A statistical analysis of The Facebook at Salisbury University

I should pre-empt this article by saying that I am an amateur as far as statistics goes, graph-visualization theory/algorithms, and probably everything else: the pains of being an auto-didact.

For the past few months I have off-and-on dabbled with a project relating to statistical analysis of the facebook at Salisbury University.

Specifically, I ran a screenscraper which stored data in a plain-text file about every available piece of information of every member registered as a student on Salisbury University's facebook page. Why Salisbury University?

1. I am an ex-student there (unfortunately), so I still have an email account to sign-up for an account on the Salisbury facebook.
2. My current school, Rutgers University, would be far too large for the scope of this study.

My first interest was in using graph-visualization algorithms to see if any patterns emerged based on the connections (edges) between the various users (nodes), the edges of course representing friendship. I ended up using the GEM3D algorithm to visualize this, through a rather shitty program called Tulip.

The original graph visualization, which took in excess of 4 hours on my computer, was an absolute mess. No matter how you render 4245 nodes and 142,208 edges, the results will rarely offer any insights. Thus I decided to take a random sample of 250 people, and make a visualization of their connections.

The 3d renderings produced by Tulip were, shall we say, subpar, so I wrote a script which translated them into Povray's syntax. Just for kicks I color coded each node according to the user's birthdate and interpolated the colors between edges. Here's what resulted:

Clearly, not very useful (other than demonstrating the obvious fact that similar age groups cluster together), but eyecandy nonetheless.

I then decided it might be interesting to geocode people's listed home-town, and then do a scatter plot over a map of the United States. Given that the school is located in southern Maryland, the results are fairly predictable, but interesting nevertheless.

Later, I decided to do something more useful with my data. I ran Pearson's correlations between the variables.¹ If this is all greek to you, read foodnote 2. I've also provided a javascript-enabled table of the correlations results [warning: The javascript in this file is very unoptimized and may crash your browser or at the very least stall it.] For those comfortable with the pdf format, or who wish to print out the results for later viewing can view the pdf version here (with additional graphs!).

Highest corr. coefficients sorted

Variable 1	Variable 2	Corr.
School year	Birthdate	0.829
Phys. Ed	Health Ed.	0.296
Biology	Chemistry	0.274
Comp. Sci.	Mathematics	0.211
Male	Liberal	-0.205
Male	OtherPoli	0.205
Male	Bus. Admin.	0.189
Accounting	Finance	0.190
Male	Nursing	-0.184
Male	Elementary Ed.	-0.182
Psychology	Social Work	0.173
Communication	Marketing	0.171
History	Secondary Ed.	0.177
Male	Psychology	-0.169
Mathematics	Physics	0.162

Most of the results are pretty obvious, as the summary table above demonstrates, but there are a few surprises in the full correlation data set. For instance: why is there a highly significant correlation between being bisexual and being a respiratory therapy major?

Anyway, I have around 13 MB of data about Salisbury University, and tons of scripts to analyze it, so if anyone has any ideas of interesting things I can do with it other than correlations and graph-visualizations, please post in the comments and I will most likely oblige.

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Notes

1. Some might question the use of Pearson's correlations, given the fact that much of the date is non-parametric. However, it's fairly well-known that parametric methods are often fine when the sample size is large enough. Additionally, non-parametric correlation coefficients, such as those derived from Spearman's r, where in fact larger that the Pearson's correlation coefficients. Thus, I decided to play it safe and stick with the smaller of the two. [Back]

2. I'm not going to go too much in detail here, just enough to allow someone without any knowledge of statistics to interpret the correlation data. A positive correlation means that, in general, the higher one variable is, the more likely that the other variable is higher than normal, and vice-versa. Conversely, a negative correlation means that, in general, the higher one variable, the more likely that the other variable is lower than normal, and again vice-versa. The correlation coefficient is a number between -1 and 1, these two extremes representing a perfect negative correlation or a perfect positive correlation. Thus, the higher (in terms of absolute values) the correlation coefficient, the stronger the correlation. The significance takes into account the number of people sampled and the correlation coefficient and determines the chances that the correlational relationship occurred simply by chance. According to convention, a significance value of less than 0.05 is considered statistically significant, and a significance value of less than 0.01 is considered highly statistically significant. Lastly, the n that you see in the tables is simply the sample size (that is, the number of people who entered valid values for both variables). [Back]