file window. Notice that it
plots nothing at first. To graph data,
drag an attribute to either the horizontal or vertical axis. Notice the drop-down menu in the upper right
corner of the graph window. This menu
indicates the various types of graphs that are possibly appropriate for the
type of variables the user has chosen to graph. For example, if charting “gender”, the software won’t allow the
possibility of a histogram.
v Explore
with graphing various attributes. We’ll look at a few different attributes in
this file.
v How to
split a chart: When charting a single attribute, you may
drag a categorical variable to the other axis to disaggregate the data within
the graph.
v Drag a
summary table from the Tool Bar
to the file window. As with the graph,
the summary table is empty initially.
Drag “sex” to the arrow point downward to the summary rows. What would be an appropriate attribute to
cross-tabulate with gender? Try
dragging “race” to the arrow pointing right to the summary columns.
v Point of
this exploration: Fathom’s ease of use; intuitive; the nature
of the software features lends itself to exploring the data and understanding
the differences between categorical and continuous data.
Exploration
# 2: Importing Data from the
Internet
Goal of
activity: To import datafiles
directly from websites on the Internet, linear regression
v
Open a new Fathom file, and minimize it.
v Open
Internet Explorer or
your preferred internet browser. Go to
the following URL: http://lib.stat.cmu.edu/DASL/,
which leads to the online Data and Story Library, a famous repository of
datafiles.
v Click on the link Data
Subjects, which
leads to a laundry list of data categories.
Click on Education, then on Reading Test Scores Datafile.
Scroll down the page and examine the data file. Go to the Location Bar, highlight the URL,
and Copy it (under Edit or Control-C).
v Pull up the blank Fathom file, go to
File, and select Import from URL.
A dialog box will appear, and Paste the URL of the Reading Test Scores
Datafile into the URL box. Click OK,
and see what happens.
v Pull down a case table, and scan the data. Pull down a graph, and plot PRE1 versus
POST1, creating a scatter plot. Is
there a positive correlation between the data?
Would you choose to fit a regression line to these data?
v Under the Graph menu, choose Moveable Line.
Drag it around and through the data.
Again, under Graph menu, choose Show Squares.
See if you can minimize the Sum of Squares. Once again, under Graph, choose Least Squares Line.
Deselect the Show Squares option.
v Under Graph, select the Median-Median
Line. What is the difference between these two
regression lines? Which one is more
robust? Drag a data point around. Which line is affected more—the least
squares or the median-median line.
v Open a
New File. Return to Internet Explorer, and visit the
following URL: http://www.census.gov/.
Select, on this page, Peopleà Estimates. On the
next page, choose from the drop-down menu, “Annual Series through 2001 by
state” and click GO. This leads to a
datafile. Again, copy the URL and return
to Fathom. Practice importing this file
directly from the internet.
v Cleaning
the data—After
importing the census file, there is some mild cleaning to do. The columns need to be named as appropriate
attributes, and a couple of cases need to be deleted. Overall, though, importing datafiles seems rather painfree.
v
Point of this Activity—Importing
datafiles is relatively painless process, and easy to modify. Linear regression can be explored
intuitively rather than the blackbox approach.