<p>I'm writing an app to help facilitate some research, and part of this involves doing some statistical calculations. Right now, the researchers are using a program called <a href="http://en.wikipedia.org/wiki/Spss" rel="noreferrer">SPSS</a>. Part of the output that they care about looks like this:</p>

<p><img src="https://i.stack.imgur.com/m0swl.png" alt="[Part of the SPSS output"></p>

<p>They're really only concerned about the <code>F</code> and <code>Sig.</code> values. My problem is that I have no background in statistics, and I can't figure out what the tests are called, or how to calculate them.</p>

<p>I thought the <code>F</code> value might be the result of the <a href="http://en.wikipedia.org/wiki/F-test#Table_on_F-test" rel="noreferrer">F-test</a>, but after following the steps given on Wikipedia, I got a result that was different from what <code>SPSS</code> gives.</p>

This website
might help you out a bit more.  Also
this one
.
I'm working from a fairly rusty memory of a statistics course, but here goes nothing:
When you're doing analysis of variance (ANOVA), you actually calculate the F statistic as the ratio from the mean-square variances "between the groups" and the mean-square variances "within the groups".  The second link above seems pretty good for this calculation.
This makes the F statistic measure exactly how powerful your model is, because the "between the groups" variance is explanatory power, and "within the groups" variance is random error.  High F implies a highly significant model.
As in many statistical operations, you back-determine Sig. using the F statistic.  Here's where your Wikipedia information comes in slightly handy.  What you want to do is - using the degrees of freedom given to you by SPSS - find the proper P value at which an
F table
will give you the F statistic you calculated.  The P value where this happens [F(table) = F(calculated)] is the significance.
Conceptually, a lower significance value shows a very strong ability to reject the null hypothesis (which for these purposes means to determine your model has explanatory power).
Sorry to any math folks if any of this is wrong.  I'll be checking back to make edits!!!
Good luck to you.  Stats is fun, just maybe not this part.  =)