SAMR

SAMR and Fathom

toc

Fathom can be utilized on all 4 levels of the SAMR model due to its ability to do rote calculations quickly, but also its ability to manipulate live data and display it in many different ways. It is a statistician's dream come true for utilizing technology. From making histograms and bar charts to computing means and standard deviations, it has many unique and powerful mathematical features that accentuate all layers of the technological model.

Substitution
Fathom has the power to take inputted data and create various different forms of graphs and tables like the one to the right.

This data can also be represented quickly and easily in a graph

. Same data, different representation. Fathom can quickly and easily convert from chart to graph. This is something, however, that can easily be done by hand also, placing it in the Substitution category. The same can be done with quantitative data, but instead can be represented using a histogram, box-plot, scatter plot, and dot plot. Below is a summary table for number of pets in 1,000 households. Fathom can easily include the mean, median, IQR, and standard deviation.

Now, to move this to a graph. The only graph to be shown is a dot plot, but the others can be easily created.



Augmentation
A way that Fathom can be used in an augmentative way is the ability to modify live data. What this means is on a graph or chart, one individual point can be moved around and that will simultaneously affect the mean, median and IQR for the data set. The video below illustrates this:

media type="youtube" key="FM4lPCroGtE?hl=en" height="349" width="425"

Notice how as the individual point was moved, the data in the summary table changed to match? Somebody can explain that the mean is affected by individual points, but this use of Fathom shows it in real time. This is what Augmentation is about, using the program to do something we can do already, just in a really different way. This can be explained, and shown using other mathematical technique, but the length of time it takes eliminates the initial 'got it!' factor that Fathom allows use for.

Fathom video made by Scott A. Bowden.

Modification
Now, Modification asks the question: "how do I use Fathom to create something totally new?"

One way it starts to do that is the ability to quickly and easily change from one graph to another. The graph from the pet data can easily be changed with one or 2 clicks to a histogram or a dot plot. Additionally, if a graph is a scatterplot (as it would be with 2 variable data), one can easily insert lines to test the fitness of a line to the data as well as instantly insert the best fit line.

A unique facet to the new Fathom (2.1) is the allowance of importation of the 2000 US Census data with the ability to select different attributes from it.

For example:

This photo is the physical collecting of the data:



And this is the collection of data that was attained by downloading it:

Notice how the collection has the same information that the census data download screen had.

This, albeit not unique to Fathom, the knowledge that this is available (and is randomized every time) on the program makes collecting random specific data easier and allows for unique new products. And this census data is perfect for modeling a real life situation (such as projected incomes of specifically aged individuals or a specific class) by selecting the appropriate data that would be good to model and let Fathom bring all the data in as well as allow Fathom's programming to build the graphs and fit the lines.

Modification is powerful here because it allows individuals to make predictions and guesses with very little work getting from raw data to something interpretable on their part.

Especially when it comes to comparing a piece of categorical data to one of quantitative on the same axes. This is a shot of the ages of individuals based on their Marital Status. What kinds of interpretations can be made? Without a quick way to combine the data, it's almost impossible to guess easily:



It takes interpretation of data and higher order thinking to a whole new and different level. Typically, these could only be talked about 1 at a time, but this allows for 6 different variables to be analyzed and compared simultaneously.

Redefinition
The best part about Fathom and how to use it is the ability to drag files in from other programs or the world wide web to work with.

The files that Fathom typically accepts is HTML, plain text, and some excel files, as well as the ability to import it directly from a website.



This is the URL to a site that has a specific stat listing that will be shown below:



The collection above came from the URL at the top. If a specific set of data is required and it's on the web, then Fathom can pull it in and work with it.

This is what the redefinition stage is about - how to use Fathom in unbelievable new ways, ways that very few other programs can. Not many can bring in data from a website, allow for live modification, and interpretation within the same program.

Combine this with online data generators (click to go there):



Or a survey site that can be completed beforehand and the data collected and finding any data set in the world is a click away because all the data can be either pulled in off the web or saved as an HTML file and imported that way. Then tables, graphs, and other methods can be employed to interpret data, model future events, or even determine correlation from a specific data set takes literally seconds, rather than taking the time to hand craft all of it.

Fathom, on its surface, looks like any other statistical program, when in reality, it is a powerful tool that allows many different opportunities, if you just know where to look.